Question

According to a 2014 CIRP Your First College Year Survey, 88% of the first-year college students said that their college experi-ence exposed them to diverse opinions, cultures, and values (www. heri.ucla.edu). Suppose in a recent poll of 1800 first-year college stu-dents, 91% said that their college experience exposed them to diverse opinions, cultures, and values. Perform a hypothesis test to determine if it is reasonable to conclude that the current percentage of all first-year college students who will say that their college experience exposed them to diverse opinions, cultures, and values is higher than 88%. Use a 2% significance level, and use both the p-value and the critical-value approaches.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.88

H_a : p > 0.88

n = 1800

= 91% = 0.91

P₀ = 0.88

1 - P₀ = 1 - 0.88 = 0.12

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.91 - 0.88 / [(0.88 * 0.12) / 1800]

= 3.92

P(z > 3.92) = 1 - P(z < 3.92) = 1 - 1 = 0

P-value = 0

= 0.02

P-value <

Reject the null hypothesis .

Z= Z_0.02 = 2.05

Critical value = 2.05

Test statistic > critical value

Reject the null hypothesis .

Claim is true