Chapter 8, Problem 4CRE

a.

To determine

To define: The parameter p involved in the setting.

Explanation of Solution

Given:

Number of trials ( n ) = 1000

Sample proportion $\left(\widehat{p}\right)$ = 0.37

Formula used:

The formula of confidence interval is:

  $\widehat{p}-z_{\alpha /2}\times \sqrt{\frac{\widehat{p}\left(1-\widehat{p}\right)}{n}}<p<\widehat{p}+z_{\alpha /2}\times \sqrt{\frac{\widehat{p}\left(1-\widehat{p}\right)}{n}}$

The population proportion p shows the proportion of adults that are aged 18 and above that believe that their favorite sport is football

b.

To determine

To check: If the conditions to construct the confidence interval for population are met.

Answer to Problem 4CRE

Yes.

Explanation of Solution

Here, following conditions are fulfilled:

(a). The sample has been chosen randomly.

(b). The number of success and failures are above 10.

(c). Size of sample is 10% lower than the population.

Thus, all the required conditions are fulfilled.

c.

To determine

To construct: The 95% confidence interval

Answer to Problem 4CRE

The confidence interval is (0.341, 0.3999)

Explanation of Solution

Calculation:

The obtained confidence interval using Ti-83 calculator is:

  

Thus, the confidence interval is (0.341, 0.3999)

d.

To determine

To interpret: The confidence interval.

Explanation of Solution

There is 95% surity that the population proportion of adults who believe that their favorite sports to watch in TV is football would fall between the 0.3401 and 0.3999.