Hypothesis Testing and Statistical Inference: Analyzing Differences in Means

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Hypothesis Testing and Statistical Inference: Analyzing Differences inMeans1.A shoe company wants to compare two materials, A and B, for use on the soles of boys' shoes. In thisexample, each of ten boys in a study wore a special pair of shoes with the sole of one shoe made fromMaterial A and the sole on the other shoe made from Material B. The sole types were randomly assignedto account for systematic differences in wear between the left and right foot. After three months, theshoes are measured for wear. Let Ho:μd= 0 versus Ha:μd≠0. From this random sample of 10 boys, thesample mean difference was 0.41 and Sdwas 0.387.What is the value of the test statistic?A)t = 0.00B)t = 3.18C)t = 3.35D)t = 4.74Feedback:First, recognize that this is a paired t-test. Then the t test statistic is 3.35 and is found bytaking the sample mean difference minus the hypothesized value then dividing by the standard error (notstandard deviation!). This, then, is (0.41-0)/(0.387/sq.rt. 10) or 0.41/0.122 = 3.35Points Earned:1.0/1.02.A shoe company wants to compare two materials, A and B, for use on the soles of boys' shoes. In thisexample, each of ten boys in a study wore a special pair of shoes with the sole of one shoe made fromMaterial A and the sole on the other shoe made from Material B. The sole types were randomly assignedto account for systematic differences in wear between the left and right foot. After three months, theshoes are measured for wear. Let Ho:μd= 0 versus Ha:μd≠0. From this random sample of 10 boys, thesample mean difference was 0.41 and Sdwas 0.387.If the p-value for this test is 0.009, then for a significance level of alpha = 0.05, are the results statisticallysignificant?A)No, results are not statistically significant because the p-value < 0.05.B)Yes, results are statistically significant because the p-value < 0.05.C)No, results are not statistically significant because the p-value > 0.05D)Yes, results are statistically significant because the p-value > 0.05.Feedback:Yes,results are statistically significant because the p-value < 0.05.Points Earned:1.0/1.03.Which of the following isnotone of the steps for hypothesis testing?

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