Question

Thi a previous pol, 29% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll..300 of 1096 adults with children under the age of 18 reported that their family to dinner together seven nights a week. Is there sufficient evidence that the aroportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the a=0.1 significance level. Because npo (-P) - 10 and the sample size is 5% of the population size, and the sample the requirements for testing the hypothesis satisfied (Round to one decimal place as needed.)

Answer 1

$p_0=0.29$

> 10 and the sample size less than 5% of the population size, and the sample can be assumed resonably random the requirements are satisfied

npo(1 - Po) 1096 * 0.29 * (1 – 0.29) = 225.67

The following information is provided: The sample size is N = 1096, the number of favorable cases is X = 300, and the sample proportion is p= * = 20 = 0.2737, and the significance level is a = 0.1 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho:p=0.29 Ha:p <0.29 This corresponds to a left-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 = 0.1, and the critical value for a left- tailed test is ze = -1.28. The rejection region for this left-tailed test is R = {z :z<-1.28} (3) Test Statistics The Z-statistic is computed as follows: P - Po Po(1 - po)/n 0.2737 -0.29 0.29(1 – 0.29)/1096 1.12 (4) Decision about the null hypothesis Since it is observed that z = -1.188 >% = -1.28, it is then concluded that the null hypothesis is not rejected. Using the P-value approach: The p-value is p = 0.118 and since p =0.118 >0.1, 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 less than Po, at the a = 0.1 significance level.