Question

A researcher wants to show that greater than 80% of the population has a cell phone. She samples 1000 individuals and 830 of them have a cell phone. What is the P-value and what decision should she make at a 5% significance level?

	A.	P =.0089, reject her claim that the percent is greater than 80% since the results are not statistically significant.
	B.	P =.0089, accept her claim that the percent is greater than 80% since the results are statistically significant.
	C.	P =.83, reject her claim that the percent is greater than 80% since the results are not statistically significant.
	D.	P =.80, accept her claim that the percent is greater than 80% since the results are statistically significant.
	E.	P =.9911, reject her claim that the percent is greater than 80% since the results are not statistically significant.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.80

H_a : p > 0.80

= x / n = 830 / 1000 = 0.830

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.83 - 0.80 / [(0.80 * 0.20) / 1000]

= 2.37

P(z > 2.37) = 1 - P(z < 2.37) = 0.0089

P-value = 0.0089

= 0.05

P-value <

Reject the null hypothesis .

A)