Question

Dr. Dommer is interested in testing whether the gender breakdown in his introductory biology class is
representative of the gender breakdown of the college population. There are 20 females and 25 males in his class. If the college population is 60 percent female, what should Dr. Dommer conclude about the representativeness of his class? Complete the 6 steps of hypothesis testing. Show your work for each step. Report your results and conclusion in APA style. Assume that alpha is set at .05.

Answer 1

The following information is provided: The sample size is N = 45, the number of favorable cases is X = 20, and the sample proportion is p = = 48 0.4444, and the significance level is a = 0.05 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho:p 0.60 Ha :p 0.60 .. This corresponds to a two-tailed test, for which a z-test for one population proportion needs to be used. (2) Rejection Region 0.05, and the Based on the information provided, the significance level is a = critical value for a two-tailed test is zc = 1.96. The rejection region for this two-tailed test is R = {2: || > 1.96} (3) Test Statistics The Z-statistic is computed as follows: P - PO V po(1 – po)/n 0.4444 – 0.60 10.60(1 – 0.60)/45 2.13 (4) Decision about the null hypothesis Since it is observed that |z| = 2.13 > ze = 1.96, it is then concluded that the null hypothesis is rejected. 0.0332 < Using the P-value approach: The p-value is p = 0.0332, and since p= 0.05, it is concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population proportion p is different than po, at the a = 0.05 significance level. Confidence Interval The 95% confidence interval for p is: 0.299 < p < 0.59. Graphically Z-Test Results: z-stats = -2.13, p-value =0.0332 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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