Question

In a previous​ poll, 41​% of adults with children under the age of 18 reported that their family ate dinner together 7 nights a week. Suppose​ that, in a more recent​ poll, 401 of 1050 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 alpha equals 0.01 significance​ level? What are the null and alternative​ hypotheses?

Answer 1

H₀: P = 0.41

H₁: P < 0.41

= 401/1050 = 0.3819

The test statistic z = ( - P)/sqrt(P(1 - P)/n)

= (0.3819 - 0.41)/sqrr(0.41 * (1 - 0.41)/1050) = -1.85

P-value = P(Z < -1.85)

= 0.0322

Since the p-value is greater than the significance level (0.0322 > 0.01), so we should not reject the null hypothesis.

At 0.01 significance level, there is not sufficient evidence to conclude that the proportion of families with children under the age of 18 who eat dinner together 7 nights a week had decreased.