Question

18) Last year the proportion of employees in a city commuting to work was 8%. A commuter van company claims that the proportion of people commuting to work is higher than 8% (0.08) now. 1000 employees are surveyed and 105 of them commute to work. At a significance level of 0.05 can we support the commuter van company's claim? Perform an appropriate hypothesis test. B) FTR H, NEETS C) Reject H, IEETR E) None of the Above B) FTR H, NEETR D) Reject H, IEETS 19) A paint manufacturer wishes to compare the drying times of two different types of paint. Independent random samples of 11 cans of type A and type B were selected and applied to similar surfaces. The drying times were recorded. The summary statistics are as follows: Type A x, =77.0 Type B X = 64.1 Sz = 5.1 s, = 4.5 n, = 11 n = 9 o, = 4.7 02 = 4.9 At a significance level of 0.01 does the data provide sufficient evidence to conclude that the mean drying time for Type a differs from the mean drying time for type B? A) Reject H, IEETS the claim B) Reject H, IEETR the claim C) FTR H. NEETR the claim D) FTR H. NEETS the claim E) None of the Above

Answer 1

18.

HO: p=0.08 H1 :p>0.08 Population proportion = po = 0.08 Sample number of events = x =105 Sample size = n =1000 Sample proportion = p = 105/1000 = 0.105 The test statistic is, P- PO Po (1-P) (0.105-0.08)/sqrt((0.08*(1-0.08))/1000] = 2.91 n P(Z < 2.91 ) = 0.9982 [using Excel function NORM.S.DIST(2.91) or Normal table] P-value = P(Z > 2.91 ) = 1-P(Z<2.91) = 1-0.9982 = 0.0018 Decision Rule : Reject H0 if P-value <a. Here a = 0.05 Conclusion : By decision rule, we reject HO

Ans :

D) Reject H, IEETS

19.

Sample 1 Sample 2 Sample Size Sample mean Sample S.D n1 = 11 X4 = 77 01 = 4.7 X2=64.1 02 = 4.9 n2 = 9 The test statistic is, X1 - X2 = (77-64.1)/sqrt[(4.72/11)+(4.92/9)] = 5.97 oi 02 n n2 Z= +

2-T P(Z<5.97 ) = 1 [using Excel function NORM.S.DIST(5.97) or Normal table] P-value = 2*P(Z>5.97) = 2 *[1-P(Z<5.97)]=2*(1-1) = 0 Decision Rule : Reject HO if P-value <a. Here a = 0.01 Conclusion: By decision rule, we reject HO

Ans:

A) Reject H IEETS the claim