Question

In a previous poll, 36% 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, 378 of 1108 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the a= 0.01 significance level. V 5% of the population size, and the sample V the requirements for testing the hypothesis satisfied. Because npo (1-P) = 10 and the sample size is (Round to one decimal place as needed.) What are the null and alternative hypotheses? Ho: versus H: (Type integers or decimals. Do not round.) Find the test statistic, Zo 20=(Round to two decimal places as needed.) Find the P-value. P-value = (Round to three decimal places as needed.) Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Choose the correct answer below. O A. No, there is not sufficient evidence because the P-value is greater than the level of significance. Therefore, do not reject the null hypothesis. B. No, there is not sufficient evidence because the P-value is greater than the level of significance. Therefore, reject the null hypothesis. O C. Yes, there is sufficient evidence because the P-value is greater than the level of significance. Therefore, reject the null hypothesis. OD. Yes, there is sufficient evidence because the P-value is greater than the level of significance. Therefore, do not reject the null hypothesis.

Answer 1

P= 0.36 no 1108 X: 378 d=0.01 X 318 1108 = 0.34 n 5% of the Because upo ( 1-Po) = f heo mpo = 1108 X0-36 = 348.88 >10) nPoll-Po) - 110840.36X0-64-255-2832 el>10 and the sample size is I less than poboulation size and the sample propostion 0.34) us close to oool hypothesis is salisfied → The nell and alternative hypothesis core :- Ho: p = 0.36 Hi :P < 0.36 ( left-tailed test) --) Test statistic :- the requirment for testing the P P Z - 0.34- 0.36 P (1-P) 0.3611-0.36) 1108 h Z -1.39 P- value P (Z Z <Z test P(Z < -1.39) Using 2- table) P-value = 0 082 [p-value > 0.01) Since P-value greater than (2) significance level fo we fail to Reject Ho no, option A there is not sufficient evidence because Pr value is greater than level of significance, Therefore do not reject the neell hypothesis.