F17_latestart M13A7-40492 Intro Statistics (T Th 3-5:15P) Test: Chapter 7 Exam S
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F17_latestart M13A7-40492 Intro Statistics (T Th 3-5:15P) Test: Chapter 7 Exam Submit Test This Question: 1 pt 20 of 26 (1 complete) This Test: 26 pts possible Next Question A car company says that the mean gas mileage for its luxury sedan is at least 23 miles per gallon (mpg). You believe the claim is incorrect and find that a random sample of 7 cars has a mean gas mileage of 21 mpg and a standard deviation of 2 mpg. At 0.025, test the company's claim. Assume the population is normally distributed. Click here to view the t-distribution table. Click here to view page 1 of the normal table, Click here to view page 2 of the normal table Which sampling distribution should be used and why? 0 A. Use a t-sampling distribution because the population is normal, and is unknown ° C. Use a normal sampling distribution because the population is normal, and is unknown O E. Use a t-sampling distribution because the population is normal, and is known. State the appropriate hypotheses to test. OB. D. F. Use a t-sampling distribution because n 30. B. Ho: #23 Ha: =23 D. Ho: =23 Ha: #23 Ha: >23 Ha:Explanation / Answer
Since the sample size is < 30, we use a t- sampling distribution. Option (B) is correct.
The Null hypothesis is: H0 >= 23 and the alternative hypothesis is Ha < 23. Option C is correct.
The test is a left-tailed t-test. The level of significance is 2.5%,i.e., 0.025
degrees of freedom = 7-1 = 6
t = (21-23) / (2/sqrt(7)) = -2.64575
The critical value of t0 corresponding to 0.025 level of significance and 6 degrees of freedom = -2.447 (From any standard t Table)
so t < t0, i.e., the test statistic lies in the rejection region. We should reject the null hypothesis.
There is enough evidence at the 2.5% level of significance to reject the claim that the mileage is at least 23 mpg.
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