Question

use the accompanying 200 los angeles commute times to test the claim that the mean los angeles commute time is less than 33 minutes. assume that a simple random sample has been selected. use a 0.10 significance level. compare the sample mean to the claimed mean of 33 minutes. is the difference between those two values statistically significant? click the icon to view the los angeles commute times. identify the null and alternative hypotheses. ( h_0: mu = 33 ) ( h_1: mu < 33 ) (type integers or decimals. do not round.) identify the test statistic. ( -1.40 ) (round to two decimal places as needed.) identify the p - value. 0.081 (round to three decimal places as needed.) state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. the null hypothesis. there sufficient evidence at the 0.10 significance level to the claim that the mean los angeles commute time is less than 33 minutes.

Explanation:

Step1: Compare P - value and significance level

We are given a significance level \(\alpha = 0.10\) and a P - value \(P=0.081\) (assuming the P - value is \(0.081\) instead of \(0.001\) as \(z=- 1.40\), for \(z\) - test, \(P(z < - 1.40)=0.0808\approx0.081\)).
Since \(P = 0.081<\alpha=0.10\)

Step2: Make conclusion about null hypothesis

When \(P<\alpha\), we reject the null hypothesis \(H_0:\mu = 33\)

Step3: Make conclusion about the claim

Since we reject \(H_0\), there is sufficient evidence at the \(0.10\) significance level to support the claim that the mean Los Angeles commute time is less than \(33\) minutes

Answer:

Reject the null hypothesis. There is sufficient evidence at the \(0.10\) significance level to support the claim that the mean Los Angeles commute time is less than \(33\) minutes.