Question

Use the accomparying 200 Los Angeles commute times to lest the claim that the mean Los Angeles commute time is loss than 32 minutes. Assume that a sirple random sample has been seiecte Use a 0.10 sgnificance level. Compare the sample moan to the daimed mean of 32 minules. is the diflerence between those two valuos statistically significant? Cick the loan to view the Lot Angeles cornmute times. Identify the null and atematie hypotheses. (Type inlegen or decimals. Do not round.) Idently the lest statisbic. (Round to two decimal ploces as needed.) Idenbly the P.ralun (Round to three becimal places as needed) stabe the conclusion about the mul moothess, as weil as the finat condusion that adgresses the onginal olam. the nuil hypothesis. There sumcient endoence at the 0,10 significance invel to the clam that the mean tos Angoles constude tine is less than 32 . minutes The sample meas is minde(s) the ciaimed mean of 32 minutesi this diference: stafiabcaly signefeant by ine sandard of thes hast. (Fhound to one decinat place at necoed)

Answer 1

To test the claim that Los Angeles commute time is less than 32 minutes, a hypothesis test is performed with a null hypothesis that the mean time is not less and an alternative hypothesis that it is less. The test statistic is calculated and compared to a significance level, and the p-value helps decide whether to reject the null hypothesis based on the evidence provided by the data.

Step-by-step explanation:

Conducting a hypothesis test requires us to define the null hypothesis (H0) and the alternative hypothesis (Ha). For this case, where we want to test if the mean Los Angeles commute time is less than 32 minutes, our hypotheses would be:

H0: μ ≥ 32 (The mean commute time is not less than 32 minutes; this is the null hypothesis.)

Ha: μ < 32 (The mean commute time is less than 32 minutes; this is the alternative hypothesis.)

The test statistic is calculated using the sample mean, standard deviation, and size. It is generally given by the formula:

Z = (x - μ0) / (σ/ √n)

Where x is the sample mean, μ0 is the mean under null hypothesis, σ is the population standard deviation and n is the sample size. The p-value is then determined from the standard normal distribution table.

To conclude the hypothesis test, if the p-value < α (significance level), we reject the null hypothesis. Otherwise, we do not reject the null hypothesis. If the null hypothesis is rejected, it implies that the data provides sufficient evidence to support the claim that the mean commute time is less than 32 minutes.