# Mathematics

- What is the age distribution of promotion-sensitive shoppers? A
*supermarket super shopper*is defined as a shopper for whom at least 70% of the items purchased were on sale or purchased with a coupon.Age range, years 18-28 29-39 40-50 51-61 62 and over Midpoint *x*23 34 45 56 67 Percent of super shoppers 5% 41% 26% 11% 17% For the 62-and-over group, use the midpoint 67 years.

(a) Using the age midpoints*x*and the percentage of super shoppers, do we have a valid probability distribution? Explain.(b) Use a histogram to graph the probability distribution of part (a).

(c) Compute the expected age

*μ*of a super shopper. (Round your answer to two decimal places.)

*μ*=(b) Use a histogram to graph the probability distribution in part (a).

(c) Find the probability that a British nurse selected at random in 1851 would be 60 years of age or older. (Round your answer to three decimal places.)

**Question 1**An independent-measures t test produced a t statistic with

*df =*20. If the same data had been evaluated with an analysis of variance, what would be the*df*values for the F-ratio?Answer

a. 1, 20 b. 2, 20 c. 1, 19 d. 2, 19 **Question 2**An analysis of variance comparing three treatment conditions produces

*df*total = 24. For this ANOVA, what is the value of*df*within?Answer

a. 3 b. 2 c. 21 d. 22 **Question 3**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?Answer

a. *df =*3, 15b. *df =*4, 24c. *df =*3, 5d. *df =*3, 20**Question 4**For an analysis of variance comparing four treatments,

*MS*betwee*n =*12. What is the value of*SS*between?Answer

a. 4 b. 48 c. 36 d. 3 **Question 5**An analysis of variance produces

*SS*withi*n =*40 and*MS*withi*n =*10. In this analysis, how many treatment conditions are being compared?Answer

a. 4 b. 5 c. 50 d. 30 **Question 6**An analysis of variance comparing three treatment conditions produces

*df*total = 24. For this ANOVA, what is the value of*df*between?Answer

a. 2 b. 3 c. 22 d. 21 **Question 7**An independent-measures research study compares three treatment conditions using a sample of

*n =*5 in each treatment. For this study, the three sample totals are, T1 = 5, T2 = 10, and T3 = 15. What value would be obtained for*SS*between?Answer

a. 15 b. 5 c. 1 d. 10 **Question 8**An independent-measures research study compares three treatment conditions using a sample of

*n =*5 in each treatment. For this study, the three sample totals are, T1 = 5, T2 = 10, T3 = 15, and 2 = 75 for the entire set of scores. What value would be obtained for*SS*total?Answer

a. 15 b. 5 c. 10 d. 1 **Question 9**The following table shows the results of an analysis of variance. Based on this table, what is the value for ?2, the percentage of variance accounted for?

Source SS df MS Between 16 2 8 *F =*2.00Within 84 21 4 Total 100 23 Answer

a. 16/100 b. 16/18 c. 84/100 d. 4/10 **Question 10**The following table shows the results of an analysis of variance comparing two treatment conditions with a sample of

*n =*11 participants in each treatment. Note that several values are missing in the table. What is the missing value for the F-ratio?Source SS df MS Between xx xx 14 *F =*xxWithin xx xx xx **Total****154****xx**Answer

a. 28 b. 2 c. 7 d. 14 **Question 11**An analysis of variances produce

*SS*betwee*n =*20,*SS*within = 30, and an F-ratio with*df =*2, 15. For this analysis, what is the F-ratio?Answer

a. 30/20 = 1.50 b. 20/30 = 0.67 c. 10/2 = 5.00 d. 2/10 = 0.20 **Question 12**An experiment compares three treatment conditions with a separate sample of

*n =*10 in each treatment. If the data are analyzed with ANOVA, the analysis would have*df*total = _____.Answer

a. 29 b. 28 c. 27 d. 30 **Question 13**An independent-measures research study compares three treatment conditions using a sample of

*n =*10 in each treatment. For this study, the three samples have*SS*1= 10,*SS*2 = 20, and*SS*3 = 15. What value would be obtained for*MS*within?Answer

a. 45/27 b. 45/3 c. 45/29 d. 45/30 **Question 14**For an F-ratio with

*df =*2, 10, the critical value for a hypothesis test using*a =*.05 would be _____.Answer

a. 99.40 b. 4.10 c. 19.39 d. 7.56 **Question 15**The following table shows the results of an analysis of variance comparing three treatment conditions with a sample of

*n =*10 participants in each treatment. Note that several values are missing in the table. What is the missing value for*SS*total?Source SS df MS Between 20 xx xx *F =*xxWithin xx xx 2 Total xx xx Answer

a. 30 b. 54 c. 22 d. 74