Question

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2. Conduct a hypothesis test showing all of your steps. A Gallup Poll reports that 65% of American adults support labor unions. In order to test this claim, 988 adults in the U.S. were surveyed, of which 617 approved of labor unions. Do 65% of Americans support them? Test this claim with a 6% level of significance. a) State the hypotheses and label the claim. b) Is it left-tailed, right-tailed, or two-tailed (circle one)? c) What are the critical values? Draw a picture. d) What are the P-value and/or test-statistics? e) Give two reasons for your decision to reject/not reject Ho based on: 1) Test statistic compared to critical value(s) 2) P-value compared to a. State the conclusion, relating it back to the original claim.

Answer 1

The following information is provided: The sample size is N = 988, the number of favorable cases is X = 617, and the sample proportion is p = * = 0.6245 and the significance level is a = 0.06 617 988 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho:p= 0.65 Ha: p = 0.65 This corresponds to a two-tailed test, for which a z-test for one population proportion needs to be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.06, and the critical value for a two-tailed test is ze 1.88. = The rejection region for this two-tailed test is R= {z:[2> 1.88} .. (3) Test Statistics The Z-statistic is computed as follows: 2 = P - po V po(1 – po)/n 0.6245 – 0.65 70.65(1 – 0.65)/988 -1.681 (4) Decision about the null hypothesis Since it is observed that |z| = 1.681 < ze = 1.88, it is then concluded that the null hypothesis is not rejected. 0.0928 > Using the P-value approach: The p-value is p 0.0928, and since p 0.06, it is concluded that the null hypothesis is not rejected. (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p is different than po, at the a = 0.06 significance level.

Z-Test Results: z-stats = -1.681, p-value =0.0928 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

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