Question

A potato chip company would like to test how happy customers are with their new recipe. To test this, they take two samples of random people. Sample 1 will taste the old recipe and Sample 2 will taste the new recipe. Sample 1 consisted of 45 people and 78% of them stated they liked the flavor. Sample 2 consisted of 50 people and 82% of them stated they liked the flavor. Test the claim that the proportion of customers that enjoy the new recipe is higher than the old recipe. (Use a 0.05 level of significance.)

Answer 1

p1cap = 0.78
p1cap = 0.82
pcap = (X1 + X2)/(N1 + N2) = (0.78 * 45 + 0.82*50)/(45+50) = 0.8011

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

Rejection Region
This is left tailed test, for α = 0.05
Critical value of z is -1.64.
Hence reject H0 if z < -1.64

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.78-0.82)/sqrt(0.8011*(1-0.8011)*(1/45 + 1/50))
z = -0.49

P-value Approach
P-value = 0.3121
As P-value >= 0.05, fail to reject null hypothesis.