Question

Complete the problem below. You may work in a small group, but each student must turn in their own worksheet! 1) Market research shows that 65% of consumers prefer Coke over Pepsi. A new Coke commercial is released to increase brand awareness of Coke. 200 consumers were surveyed showed that 135 preferred Coke over Pepsi. We want to test to see if the commercial resulted in an increased preference for Coke i) What are the null and alternative hypotheses that we are testing? 1) What is our test statistic, 2? in) What is the p-value for this test and what conclusions can we draw? (Test at a significance level of 5%)

Answer 1

The following information is provided: The sample size is N = 200, the number of favorable cases is X = 135, and the sample proportion is p= 135 0.675, 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=0.65 Ha:p > 0.65 This corresponds to a right-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 = 0.05, and the critical value for a right-tailed test is ze = 1.64. The rejection region for this right-tailed test is R={z:z> 1.64} (3) Test Statistics The Z-statistic is computed as follows: p - po V po(1 – po)/n 0.675 -0.65 0.65(1 – 0.65)/200 = 0.741 (4) Decision about the null hypothesis Since it is observed that z = 0.741 < ze = 1.64, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p= 0.2293, and since p= 0.2293 > 0.05, 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 pis greater than po, at the a = 0.05 significance level. Confidence Interval The 95% confidence interval for p is: 0.61 <p < 0.74.