Question

USF is interested in learning about the average time students spend taking selfies. The university sampled 38 students and asked each to provide the amount of time they spent taking selfies. This variable, selfie time, was then used to conduct a test of hypothesis. The goal was to determine if the average selfie time for all USF's students differed from 20 minutes. Suppose the large-sample test statistic was calculated to be z = 2.14. Find the p-value for this test of hypothesis.

Answer 1

the p-value for this test of hypothesis is 0.0324

Explanation:

Given the data in the question;

sample size n = 38

Null hypothesis H₀ : μ = 20

Alternative hypothesis Hₐ : μ ≠ 20

z = 2.14

Test Statistic;

since its a two tailed test, p-value will be;

⇒ 2 × P( Z > |z| )

= 2 × ( 1 - P( Z < |z| ) )

we substitute in the value of z

= 2 × ( 1 - P( Z < 2.14 ) )

from z score table, P( Z < 2.14 ) = 0.9838

= 2 × ( 1 - 0.9838 )

= 2 × ( 0.0162 )

P-value = 0.0324

Therefore, the p-value for this test of hypothesis is 0.0324