A company decided to test the hypothesis that the average time a company's employees are spending to check their private e-mails at work is more than 6 minutes. A random sample of 40 employees were selected and they averaged 6.6 minutes. It is believed that the population standard deviation is 1.7 minutes. The α is set to 0.05. The p-value for this hypothesis test would be ________.
A) 0.0644
B) 0.0128
C) 0.0268
D) 0.0395

Question

Quizplus · Accepted Answer

The hypothesis test is a one-tailed test since we are testing if the average time is more than 6 minutes. Using the given data (sample mean = 6.6, population standard deviation = 1.7, sample size = 40, and significance level α = 0.05), we calculate the test statistic and then find the p-value. The calculation of the test statistic would involve the formula for a z-test since the population standard deviation is known. The p-value associated with this test statistic, given the direction of the hypothesis (greater than), is 0.0128. This indicates the probability of observing a sample mean of 6.6 minutes or more, given that the true population mean is 6 minutes, under the normal distribution assumption.

A Company Decided to Test the Hypothesis That the Average