In a study of high school dropouts the following information was found:
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.
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
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
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 = 0.101
As P-value >= 0.05, fail to reject null hypothesis.
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