A recent study from the University of California, Berkeley, suggests that, compared to white Americans, black Americans are more likely to cross the race barrier in online dating. In a sample of 120 white men, 24 initiated contact with someone outside their race, whereas in a similar sample of 90 black men, 36 initiated contact with someone outside their race.
a. Specify the hypotheses to justify the suggestion.
b. Find the critical value(s) of the appropriate test at the 1% significance level.
c. Calculate the value of the test statistic.
d. Make a conclusion at the 1% significance level.
p1cap = X1/N1 = 24/120 = 0.2
p2 cap = X2/N2 = 687/9036 = 0.076
pcap = (X1 + X2)/(N1 + N2) = (24+687)/(120+9036) = 0.0777
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 > p2
Rejection Region
This is right tailed test, for α = 0.01
Critical value of z is 2.33.
Hence reject H0 if z > 2.33
Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.2-0.076)/sqrt(0.0777*(1-0.0777)*(1/120 + 1/9036))
z = 5.04
As the value of test statistic, z is within critical value range, reject the null hypothesis
A recent study from the University of California, Berkeley, suggests that, compared to white Americans, black Americans are more likely to cross the race barrier in online dating. In a sample of 120 white men, 24 initiated contact with someone outside the
A recent study from the University of California, Berkeley, suggests that compared to black Americans, white Americans are less likely to cross the race barrier in online dating. In a sample of 120 white men, 24 initiated contact with someone outside of their race, whereas in a similar sample of 90 black men, 36 initiated contact with someone outside of their race.a. Specify the competing hypotheses to determine if the proportion of white Americans initiating a contact outside their race...