A marketing firm asked a random set of married and single men how much they were
ID: 3391579 • Letter: A
Question
A marketing firm asked a random set of married and single men how much they were willing to spend on a vacation. Is there sufficient evidence at = 0.05 to conclude that is there a difference in the two amounts? Married men Single men Sample size 50 40 Sample mean $640 $665 Population variance 5700 9100 A) No, because the test value -0.07 is not in the critical region -1.96 < z < 1.96. B) No, because the test value -1.35 is inside the noncritical region -1.96 < z < 1.96. D) No, because the test value -1.60 is not in critical region -1.96 < z < 1.96. D) No, because the test value -1.60 is in the critical region -1.96 < z < 1.96.
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u1 - u2 = 0
Ha: u1 - u2 =/ 0
At level of significance = 0.05
As we can see, this is a two tailed test.
Calculating the means of each group,
X1 = 640
X2 = 665
Calculating the standard deviations of each group,
s1 = 75.49834435
s2 = 95.39392014
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 50
n2 = sample size of group 2 = 40
Also, sD = 18.47971861
Thus, the z statistic will be
Z = [X1 - X2 - uD]/sD = -1.352834452
where uD = hypothesized difference = 0
Now, the critical value for z is
zcrit = +/- 1.96
Thus,
OPTION B) No, because the test value -1.35 is inside the noncritical region -1.96 < z < 1.96. [ANSWER, B]
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