Question

In December 2001, 38% of adults with children under the age of 18 reported that their family at dinner together seven nights a week. In recent poll, 403 of 1122 adults with children under the age of 18 reported that their family at dinner together seven nights a week. the researcher wishes to estimate the current proportion of families with children under the age of 18 who eat dinner together seven nights a week with 95% confidence.

a. what type of procedure should you do?

b. show/explain why the requirements are met

c. estimate the proportion of families with children under the age of 18 who eat dinner together 7 nights a week with 95% confidence

d. interpret the confidence interval in the context of the question

e. what is the point estimate?

Answer 1

a. Here we will find 95% confidence interval

b. n is sufficient size so np>10 and nq>10 condition is satisfied, hence normal approximation for proportion distribution can be used

c. z value for 95% CI is 1.96 as P(-1.96<z<1.96)=0.95

Now

So Margin of Error is

Hence CI is

d. Hence the current proportion of families with children under the age of 18 who eat dinner together seven nights a week with 95% confidence will lie in the range of 0.331 to 0.387

e.