Commute times in the U. S. are heavily skewed to the right. We select a random sample of 200 people from the 2000 U. S. Census who reported a non-zero commute time. In this sample the mean commute time is 27.5 minutes with a standard deviation of 18.9 minutes. Can we conclude from this data that the mean commute time in the U. S. is less than half an hour? Conduct a hypothesis test at the 5% level of significance. What is the p -value for this hypothesis test?

Step-by-step explanation:

Given that:

The population mean = 30

The sample size n = 200

The sample-mean = 27.5

The sample standard deviation s = 18.9

The level of significance ∝ = 0.05

The null hypothesis and the alternative hypothesis can be written as:

Since the alternative hypothesis indicates < sign, then this test is left-tailed

The  t-test statistics is:

t = -1.871

The p-value = P(t< -1.871)

From the standard normal t tables

The p-value = 0.0314

Thus, since the p-value is less than the level of significance ∝ = 0.05, then we reject the null hypothesis.

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step-by-step explanation:

here is a big fat