Question

A researcher claims that more than 75% of the adults believe in global warming. Ryan conducted a survey on a random sample of 200 adults. The survey showed that 155 adults in the sample believe in global warming. Assume Ryan wants to use a 0.05 significance level to test the researcher’s claim.

(a) What is the appropriate hypothesis test to use for this analysis? Please identify and explain why it is appropriate.

(b) Identify the null hypothesis and the alternative hypothesis.

Answer 1

Solution :

Given that,

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.75

H_a : p > 0.75

x = 155

n = 200

= x / n = 155 / 200 = 0.77

P₀ = 0.75

1 - P₀ = 1 - 0.75 =0.25

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.77 - 0.75/ [0.75 * 0.25 /200 ]

= 0.816

Test statistic z value = 0.816

P(z > 0.816 ) = 1 - P(z < 0.816 ) = 1 - 0.7927 = 0.2073

P-value = 0.2073

= 0.05

P-value ≥

0.2073 ≥ 0.05

:a ) The p-value is p = 0.2073 and since 0.2073 ≥ 0.05 it is concluded that the null hypothesis is not rejected

b ) It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p is greater than p₀​, at the α = 0.05 significance level.