Chapter 8, Problem 11PT

a.

To determine

To construct: The 99% confidence interval and interpret it.

Answer to Problem 11PT

The confidence interval is (0.49, 0.70).

Explanation of Solution

Given:

Number of successes ( x ) = 89

Number of trials ( n ) = 150

Formula used:

The formula to compute the confidence interval is:

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

Calculation:

The confidence interval using Ti-83 calculator could be computed as:

  

Thus, the confidence interval is (0.49, 0.70)

Interpretation:

There is 95% probability that the population proportion is between 0.49 and 0.70.

b.

To determine

To explain: If it could be concluded that more than half of the visitors are in favor of proposal.

Answer to Problem 11PT

No, it cannot be concluded.

Explanation of Solution

From the above part, it is known that the population proportion is between 0.49 and 0.70. Since, the interval is also containing the value 0.49. Thus, it cannot be concluded that more than half of the visitors are in favour of proposal