429 Section 8-2 z Test for a Mean 23. Transmission Service A car dealer recommen

Question

429 Section 8-2 z Test for a Mean 23. Transmission Service A car dealer recommends that transmissions be serviced at 30,000 miles. To see whether her customers are adhering to this recommen- dation, the dealer selects a random sample of 40 cus- tomers and finds that the average mileage of the auto- mobiles serviced is 30,456. The standard deviation of the population is 1684 miles. By finding the P-value, determine whether the owners are having their trans- missions serviced at 30,000 miles. Use 0.10. Do you think the value of 0.10 is an appropriate significance level? 24. Speeding Tickets A motorist claims that the South Boro Police issue an average of 60 speeding tickets

Explanation / Answer

Solution:-

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

Null hypothesis: = 30,000

Alternative hypothesis: 30,000

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

Formulate an analysis plan. For this analysis, the significance level is 0.10. 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 = 266.3

DF = n - 1 = 40 - 1

D.F = 39

t = (x - ) / SE

t = 1.713

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.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 39 degrees of freedom is less than -1.713 or greater than 1.713.

Thus, the P-value = 0.0946

Interpret results. Since the P-value (0.0946) is less than the significance level (0.10), we have to reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that the owners are having their transmission serviced at 30,000 miles.

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