Two sample hypothesis testing – Chapter 12A) Hypothesis testing for the difference between two population means (μ1−μ2¿−¿when σ1and σ2is known - Z- distribution – Independent samples 1) Assume that you have a sample of n1=¿8 with the sample mean of ´X1=and a population standard deviation of σ1= 4 and you have an independent sample of n2=15from another population with a sample mean of ´X2=34and a population standard deviation of σ2= 5.a)What is the value of the ZSTATfor testing H0: μ1=μ42

b)Using the level of significance α=0.01,what is/are the critical value(s)?

c) Using the level of significance α=0.01,what is/are the critical value(s) forH0: μ1≤ μ2? (2.33)2) A recent study found that children who watched a cartoon with food advertising ate, on average, 28.5 grams of Goldfish crackers as compared to an average of 19.7grams of Goldfish crackers for children who watched a cartoon without food advertising. Suppose that there were 59 children in each group, and the population standard deviation for those children who watched the food ad was 8.6 grams and the population standard deviation for those children who did not watch the food ad was 7.9 grams. To test at 0.05 level whether there is evidence that the mean amountof Goldfish crackers eaten was significantly higher for the children who watched food ads, answer the following questions. Consider sample 1 as the children who watched food ads and sample 2 as the children who did not watch food ads.a) What are the null and alternative hypotheses? (H0: μ1−μ2≤0,H1: μ1−μ2>0b) What is the test statistic and the p-value? )

c) What is/are the critical value(s)? (1.645)d) What is the managerial conclusion? (There is evidence that the population meanamount of Goldfish crackers eaten was significantly higher for the children who watched food ads)B) Hypothesis testing for the difference between two population means (μ1−μ2¿−¿when σ1and σ2are unknown and assumed to be equal (σ2=¿σ2¿

1

3) The Computer Anxiety Rating Scale (CARS) measures an individual’s level ofcomputer anxiety, on a scale from 20 (no anxiety) to 100 (highest level of anxiety).Researchers at Miami University administered CARS to 172 business students. One of the objectives of the study was to determine whether there is a difference inthe level of computer anxiety experienced by female and male business students. Males Females´X40.26 36.85S 13.35 9.42n 100 To test at 0.05 level, assuming equal variances, whether there is evidence that thereis a difference in the mean computer anxiety experienced by female and male business students, answer the following questions. Consider sample 1 as males andsample 2 as females.a) What are the null and alternative hypotheses? 72

)