Question

In December 2001, 38% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. In a recent poll, 403 of 1122 adults with children under the age of 18 reported that their family ate 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 seven 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. What type of procedure should you do?

we will be using the confidence interval approach in which first we calculate the point estimate and then convert this into an interval by adding and subtracting the margin of errors.

b. Show/explain why the requirements are met.

Favorable Cases X =	403
Sample Size N =	1122

Observe that:

np = (1122)⋅(0.359) =402.798 ≥ 10 , nq = (1122)⋅(0.641) = 719.202 ≥ 10

which indicates that the assumption for normal approximation for the sampling distribution is met.

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

The sample proportion is computed as follows, based on the sample size N = 1122

and the number of favorable cases X = 403

The critical value for α=0.05 is

The corresponding confidence interval is computed as shown below:

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

based on the data provided, the 95% confidence interval for the population proportion is 0.331<p<0.387,

which indicates that we are 95% confident that the true population proportion p which is the current proportion of families with children under the age of 18 who eat dinner together seven nights a week is contained by the interval (0.331, 0.387.)

e. What is the point estimate?

The sample proportion is computed as follows, based on the sample size N = 1122

and the number of favorable cases X = 403

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