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 these 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.
(round to three decimal places as needed.)

Explanation:

Step1: Determine the distribution

Since we are dealing with a hypothesis test for the population mean and the sample size \(n = 200\) (assuming the sample size from "200 Los Angeles commute times"), and if the population standard deviation \(\sigma\) is unknown (but for large \(n\), we can use the \(z\) - test approximation or \(t\) - test. Here, if we assume the test statistic \(t=-1.40\) (given), and for a one - tailed \(t\) - test with \(n - 1=199\) degrees of freedom.

Step2: Calculate the P - value

For a one - tailed \(t\) - test with \(t=-1.40\) and \(df = 199\). Using a \(t\) - distribution table or a calculator (e.g., in R: pt(-1.40,199)), the P - value is the probability that \(T

$$P - value=\text{pt}(-1.40,199)\approx0.081$$

Answer:

\(0.081\)