Question

In May 2008, CNN reported that sports utility vehicles (SUVs) are plunging toward the “endangered” list. Due to soaring oil prices and environmental concerns, consumers are replacing gas-guzzling vehicles with fuel-efficient smaller cars. As a result, there has been a big drop in the demand for new as well as used SUVs. A sales manager of a used car dealership believes that it takes 30 days longer to sell an SUV as compared to a small car. In the last two months, he sold 18 SUVs that took an average of 95 days to sell with a standard deviation of 32 days. He also sold 38 small cars with an average of 48 days to sell and a standard deviation of 24 days. (Assumption: the populations are normally distributed and that the variability of selling time for the SUVs and the small cars is the same.) Use a 5% level of significance.

Select one:

a. Ho: µSUV - µCAR = 30 Ha: µSUV - µCAR ≠ 30 We would reject Ho is the calculated test statistic is above +1.96 or below -1.96. The test statistic is 2.003 with a p-value of 0.0456. As a result we would reject Ho and say that the difference is not 30 days and most likely more.

b. Ho: µSUV - µCAR = 30 Ha: µSUV - µCAR ≠ 30 We would reject Ho is the calculated test statistic is above +1.96 or below -1.96. The test statistic is 2.003 with a p-value of 0.0228. As a result we would reject Ho and say that the difference is not 30 days and most likely more.

c. Ho: µSUV - µCAR = 30 Ha: µSUV - µCAR ≠ 30 We would reject Ho is the calculated test statistic is above +2.005 or below -2.005. The test statistic is 2.027. As a result we would reject Ho and say that the difference is not 30 days and most likely more.

d. Ho: µSUV - µCAR = 0 Ha: µSUV - µCAR ≠ 0 We would reject Ho is the calculated test statistic is above +2.005 or below -2.005. The test statistic is 5.6036. As a result we would reject Ho and say that the difference is not 30 days and most likely more.

Answer 1

Null and Alternative hypothesis:

Ho : µ1 - µ2 = 30

H1 : µ1 - µ2 ≠ 30

Test statistic:

z = (x̅1 - x̅2 - (µ1 - µ2))/√(s1²/n1 + s2²/n2 ) = (95 - 48 - 30)/√(32²/18 + 24²/38) = 2.003

p-value :

p-value = 2*(1-NORM.S.DIST(ABS(2.003, 1) = 0.0456

Critical value :

Two tailed critical value, z crit = ABS(NORM.S.INV(0.05/2)) = 1.960

Reject Ho if z < -1.96 or if z > 1.96

Answer: a)

a. Ho: µSUV - µCAR = 30 Ha: µSUV - µCAR ≠ 30 We would reject Ho is the calculated test statistic is above +1.96 or below -1.96. The test statistic is 2.003 with a p-value of 0.0456. As a result we would reject Ho and say that the difference is not 30 days and most likely more.