Question

URGENT

People use several methods to organize their lives by keeping track of appointments, meetings, and deadlines. Some of these include using a desk calendar, using informal notes of scrap paper, keeping them “in your head,” using a day planner, and keeping a formal “to do” list. Suppose we want to test the hypothesis that a greater proportion of marketing managers keep track of such obligations in their head than do accountants. To test this, we sample 400 marketing managers and 450 accountants. Of those sampled, 213 marketing managers keep track in their head while 211 of the accountants do so. Using a 1% level of significance, what do we find?

Find the z-score to make a conclusion. (Round your answer to 2 decimal places. )

Observed z = ?

The decision is to ( choose between a or b)

a) reject the null hypothesis fail to

b) reject the null hypothesis .

Answer 1

p1cap = X1/N1 = 213/400 = 0.5325
p1cap = X2/N2 = 211/450 = 0.4689
pcap = (X1 + X2)/(N1 + N2) = (213+211)/(400+450) = 0.4988

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 > p2

Rejection Region
This is right tailed test, for α = 0.01
Critical value of z is 2.33.
Hence reject H0 if z > 2.33

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.5325-0.4689)/sqrt(0.4988*(1-0.4988)*(1/400 + 1/450))
z = 1.85

Failed to reject H0