Question

A company has the view of ads on client's newsfeeds. When showing clients one of two ads, the co. asks the clients if they remember seeing the ad. The co. wants to know if a different proportion of clients remember seeing each ad.

	Ad 1	Ad 2
# of clients who report seeing the ad	54	41
# of clients asked if they saw the ad	153	221

Is there enough data to determine that a different proportion of clients remember seeing each ad? α= 0.01.

Answer 1

p1cap = X1/N1 = 54/153 = 0.3529
p2cap = X2/N2 = 41/221 = 0.1855
pcap = (X1 + X2)/(N1 + N2) = (54+41)/(153+221) = 0.254

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 = 0.01
Critical value of z are -2.58 and 2.58.
Hence reject H0 if z < -2.58 or z > 2.58

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.3529-0.1855)/sqrt(0.254*(1-0.254)*(1/153 + 1/221))
z = 3.66

P-value Approach
P-value = 0.0003
As P-value < 0.01, reject the null hypothesis.