Review of Basic Statistical Concepts

Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.

____	1.	A researcher is interested in the eating behavior of elementary school children and selects a group of 25 children to be tested in a research study. The group of 25 children is a ______.
a.	sample	
b.	statistic	
c.	population	
d.	parameter	

____	2.	A researcher is interested in the effect of St. Johns Wort on memory. A group of 25 college students is selected to participate in a research study. The average memory score obtained for the students is a ______.
a.	sample	
b.	statistic	
c.	population	
d.	parameter	

____	3.	A researcher is curious about the average IQ of registered voters in the state of Florida. The entire group of registered voters in Florida is an example of a ______.
a.	sample	
b.	statistic	
c.	population	
d.	parameter	

____	4.	Statistical techniques that summarize, organize, and simplify data are classified as ____________.
a.	population statistics	
b.	sample statistics	
c.	descriptive statistics	
d.	inferential statistics	

____	5.	A characteristic, usually a numerical value, that describes an entire population of scores is a _________.
a.	parameter	
b.	statistic	
c.	variable	
d.	constant	

____	6.	How would the following mathematical operation be expressed in summation notation? "Add two points to each score, square the resulting value, then find the sum of the squared numbers."
a.	SX + 22	
b.	(SX + 2)2	
c.	S(X + 2)2	
d.	SX2 + 2	

____	7.	Frequency distribution polygons are intended for use with ______.
a.	either interval or ratio scales of measurement	
b.	only ratio scales	
c.	either nominal or ordinal scales	
d.	only nominal scales	

	
____	9.	In a frequency distribution graph, frequencies are presented on the __________ and the scores (categories) are listed on the __________.
a.	X axis, Y axis	
b.	horizontal line, vertical line	
c.	Y axis, X axis	
d.	class interval, horizontal line	

____	10.	In a distribution with positive skew, scores with the highest frequencies are
a.	on the right side of the distribution	
b.	on the left side of the distribution	
c.	in the middle of the distribution	
d.	represented at two distinct peaks	

Table 2-2
The following table shows a frequency distribution of quiz scores.

X	f	
5	6	
4	5	
3	5	
2	3	
1	2	

____	11.	Refer to Table 2-2. How many individuals had a score of X = 2?
a.	1	
b.	3	
c.	5	
d.	cannot be determined from the information given	

____	12.	A sample of n = 5 scores has a mean of X (over-bar) = 9. What is SX for this sample?
a.	9/5 = 1.80	
b.	5/9 = 0.555	
c.	5(9) = 45	
d.	cannot be determined from the information given	

____	13.	One sample of n = 4 scores has a mean of X (over-bar) = 10, and a second sample of n = 8 scores has a mean of X (over-bar) = 20. If the two samples are combined, the mean for the combined sample will be ______.
a.	equal to 15	
b.	greater than 15 but less than 20	
c.	less than 15 but more than 10	
d.	none of the above	

____	14.	A sample of n = 20 scores has a mean of X (over-bar) = 55. After one score is removed from the sample, the mean for the remaining scores is found to be X (over-bar) = 51. From this information you can conclude that the removed score was ______.
a.	greater than 55	
b.	less than 55	
c.	It is impossible to estimate the magnitude of the score.	

____	15.	For a distribution of scores, the mean is equal to the median. This distribution is most likely to be ______.
a.	symmetrical	
b.	positively skewed	
c.	negatively skewed	
d.	impossible to determine the shape	

____	16.	For any distribution, you can be sure that at least one individual has a score equal to the ______.
a.	mean	
b.	median	
c.	mode	
d.	all of the above	

____	17.	For an extremely skewed distribution of scores the best measure of central tendency would be the ______.
a.	mean	
b.	median	
c.	mode	
d.	Central tendency cannot be determined for a skewed distribution.	

____	18.	A population of N = 5 scores has SS = 40. What is the variance for this population?
a.	40/5 = 8	
b.	82 = 64	
c.	40/4 = 10	
d.	102 = 100	

____	19.	A population has m = 40 and s = 8. If each score is multiplied by 2, the new standard deviation will be ______.
a.	4	
b.	8	
c.	16	
d.	insufficient information, cannot be determined	

____	20.	To compute sample variance, the value of SS is divided by ____.
a.	n	
b.	N	
c.	n - 1	
d.	N - 1	

____	21.	You must determine Q1 and Q3 to compute the _______.
a.	sum of squared deviations	
b.	semi-interquartile range	
c.	variance	
d.	standard deviation	

____	23.	Of the following z-score values, which one represents the most extreme location on the left-hand side of the distribution?
a.	z = +1.00	
b.	z = +2.00	
c.	z = -1.00	
d.	z = -2.00	

____	24.	For a population with m = 80 and s = 10, the z-score corresponding to X = 85 would be ______.
a.	+0.50	
b.	+1.00	
c.	+2.00	
d.	+5.00	

____	25.	For a population with m = 60 and s = 8, the X value corresponding to z = -0.50 would be ______.
a.	-4	
b.	56	
c.	64	
d.	59.5	

____	26.	For a population with m = 60 and s = 8, the X value corresponding to z = 1.50 would be ______.
a.	12	
b.	61.5	
c.	72	
d.	90	

____	27.	A population of scores has s = 20. In this population, a score of X = 80 corresponds to z = +0.25. What is the population mean?
a.	70	
b.	75	
c.	85	
d.	90	

____	28.	Under what circumstances would a score that is 15 points above the mean be considered an extreme score?
a.	when the population mean is much larger than 15	
b.	when the population standard deviation is much larger than 15	
c.	when the population mean is much smaller than 15	
d.	when the population standard deviation is much smaller than 15	

____	29.	Suppose you earned a score of X = 54 on an exam. Which set of parameters would give you the highest grade?
a.	m = 50 and s = 2	
b.	m = 50 and s = 8	
c.	m = 58 and s = 2	
d.	m = 58 and s = 8	

____	30.	A population has m = 50 and s = 10. If these scores are transformed into z-scores, the population of z-scores will have a mean of ____ and a standard deviation of ____.
a.	50, 10	
b.	50, 1	
c.	0, 10	
d.	0, 1	

____	31.	A distribution with m = 35 and s = 8 is being standardized so that the new mean and standard deviation will be m = 50 and s = 10. In the new, standardized distribution your score is X = 60. What was your score in the original distribution?
a.	X = 45	
b.	X = 43	
c.	X = 1.00	
d.	impossible to determine without more information	

____	32.	A colony of laboratory rats contains 7 albino rats and 23 hooded rats. What is the probability of randomly selecting an albino rat from this colony?
a.	7/23	
b.	7/30	
c.	23/30	
d.	23/7	

____	33.	An introductory psychology class has 9 freshman males, 11 freshman females, 8 sophomore males, and 12 sophomore females. What is the probability of randomly selecting a male from this group?
a.	9/20	
b.	8/20	
c.	17/20	
d.	17/40	

____	34.	What proportion of a normal distribution is located in the tail beyond a z-score of z = -1.50?
a.	-0.668	
b.	-0.9332	
c.	0.0668	
d.	0.9332	

____	35.	What proportion of a normal distribution is located in the tail beyond z = 2.00?
a.	1.14%	
b.	2%	
c.	2.28%	
d.	97.72%	

____	36.	What proportion of the scores in a normal distribution correspond to z-scores greater than +1.04?.
a.	0.3508	
b.	0.1492	
c.	0.6492	
d.	0.8508	

____	37.	What proportion of the scores in a normal distribution have z-scores less than z = 0.86?
a.	0.3051	
b.	0.1949	
c.	0.8051	
d.	0.6949	

____	38.	For a normal distribution with a mean of m = 40 and s = 4, what is the probability of sampling an individual with a score greater than 46?
a.	0.0668	
b.	0.4452	
c.	0.9332	
d.	0.0548	

____	39.	For a normal distribution with a mean of m = 40 and s = 4, what is the probability of sampling an individual with a score less than 46?
a.	0.0668	
b.	0.4452	
c.	0.9332	
d.	0.0548	

____	40.	A normal distribution has a mean of m = 36 and s = 4. What proportion of the distribution is located between scores of X = 30 and X = 38?
a.	0.3753	
b.	0.6247	
c.	0.2583	
d.	0.7417	

____	41.	The distribution of sample means consists of ______.
a.	all the scores contained in a particular sample	
b.	all the scores contained in a specific population	
c.	the sample means for all the possible random samples (of a specific size) from a particular population	
d.	the sample means for all the possible random samples (for all sample sizes) from a particular population	

____	42.	The standard error of X (over-bar) provides a measure of ______.
a.	the maximum possible discrepancy between X (over-bar) and m	
b.	the minimum possible discrepancy between X (over-bar) and m	
c.	the exact discrepancy between each specific X (over-bar) and m	
d.	none of the above	

____	43.	As sample size increases, the standard error of X (over-bar) ______.
a.	also increases	
b.	decreases	
c.	stays constant	

____	44.	A random sample is obtained from a population with m = 80 and s = 10. Which of the following samples would have the largest z-score?
a.	n = 25 with X (over-bar) = 82	
b.	n = 25 with X (over-bar) = 84	
c.	n = 100 with X (over-bar) = 82	
d.	n = 100 with X (over-bar) = 84	

____	45.	A sample of n = 25 scores is determined to have a standard error of 2 points. What is the standard deviation for the population from which the sample was obtained?
a.	2	
b.	2/5	
c.	10	
d.	50	

____	46.	A random sample is selected from a population with m = 80 and s = 10. To ensure a standard error of 2 points or less, the sample size should be at least ____.
a.	n = 5	
b.	n = 10	
c.	n = 25	
d.	It is impossible to obtain a standard error less than 2 for any sized sample.	

____	47.	If sample size (n) is held constant, the standard error will _______ as the population variance increases.
a.	increase	
b.	decrease	
c.	stay constant	
d.	cannot answer with the information given	

____	48.	The final step of hypothesis testing is to ______.
a.	locate the values associated with the critical region	
b.	make a statistical decision about H0	
c.	collect the sample data and compute the test statistic	
d.	state the hypotheses and select an alpha level	

____	49.	The critical region for a hypothesis test consists of ______.
a.	outcomes that have a very low probability if the null hypothesis is true	
b.	outcomes that have a high probability if the null hypothesis is true	
c.	outcomes that have a very low probability whether or not the null hypothesis is true	
d.	outcomes that have a high probability whether or not the null hypothesis is true	

____	50.	In a hypothesis test, an extreme z-score value, like z = +3 or z = +4, _____.
a.	is probably in the critical region	
b.	means that you should probably reject the null hypothesis	
c.	is strong evidence of a statistically significant effect	
d.	all of the above	
e.	none of the above	

____	51.	A Type I error means that a researcher has ______.
a.	falsely concluded that a treatment has an effect	
b.	correctly concluded that a treatment has no effect	
c.	falsely concluded that a treatment has no effect	
d.	correctly concluded that a treatment has an effect	

____	52.	The probability of committing a Type I error ______.
a.	is determined solely by the size of the treatment effect	
b.	cannot be controlled by the experimenter	
c.	is determined by the level of significance that one chooses	
d.	is determined by the value for beta (b) one selects	

____	53.	The critical boundaries for a hypothesis test are z = +1.96 and -1.96. If the z-score for the sample data is z = -1.90, then the correct statistical decision is
a.	fail to reject H1	
b.	fail to reject H0	
c.	reject H1	
d.	reject H0	

____	54.	A researcher reports that there is a significant difference between two treatments at the .05 level of significance. This means that _______.
a.	if the researcher repeated the experiment, there is a 95% probability that the same decision would be reached	
b.	the difference obtained in the experiment is at least 5% larger than the standard error	
c.	there is a 5% probability (or less) that the difference is due to chance	
d.	the average score for one treatment is at least 5% higher than the average score for the other treatment	

____	55.	Which of the following terms is not required when using the t statistic?
a.	n	
b.	s	
c.	df	
d.	s or s2 or SS	

____	56.	The magnitude of the estimated standard error is ______.
a.	directly related to sample variance and directly related to sample size	
b.	directly related to sample variance and inversely related to sample size	
c.	inversely related to sample variance and directly related to sample size	
d.	inversely related to sample variance and inversely related to sample size	

____	57.	What is the estimated standard error of the mean, in the population, obtained from a sample with n = 9 and s2 = 36?
a.		
b.		
c.		
d.		

____	59.	A sample has a mean of X (over-bar) = 39.5 and a standard deviation of s = 4.3. In a two-tailed hypothesis test with a = .05, this sample produces a t statistic of t = 2.14. Based on this information, the correct statistical decision is ______.
a.	reject the null hypothesis	
b.	fail to reject the null hypothesis	
c.	cannot answer without additional information	

____	60.	A sample of n = 25 scores produces a t statistic of t = -2.05. If the researcher is using a two-tailed test with a = .05, the correct statistical decision is ______.
a.	reject the null hypothesis	
b.	fail to reject the null hypothesis	
c.	cannot answer without additional information	

____	61.	What is the pooled variance for the following two samples?
Sample 1: n = 6 and SS = 200.
Sample 2: n = 10 and SS = 300
a.	250	
b.	500	
c.	500/14	
d.	500/16	

____	62.	One sample has n = 6 and SS = 20 and a second sample has n = 6 and SS = 30. What is the pooled variance for the two samples?
a.	25	
b.	50	
c.	50/10	
d.	50/12	

____	63.	A researcher reports t(24) = 5 for an independent-measures experiment. How many subjects participated in the entire experiment?
a.	24	
b.	25	
c.	26	
d.	12	

____	64.	For an independent-measures research study, the data show a 10-point difference between the two treatment means and a pooled variance of 4. Given this information, the value of Cohen's d is ______.
a.	10/4	
b.	10/2	
c.	4/10	
d.	2/10	

____	65.	A repeated-measures study would not be appropriate for which of the following situations?
a.	A researcher would like to study the effect of practice on performance.	
b.	A researcher would like to compare individuals from two different populations.	
c.	The effect of a treatment is studied in a small group of individuals with a rare disease.	
d.	A developmental psychologist examines how behavior unfolds by observing the same group of children at different ages.	

____	67.	A repeated-measures experiment with a sample of n = 16 subjects would produce a t statistic with df = ____.
a.	15	
b.	16	
c.	30	
d.	32	

____	68.	A researcher is using a repeated-measures study to evaluate the difference between two treatments. If there is a consistent difference between the treatments then the data should produce ______.
a.	a small variance for the difference scores and a small standard error	
b.	a small variance for the difference scores and a large standard error	
c.	a large variance for the difference scores and a small standard error	
d.	a large variance for the difference scores and a large standard error	

____	70.	A repeated-measures study produces a sample mean difference of D (over-bar) = 4.5 with SS = 2400 for a sample of n = 25 individuals. Based on this information, the effect size using Cohen's d would be ______.
a.	d = 4.5/100 = 0.045	
b.	d = 4.5/10 = 0.45	
c.	d = 4.5	
d.	d cannot be determined from the information provided.	

____	71.	A researcher knows that a special reading program will improve students' reading scores. To determine how much improvement will occur, the researcher obtains a sample of n = 25 students and measures each individual's reading performance before and after the special program. The data will be used to estimate the mean amount of improvement. Which estimation equation should the researcher use?
a.	the single-sample t equation	
b.	the independent-measures t equation	
c.	the repeated-measures t equation	

____	72.	Which of the following most closely resembles the general form of an interval estimate?
a.	statistic = parameter ± error	
b.	statistic = parameter ´ error	
c.	parameter = statistic ± error	
d.	error = parameter ± statistic	

____	73.	If all other factors are held constant, increasing the sample size will ______.
a.	increase the standard error	
b.	decrease the width of the confidence interval	
c.	increase the width of the confidence interval	
d.	none of the above	

____	74.	Which combination of factors would definitely reduce the width of a confidence interval?
a.	use a larger sample and increase the level of confidence	
b.	use a smaller sample and increase the level of confidence	
c.	use a larger sample and decrease the level of confidence	
d.	use a smaller sample and decrease the level of confidence	

____	76.	The 90% confidence interval for the difference between two population means extends from 4.00 to 8.00. Based on this information you can conclude that the difference between the two sample means was ______.
a.	2 points	
b.	4 points	
c.	6 points	
d.	8 points	

____	78.	A researcher uses analysis of variance to test for mean differences among four treatments with a sample of n = 6 in each treatment. The F-ratio for this analysis would have what df values?
a.	df = 3, 5	
b.	df = 3, 15	
c.	df = 3, 20	
d.	df = 4, 24	

____	79.	A researcher reports an F-ratio with df = 3, 36 for an independent-measures experiment. How many treatment conditions were compared in this experiment?
a.	3	
b.	4	
c.	36	
d.	39	

____	80.	An experiment compares two treatment conditions with a sample of n = 20 in each treatment. If the data are analyzed with ANOVA, the analysis would have dftotal = _____.
a.	18	
b.	19	
c.	38	
d.	39	

____	81.	A treatment effect refers to differences between scores that are caused by the different treatment conditions. The differences (or variability) produced by treatment effects will contribute to ______.
a.	the numerator of the F-ratio	
b.	the denominator of the F-ratio	
c.	both the numerator and the denominator of the F-ratio	
d.	Treatment effects do not contribute to the F-ratio because they are removed before the F-ratio is computed.	

____	83.	Under what circumstances are post tests necessary?
a.	reject the null hypothesis with k = 2 treatments	
b.	reject the null hypothesis with k > 2 treatments	
c.	fail to reject the null hypothesis with k = 2 treatments	
d.	fail to reject the null hypothesis with k > 2 treatments	

____	85.	A research study compares three treatments with n = 5 in each treatment. If the data were examined using an analysis of variance, the F-ratio would have df = _____.
a.	12	
b.	14	
c.	2, 12	
d.	2, 14	

____	89.	In a two-factor analysis of variance a main effect is defined as ______.
a.	the mean differences among the levels of one factor	
b.	the mean differences among all treatment conditions	
c.	the mean difference between the two factors	
d.	the difference between the largest treatment mean and the smallest treatment mean	

____	90.	If the mean and variance are computed for each sample in an independent-measures two-factor experiment, then which of the following types of sample data will tend to produce large F-ratios for the two-factor ANOVA?
a.	big values for the sample means	
b.	small values for the sample means	
c.	big values for the sample variances	
d.	small values for the sample variances	

____	91.	A set of n = 5 pairs of X and Y values has SSX = 10, SSY = 40 and SP = 10. For these data, the Pearson correlation is ______.
a.	r = 10/20 = 0.50	
b.	r = 10/400 = 0.025	
c.	r =  = 0.707	
d.	r = 40/100 = 0.40	

____	92.	In the general linear equation Y = bX + a, the value of a is called ______.
a.	the slope constant	
b.	the Y-intercept	
c.	the X-intercept	
d.	the beta factor	

____	93.	What information cannot be determined from the general linear equation Y = bX + a?
a.	the correlation between X and Y	
b.	the slope	
c.	the Y intercept	
d.	a and c	

____	94.	Which of the following points is on the line defined by the equation Y = 4X + 2?
a.	X = 1 and Y = 4	
b.	X = 0.5 and Y = 4	
c.	X = 2 and Y = 8	
d.	X = 3 and Y = 9	

____	95.	The entrance fee for a theme park is $20. Tickets for each ride and attraction are $3 a piece. Which of the following equations describes the relation between the total cost (Y) and the number of tickets purchased (X) in a single visit to the park?
a.	Y = 20X + 3	
b.	Y = 60X	
c.	Y = 3X + 20	
d.	X = 3Y + 20	

____	96.	In the test for goodness of fit, the chi-square statistic has degrees of freedom equal to ______.
a.	n - 1	
b.	n - 2	
c.	n - C (where C is the number of categories)	
d.	none of the above	

____	97.	The chi-square test for independence is used to test for ______.
a.	a mean difference between two populations	
b.	a difference between a sample distribution and a population distribution	
c.	a difference in variance between two populations	
d.	a relationship between two variables	

____	98.	The chi-square test for independence can be used to evaluate ______.
a.	the relationship between two variables	
b.	differences between two or more population frequency distributions	
c.	both of the above	
d.	neither of the above	

____	99.	The chi-square test for independence has degrees of freedom given by _____.
a.	R x C	
b.	R x C(n - 1)	
c.	n - R x C	
d.	(R - 1)(C - 1)	

____	100.	A chi-square test for independence is being used to evaluate the relationship between two variables, one of which is classified into 3 categories and the second of which is classified into 4 categories. The chi-square statistic for this test would have df equal to ______.
a.	6	
b.	7	
c.	10	
d.	11	

	101.	Describe the sequence of mathematical operations that would be used to evaluate each of the following expressions.
a.	SX2	
b.	(SX)2	
c.	SX + 1	
d.	S(X + 1)	
e.	S(X + 1)2	

	102.	Calculate each value requested for the following set of scores. Scores: 0, 1, 4, 2
a.	SX + 2	
b.	S(X + 2)	
c.	S(X + 2)2	

	

103.	Find the mean, the median, and the mode for the set of scores in the frequency distribution histogram below.

	104.	For the following population of scores, use the definitional formula (the definition) to compute SS. Then compute the variance and the standard deviation for the population.
Scores: 9 1 8 6

	105.	A distribution of N = 10 scores has m = 50 and s = 10. If another five individuals, all with scores of X = 50, are added to this distribution, what will happen to the standard deviation? Will it increase, decrease, or stay the same? Explain your answer.

	106.	A set of exam scores are reported as X values and z-scores. On this exam a score of X = 75 corresponds to a z-score of z = +2.00, and a score of X = 60 corresponds to a z-score of z = -1.00. What are the values for the mean and standard deviation for this exam? (Hint: Sketch a distribution and locate each of the z-score positions.)

	107.	A researcher knows that the weights of 6-year olds are normally distributed with m = 20.9 kg and s = 3.2. She suspects that children in poverty-stricken regions are undernourished and therefore underweight. With a sample of n = 16 children, the researcher obtains a sample mean of X (over-bar) = 18.3. Use a one-tailed test and the .01 of significance to determine if the weights for this sample are significantly lower than what would be expected for the regular population of 6-year- olds.

	108.	How does the shape of a t distribution compare with the normal distribution? How does the shape of a t distribution depend on sample size (n)?

	109.	The following data are from an independent-measures experiment comparing two treatment conditions. Do these data indicate a significant difference between the treatments at the .05 level of significance?

Treatment 1	Treatment 2	
13	9	
9	5	
7	5	
11	9	

	110.	The following data were obtained from an independent measures study. Determine if there is a significant difference between the treatments. Use a = .01

Treatment 1	Treatment 2	
5	6	
1	10	
2	14	
3	12	
4	18	

	111.	A researcher would like to determine if relaxation training will affect the number of headaches for chronic headache sufferers. For a week prior to training, each subject records the number of headaches suffered. Subjects then receive relaxation training and for the week following training the number of headaches is again measured. The change in number of headaches before and after training is as follows (minus signs indicate a reduction):
Difference scores: -5 -1 -4 -3 -6 -8 0 +1 -1
Is there an effect of training? Use a two-tailed test with a = .05

	112.	A therapist would like to evaluate the effectiveness of a procedure for treating depression. A sample of n = 16 depressed clients is obtained and each person's level of depression is measured using a standardized questionnaire before they begin the therapy program. Two weeks after therapy, each client's level of depression is measured again. For this sample, the average level of depression dropped by D (over-bar) = 6.8 points following therapy. The difference scores had a variance of s2 = 64. Do these data indicate a significant change in depression? Use a two-tailed test at the .05 level of significance.

	113.	Describe point estimates and interval estimates in terms of their confidence and precision in estimating m.

	114.	A sample of n = 9 has a mean of X (over-bar) = 72 with SS = 800. Use the sample to make a point estimate of m and to construct the 90% confidence interval for m.

	115.	A researcher would like to estimate how much difference in cigarette smoking results from viewing graphic videos (including an autopsy) on the harmful effects of smoking. A sample of 16 smokers is obtained. Half of the smokers (n = 8) view the video and the other half (n = 8) serves as a control group. The number of packs of cigarettes each person smoked during the following week is recorded. The data are as follows:

Controls	Video Viewers	
X (over-bar) = 17.5	X (over-bar) = 8.1	
SS = 122	SS = 102	

a.	Use the sample data to make a point estimate of the mean difference in smoking behavior between the control group and the video viewers.	
b.	Make an interval estimate of the mean difference so that you are 80% confident that the population mean difference is in your interval.	

	116.	State the alternative hypothesis (H1) for an ANOVA comparing four treatment conditions. Explain why the hypothesis is stated in this way.

	117.	A psychologist would like to know whether the change in seasons has any consistent effect on people's mood. In the middle of each of the four seasons the psychologist selects a random sample of n = 10 students. Each individual in these four separate samples is given a standardized mood/depression questionnaire. The data from this study are examined using an analysis of variance and the results are shown in the summary table below. Fill in all missing values in the table.

Source	SS	df	MS		
Between Treatments	____	____	____	F = ____	
Within Treatments	____	____	2		
Total	132	____			

	118.	A psychologist examines long term retention of a learned task in a sample of n = 6 rats. At 90 days of age, rats are trained on a discrimination task. Their initial performance is recorded to serve as a baseline for subsequent comparisons. Then their performance is tested again at 6 months, 1 year, 1 1/2 years, and 2 years of age. A partial ANOVA summary table follows. Provide the missing values. (Hint: Begin with values for df).

Source	SS	df	MS	
	
Between treatments	____	____	11	F = _____	
Within treatments	____	____			
   Between subjects	____	____			
   Error	40	____	____		
Total	152	____			

	119.	The following data were collected from a repeated-measures study. Determine if an effect exists at the .05 level of significance.

	Treatments	
Subject	A	B	C	D	
	
1	6	3	3	0	G = 44	
2	4	4	2	2		
3	4	2	0	2	SX2 = 172	
4	6	3	3	0	
	
	T = 20	T = 12	T = 8	T = 4		
	SS = 4	SS = 2	SS = 6	SS = 4		

	120.	The following table summarizes the results of a two-factor ANOVA evaluating an independent-measures experiment with two levels of factor A, three levels of factor B, and n = 5 subjects in each separate sample. Fill in all missing values in the table. (Hint: Start with the df column.)

Source	df	SS	MS		
Between Treatments	____	60			
   Factor A	____	____	____	FA =  5        	
   Factor B	____	____	____	FB = ____    	
   A x B	____	30	____	FAxB = ____	
Within Treatments	____	____	2		
Total	____	____			

	121.	Describe what is meant by a negative relationship between two variables.

	122.	Find the regression equation for predicting Y from X for the following set of scores.

X	Y	
0	9	
1	7	
2	11	

	123.	Explain how the chi-square tests differ from parametric tests (such as t tests or ANOVA) with respect to
a.	the hypotheses,	
b.	the data, and	
c.	the assumptions underlying the test.	

	124.	A sample of thirty people is obtained and each person tastes three brands of instant coffee and identifies his/her preference. The resulting frequency data are as follows:

Brand A	Brand B	Brand C	
5	14	11	

a.	A researcher wants to use these data to test for preferences among the three brands. State the hypotheses and find the expected frequencies for the chi-square test.	
b.	Consumer data show that ten years ago Brand A was preferred by 20% of the population and Brands B and C were each preferred by 40% of the population. A researcher wants to use the data to test whether there has been a significant change in preferences during the past ten years. State the hypotheses and find the expected frequencies for the chi-square test.	

	125.	A statistics instructor would like to know whether it is worthwhile to require students to do weekly homework assignments. For one section of the statistics course, homework is assigned, collected, and graded each week. For another section, the same problems are suggested each week, but the students are not required to turn in their homework. At the end of the semester, all students take the same final exam. The grade distributions for the two sections are as follows:

	FINAL EXAM GRADE	
A	B	C	D	F	
Homework	12	15	17	5	1	
No Homework	12	21	28	25	14	

Do these data indicate a significant difference between the grade distributions for students with homework versus students with no homework? Test with a = .05.

Review of Basic Statistical Concepts
Answer Section

MULTIPLE CHOICE

	1.	A

	2.	B

	3.	C

	4.	C

	5.	A

	6.	C

	7.	A

	8.	D

	9.	C

	10.	B

	11.	B

	12.	C

	13.	B

	14.	A

	15.	A

	16.	C

	17.	B

	18.	A

	19.	C

	20.	C

	21.	B

	22.	C

	23.	D

	24.	A

	25.	B

	26.	C

	27.	B

	28.	D

	29.	A

	30.	D

	31.	B

	32.	B

	33.	D

	34.	C

	35.	C

	36.	B

	37.	C

	38.	A

	39.	C

	40.	B

	41.	C

	42.	D

	43.	B

	44.	D

	45.	C

	46.	C

	47.	A

	48.	B

	49.	A

	50.	D

	51.	A

	52.	C

	53.	B

	54.	C

	55.	B

	56.	B

	57.	A

	58.	C

	59.	C

	60.	B

	61.	C

	62.	C

	63.	C

	64.	B

	65.	B

	66.	C

	67.	A

	68.	A

	69.	C

	70.	B

	71.	C

	72.	C

	73.	B

	74.	C

	75.	C

	76.	C

	77.	C

	78.	C

	79.	B

	80.	D

	81.	A

	82.	C

	83.	B

	84.	C

	85.	C

	86.	C

	87.	D

	88.	D

	89.	A

	90.	D

	91.	A

	92.	B

	93.	A

	94.	B

	95.	C

	96.	D

	97.	D

	98.	C

	99.	D

	100.	A

OTHER

	101.	a. To compute SX2, you first square each score, then sum the squared values.
b. To compute (SX)2, you first sum the scores, then square the sum.
c. To compute SX + 1, you first sum the scores, then add 1 to the sum.
d. To compute S(X + 1) you first add 1 to each score, then sum the resulting values.
e. To compute S(X + 1)2, you first add 1 to each score, then square the resulting values, then sum the squared numbers.

	102.	a. 9
b. 15
c. 65

	103.	Mean = 27/10 = 2.70. Median = 2.5. Mode = 2.

	104.	SS = 38; s2 = 9.5; s = 3.08

	105.	6. The variability will decrease. Adding new scores at the mean will not change the mean, but it does result in more scores being clustered at the mean. As a result the standard deviation (average distance from the mean) will decrease.

	106.	m = 65 and s = 5

	107.	6. H0: m ³ 20.9. H1: m < 20.9. The critical region is in the tail beyond -2.33. sx (over-bar) = 0.8 and z = -3.25. Reject H0 and conclude that children from poverty stricken areas weigh significantly less than other children.

	108.	The t distributions tend to approximate a normal shape, but they generally have greater variability (look flatter) than a normal distribution. As sample size increases, the t distribution becomes closer to a normal shape.

	109.	For treatment 1, X (over-bar) = 10 and SS = 20. For treatment 2, X (over-bar) = 7 and SS = 16. For these data the pooled variance is 6, the standard error is  = 1.73, and the t statistic is t(6) = 1.73. Fail to reject H0.

	110.	For treatment 1, X (over-bar) = 3 and SS = 10. For treatment 2, X (over-bar) = 12 and SS = 80. The pooled variance = 11.25, standard error = 2.12, t(8) = -4.25. Reject H0.

	111.	For these data D (over-bar) = -3, s2 = 9 and t(8) = -3.00. Reject H0 and conclude that the relaxation training has a significant effect.

	112.	For these data the standard error is s = 2 and t(15) = 3.4. Reject H0. These data are sufficient to conclude that there has been a change in depression with a = .05.

	113.	Point estimates are perfectly precise but have no confidence. Interval estimates provide confidence (the wider the interval, the more confidence), but they give up precision (the wider the interval, the less precision).

	114.	For the point estimate, use X (over-bar) = 72. m = 72 ± 1.86(3.33), df = 8. The confidence interval extends from 65.81 to 78.19.

	115.	a. Use X(over-bar)1 - X(over-bar)2 = 9.4 for the point estimate of m1 - m2.
b. m1 - m2 = 9.4 ± 1.345(2), df = 14. The confidence interval extends from 6.71 to 12.09.

	116.	With k = 4 treatments the alternative hypothesis would simply state, "At least one mean is different from the others." This general statement is used because there are several different alternatives to H0 and it usually is not productive to try to list them all.

	117.	
Source	SS	df	MS	
	
Between Treatments	60	3	20	F = 10	
Within Treatments	72	36	2		
Total	132	39			

	118.	
Source	SS	df	MS		
Between Treatments	44	4	11	F = 5.50	
Within Treatments	108	25			
   Between Subjects	68	5			
   Error	40	20	2		
Total	152	29			

	119.	
Source	SS	df	MS		
Between Treatments	18	1	18	F(1,3) = 9.00	
Within Treatments	12	6			
   Between Subjects	6	3			
   Error	6	3	2		
Total	30	7			

With df = 1,3 the critical value is 10.13. Fail to reject the null hypothesis. There is not a significant difference between treatments.

	120.	
Source	df	SS	MS		
Between Treatments	5	60			
   Factor A	1	10	10	FA = 5       	
   Factor B	2	20	10	FB = 5       	
   A x B	2	30	15	FAxB = 7.5	
Within Treatments	24	48	2		
Total	29	108			

	121.	In a negative relationship there is a tendency for one variable to decrease as the other variable increases. The two variables tend to move in opposite directions.

	122.	SSX = 2, SP = 2, X (over-bar) = 1, and Y = 9. Y (hat) = (1)X + 8.

	123.	As nonparametric tests, the chi-square tests state general hypotheses about the entire population without any reference to a specific population parameter. The data for a chi-square test consist of frequencies, but the data for a t test or ANOVA consist of scores that can be added, multiplied, squared, etc. Finally, the chi-square tests do not require any assumptions about population parameters. The t tests and ANOVA require normal populations and homogeneity of variance for tests with independent-measures designs.

	124.	a. The null hypothesis states that the three brands are equally preferred in the population (p = 1/3 for each brand). The expected frequency is 10 for each of the three brands.
b. The null hypothesis states that there has been no change in the population proportions; that is, 20% still prefer Brand A, 40% prefer Brand B, and 40% prefer Brand C. The expected frequencies are 6 for Brand A, 12 for Brand B, and 12 for Brand C.

	125.	The null hypothesis states that there is no difference between the grade distributions for the two sections. With a = .05 and df = 4, the critical value is 9.49. The expected frequencies are as follows:

	FINAL EXAM GRADE	
A	B	C	D	F	
Homework	8	12	15	10	5	
No Homework	16	24	30	20	10	

For these data, chi-squared = 13.08. Reject H0 and conclude that there is a significant difference between the two sections.