Test: Chapter 7 Exam This Question: 1 pt Submit Test 24 of 26 (0 complete) This

Question

Test: Chapter 7 Exam This Question: 1 pt Submit Test 24 of 26 (0 complete) This Test: 26 pts possible A car company says that the mean gas mileage for its luxury sedan is at least 20 miles per gallon (mpgl) sample of 8 cars has a mean gas mileage of 18 mpg and a standard deviation o 2m You believe the claim is incorrect and find that a random At . 25, test the company's lain. Assume the population is no Click here to view page 1 of the normal table. Click here to view Which sampling distribution should be used and why? ay A Use a normal sampling distribution because the ulation is normal, and B. Use a t-sampling distribution because n

Explanation / Answer

Solution:-

C) Use t-sampling distribution becuase the population is normal and   is unknown.

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

Null hypothesis: > 20
Alternative hypothesis: < 20

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 0.025. 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 = 0.707
DF = n - 1

D.F = 7
t = (x - ) / SE

t = - 2.83

tcritical = - 2.36

Rejection region t < - 2.36

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.

The observed sample mean produced a t statistic test statistic of - 2.83. We use the t Distribution Calculator to find P(t < - 2.83) .

Thus the P-value in this analysis is 0.0127.

Interpret results. Since the P-value (0.0127) is less than the significance level (0.025), we have to reject the null hypothesis.

Reject H0, there is sufficient evidence to reject the car's company claim of > 20.

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