3. Lube-Tech is a major chain whose primary business is performing lube and oil
ID: 3046541 • Letter: 3
Question
3. Lube-Tech is a major chain whose primary business is performing lube and oil changes for passenger vehicles. The national operations manager has stated in an industry newsletter that the mean number of miles between oil changes for all passenger cars is 5,200 miles. To test this, an industry group has selected a random sample of 90 vehicles that have come into a lube shop and determined the number of miles since the last oil change and lube. The sample mean was 5,278 and the standard deviation was known to be 780 miles. Based on this information, a) Do you agree with operations manager? Use 0.05. b) What is the p-value for part a.Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: = 5200
Alternative hypothesis: 5200
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 0.05. 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 = 82.22
DF = n - 1 = 90 - 1
D.F = 89
t = (x - ) / SE
t = 0.95
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 89 degrees of freedom is less than -0.95 or greater than 0.95
Thus, the P-value = 0.35.
Interpret results. Since the P-value (0.35) is greater than the significance level (0.05), we cannot reject the null hypothesis.
Hence we have sufficient evidence in the favor of operations managers claim.
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