Question

Consider the hypothesis statement to the right using α-0.10 and the data to the right from two independent samples. a) Calculate the appropriate test statistic and interpret the result. b) Calculate the p-value and interpret the result. x87 ƠI : 22 n-55 σ2 18 a) The test statistic is Round to two decimal places Determine the appropriate critical value(s. The critical value(s) is(are) as needed.) Round to two decimal places as needed. Use a comma to separate answers as needed.) Since the test statistic in the rejection region. Ho.There is evidence to conclude that the mean of population 1 is greater than the mean of population 2. b) The p-value is Round to three decimal places as needed.) Since the p-value is VHo. There is V evidence to conclude that the mean of population 1 is less than the mean of population 2

Answer 1

Given that, Population 1 87 Population 2 72 18 50 mean std. dev Null hypothesis: F, : M-A's Alternative hypothesis: H Level of significance, α 0.10 a) 0 H->0 Test statistic: m n2 (87-72)-0 222 182 55 50 = 3.84

Critical value: By using z-table, the critical value at 0.10 level of significance for a right tailed test is -0.1,-1.28 Decision rule: Reject Ho if z >-α otherwise accept Ho" The rejection region isz> 1.28 Since the test statistic falls in the rejection region, reject H. There is sufficient evidence to conclude that the mean of population 1 is greater than mean of population 2. b) The p-value is, p-value P(Z>z) -1-P(Zs) -1-(3.84) 1-0.9999(- z-table 0.0001 Since the p-value is less than a reject H, There is sufficient evidence to conclude that the mean ofpopulation 1 is greater than mean ofpopulation 2.