I1. Based on the sample results at a- 5% the FDA\'s conclusion to this hypothesi
ID: 2909567 • Letter: I
Question
I1. Based on the sample results at a- 5% the FDA's conclusion to this hypothesis test is: 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. city driving conditions. A Federal Agency believes this claim is too high and decides to randomly of the manufacturer's autos. The Agency determines the average mpg for the sample to be 48 sample standard deviation of 4 mpg under city driving conditions. An auto manufacturer claims that its new 4 cylinder auto with manual shift averages 50 mp 12. The alternative hypothesis for the Federal Agency's 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)I c) binomial d) chi-square e) none of these 14. The standard error for this test is: a) 4 b)2.5 c)0.8 d) 0.009 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 reject the null hypothesis and accept the alternative hypothesis e) , Does the sample data support the Federal Agency's claim at-5%? No b) Yes c) Undecided 9Explanation / Answer
define
X: mpg of new 4 cylinder auto
X~ Normal(mu,sigma2)
according to the manufacturer's claim mu=50 mpg
according to the Federal Agency's belief mu < 50 mpg
we are to test the null hypothesis H0 : mu=mu0= 50
aganist the alternative hypothesis H1 : mu < mu0 (50)
the test statistic is given by
T=sqrt(n)*(x bar-mu0)/ s, which under H0 follows tn-1 distribution
where n= sample size= 25
x bar= sample mean=48 mpg
s= sample standard deviation = 4 mpg
at alpha % (here 5%) level of significance we reject H0 against H1 if the observed value of the test statistic T < - talpha;n-1
i.e. if T< - t 0.05;24
observed value of T = sqrt(25)*(48-50) / 4= - 2.5
from the Statistical Table t0.05;24 = 1.711
since T (-2.5) < - t0.05;24 (-1.711)
we reject H0 aganist H1 at 5 % level of significance and conclude that at 5 % level of significance the data supports the Federal Agency's claim (i.e. average mpg is less than 50 mpg)
the answers are :
13. (a)
14. (a)
15. (a)
16. (d)
17. (d) p value= 0.00982 ( using online p value calculator)
18. (e)
19. (b) Yes
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