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?

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

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.

the sample mean is minutes(s) less than the claimed mean of 33 minutes, this difference is statistically significant by the standard of this test.
(round to one decimal place as needed.)

Explanation:

Step1: Hypotheses

The null hypothesis \(H_0:\mu = 33\) (claiming no difference from the mean of 33 minutes). The alternative hypothesis \(H_1:\mu<33\) (claiming the mean is less than 33 minutes).

Step2: Test Statistic

The test statistic is calculated (value given as - 1.40). It measures how many standard errors the sample mean is from the hypothesized mean.

Step3: P - value

The P - value (0.081) is the probability of getting a test statistic as extreme or more extreme than the observed one, assuming \(H_0\) is true.

Step4: Conclusion

Since \(P - value=0.081<\alpha = 0.10\), 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.