Question

6. We want to know whether the difference in the population proportions between group 1 and group 2 differs from 0. Specifically, we want to test H0 : p1 − p2 = 0 versus Ha : p1 − p2 6= 0. We know that 332 of the 529 observations in group 1 have the characterisitic. And, we know that 346 of the 595 observations in group 2 have the characterisitic. 2

(a) What is the sample proportion for group 1? (round to 5 digits after the decimal place)

(b) What is the sample proportion for group 2? (round to 5 digits after the decimal place)

(c) What is the pooled estimator for p? (round to 5 digits after the decimal place)

(d) What is the standard error for the difference in the sample proportions? (Use ˜σp1−p2 and round to 5 digits after the decimal place.)

(e) What is the value of the test statistic? (Round to 2 digits after the decimal place.)

(f) What is the p-value of the test? (Round to 3 digits after the decimal place.)

(g) Do we reject or not reject the null hypothesis at the .05 level of significance? Reject Not reject

Answer 1

a)

p1cap = X1/N1 = 332/529 = 0.6276

b)

p1cap = X2/N2 = 346/595 = 0.58151

c)

pcap = (X1 + X2)/(N1 + N2) = (332+346)/(529+595) = 0.6032

d)
Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.6276 * (1-0.6276)/529 + 0.58151*(1-0.58151)/595)
SE = 0.02917

e)

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.6276-0.58151)/sqrt(0.6032*(1-0.6032)*(1/529 + 1/595))
z = 1.58

f)

P-value Approach
P-value = 0.114

g)

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