Question

a) the sample proportion of women who suffer side effects is 10 b) the population proportion of women who suffer side effects is 10%. c) the sample proportion of women who suffer side effects is not equal to 10%. d) the population proportion of women who suffer side effects is greater than 10% e) the sample proportion of women who suffer side effects is less than 10%. 12-19. An auto manufacturer claims that its new 4 cylinder auto with manual shift averages 50 mpg under city driving conditions. A Federal Agency believes this claim is too high and decides to randomly test 25 of the manufacturers autos. The Agency determines the average mpg for the sample to be 48 with a sample standard deviation of 4 mpg under city driving conditions. 12. The alternative hypothesis for the Federal Agencys hypothesis test is the mean of the: a) sample mean mpg of 25 autos is less than 50 mpg b) population mean mpg of the new 4 cylinder autos is less than 50 mpg c) population mean mpg of the new 4 cylinder autos is not equal to 50 mpg d) sample mean mpg is greater than 50 mpg 13. The hypothesis testing model is a: a) normal b) t e) none of these 14. The standard error for this test is: b)2.5 c)0.8 a) 4 d) 0.009 e) -2.5 15. The decision rule at ?-5% is: a) Reject Ho if the test statistic is less than -1.71 b) Reject Ho if the test statistic is greater than 1.65. c) Reject Ho if the test statistic is less than -1.96 or greater than 1.96. d) Reject Ho if the test statistic is less than -1.65. 16. The test statistic is: a)-1.75 b)-2.00 c)-2.48 d) -2.50 e) none of these 17. The p-value is: a) 0.03523 b) 0.04527 c) 0.04821 d 0.00982 18. At 5%, the conclusion of this hypothesis test is: a) accept both the null and alternative hypotheses b) reject the alternative hypothesis c) fail to reject the alternative hypothesis d) fail to reject the null hypothesis e) reject the null hypothesis and accept the alternative hypothesis 19. Does the sample data support the Federal Agencys claim at a-5%? a) No b) Yes c) Undecided
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Answer #1

12)option b

ALTERNATIVE HYPOTHESIS IS THAT POPULATION MEAN MPG OF NEW 4 CYLINDER AUTOS IS LESS THAN 50

13)option b

14)option c (4/sqrt25= 0.08)

15)option a

16) option d

17)option d

18)option e

19)option b

The provided sample mean is X 48 and the sample standard deviation is s 4, and the sample size is25 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: 50 Ha: ? < 50 This corresponds to a left-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the critical value for a left- tailed test is te-1.711. The rejection region for this left-tailed test is R-tit<-1.711 (3) Test Statistics The t-statistic is computed as follows: X 48-50 4 2 =-2.5 (4) Decision about the null hypothesis Since it is observed that t-2.5te1.711, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p = 0.0098, and since p = 0.0098 < 0.05, it is concluded that the null hypothesis is rejected. (5) Conclusion that the population mean ? is less than 50, at the 0.05 significance level

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