Question

In a study of high school dropouts the following information was found:

• Dallas, Texas: n₁ = 225 people ages sixteen to nineteen and 33 were found to be HS dropouts.
• Lawrence, Kansas: n₂ = 127 people ages sixteen to nineteen and 11 were found to be HS dropouts.

Do these data indicate that the population proportion of high school dropouts in Dallas is different (either way) from that of Lawrence? Use a 5% level of significance.

Show all work and calculations.

Answer 1

p1cap = X1/N1 = 33/225 = 0.1467
p1cap = X2/N2 = 11/127 = 0.0866
pcap = (X1 + X2)/(N1 + N2) = (33+11)/(225+127) = 0.125

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 = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.1467-0.0866)/sqrt(0.125*(1-0.125)*(1/225 + 1/127))
z = 1.64

P-value Approach
P-value = 0.101
As P-value >= 0.05, fail to reject null hypothesis.