The Department of Transportation would like to test the hypothesis that the aver

Question

The Department of Transportation would like to test the hypothesis that the average age of cars on the road is less than 12 years. A random sample of 45 cars had an average age of 10.6 years. It is believed that the population standard deviation for the age of cars is 4.1 years. The Department of Transportation would like to set a = 0.05. The conclusion for this hypothesis test would be that because the test statistic is ______. A. less than the critical value, we can conclude that the average age of cars on the road is less than 12 years B. more than the critical value, we cannot conclude that the average age of cars on the road is less than 12 years C. less than the critical value, we cannot conclude that the average age of cars on the road is less than 12 years D. more than the critical value, we can conclude that the average age of cars on the road is less than 12 years

Explanation / Answer

Solution:- (A) t value is less than the critical value, so we can conclude that the average age of cars on the road is less than 12 years.

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

Null hypothesis: > 12

Alternative hypothesis: < 12

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 0.05. 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 = 0.611

DF = n - 1

D.F = 45 - 1

D.F = 44

t = (x - ) / SE

t = - 2.29

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.

t critical = - 2.015

Interpret results:- Since t value (- 2.29) is less than the t critical (- 2.015), hence we have to reject the null hypothesis.

t value is less than the critical value, so we can conclude that the average age of cars on the road is less than 12 years.

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