44 of adults with children under the age of 18 previously re

44% of adults with children under the age of 18 previously reported that their family ate dinner together 7 nights a week. Suppose in a recent poll, 514 of 1250 adults with children under the age of 18 reported that their family ate dinner together 7 nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together 7 nights a week has decreased at the ?= 0.1 significance level?

Choose the correct answer below.

a. No, there is not sufficient evidence, because the test statistic is less than the critical value, meaning that we reject the null hypothesis.

b. Yes, there is sufficient evidence. Because the test statistic is less than the critical value, meaning that we do not reject the null hypothesis.

c. Yes, there is sufficient evidence, because the test statistic is less than the critical value,meaning that we reject the null hypothesis.

d. No, there is not sufficient evidence, because the test statistic is less than the critical value, meaning that we do not reject the null hypothesis.

Solution

hypothesis :

Ho: u = 0.44

Ha: u != 0.44

p = 514/1250 = 0.4112

standard deviation = sqrt( 0.4412 * 0.5888/1250) = 0.01392

test static = 0.4112 - 0.44/0.01392 = -2.067

critical value = +/- 1.645

hence the corrcect choice

a. No, there is not sufficient evidence, because the test statistic is less than the critical value, meaning that we reject the null hypothesis.