Question

You conduct a hypothesis test about a population proportion p at a significance level of a = .01 using a random sample of size n = 38. Your test statistic follows a standard normal distribution when the null hypothesis is true as an equality, and its value obtained from the sample is z = -2.75. Use the Distributions tool to help you answer the questions that follow. Select a Distribution Distributions 0 1 2 3 If you perform a lower tail test, the critical value for your test statistic is: -Za In this case, you the null hypothesis, because the test statistic is: Greater than the critical value -Za Less than the critical value -20 If you perform a two-tailed test, the critical values for your test statistic are: -20/2 = and 2a/2= In this case, you the null hypothesis, because the test statistic is:

Answer 1

Solution: Sample size = n = 38 Test Statistic = z = -2.75 Level of significance =a=0.01 Lower Tail Test: Critical Value: Level of significance =a=0.01 From normal distribution table; the critical value of '2', having area in the left equal to 0.01, is given by: -Za = -2.326 Hence, Critical value = -2.326 In this case, we reject the null hypothesis, because the test statistic is less than the critical value - za Two Tailed Test: Critical Values: The test is a two tailed test. Level of significance =a=0.01 a/2=0.01/2 = 0.005 From normal distribution table; the critical value of 'z', having area in the right equal to 0.005, is given by: Zcritical = 2.576 Hence, Critical values = -za = -2.576, za = 2.576 In this case, we reject the null hypothesis, because the test statistic is less than the critical value - za