Question

1. Calculate is p^ and q^.
2. Find the critical value Zc that corresponds to being 90% confident.
3. Find the margin of error.
4. Construct a 90% confidence interval.
5. Explain the confidence interval.

n = 86. x = 21.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 21 / 86 = 0.244

1 - = 1 - 0.244 = 0.765

Z/2 = 1.645

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.645 * (((0.244 * 0.756) / 86)

= 0.076

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.244 - 0.076 < p < 0.244 + 0.076

0.168 < p < 0.320

The 90% confidence interval for the population proportion p is : 0.168 , 0.320