Question

A study is made of residents in Phoenix and its suburbs concerning the proportion of residents who subscribe to Sporting News. A random sample of 88 urban residents showed that 9 subscribed, and a random sample of 97 suburban residents showed that 20 subscribed. Does this indicate that a higher proportion of suburban residents subscribe to Sporting News? Use a 1% level of significance. Show all 5 steps please

Answer 1

p1cap = X1/N1 = 9/88 = 0.1023
p1cap = X2/N2 = 20/97 = 0.2062
pcap = (X1 + X2)/(N1 + N2) = (9+20)/(88+97) = 0.1568

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 = 0.01
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 = (0.1023-0.2062)/sqrt(0.1568*(1-0.1568)*(1/88 + 1/97))
z = -1.94

P-value Approach
P-value = 0.0262
As P-value >= 0.01, fail to reject null hypothesis.

There is not sufficient evidence to conclude that a higher proportion of suburban residents subscribe to Sporting News