A survey of 15 large U.S. cities finds that the average commute time one way is

Question

A survey of 15 large U.S. cities finds that the average commute time one way is 25.4 minutes. A chamber of commerce executive feels that the commute time in his city is less and wants to publicize this. He randomly selects 25 commuters and finds the average is 24.3 minutes with a standard deviation of 5.3 minutes. At alpha = 0.01, is he correct? Assume the population is normally distributed. Source: New York Times Almanac State the hypotheses and identify the claim with the correct hypothesis. H_0: mu = 25.4 H_1: mu

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: > 25.4

Alternative hypothesis: < 25.4

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 1.06

DF = n - 1 = 25 - 1

D.F = 24

t = (x - ) / SE =

t = - 1.038

tcritical = - 2.492

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Interpret results. Since thet value is more than the t critical hence, we cannot reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that average commute time is less than 25.4

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.