Question

lesson 40 homework study of different in tow population proportions

Sam's Sweets have two stores in California. They collect comment cards and classify them whether they are a complaint or compliment. The owner wants to know if the proportion of complaints differ.

Store	# of comment cards submitted	# that are complaints
A	200	60
B	150	40

Test whether the proportion of complaints between the two stores differs. Significance level is 10%.

Answer 1

p1cap = X1/N1 = 60/200 = 0.3
p1cap = X2/N2 = 40/150 = 0.2667
pcap = (X1 + X2)/(N1 + N2) = (60+40)/(200+150) = 0.2857

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

Rejection Region
This is two tailed test, for α = 0.1
Critical value of z are -1.64 and 1.64.
Hence reject H0 if z < -1.64 or z > 1.64

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.3-0.2667)/sqrt(0.2857*(1-0.2857)*(1/200 + 1/150))
z = 0.68

P-value Approach
P-value = 0.4965
As P-value >= 0.1, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the proportion is different.