The P-value = 0.1314.
Sample Test Statistic and P-Value
Assumptions:
We are comparing two independent proportions.
The sample sizes are large enough (n1 = 87 and n2 = 95).
The populations are normally distributed.
Step 1: Calculate the sample proportions:
Sample proportion of urban residents subscribing to Sporting News (p1): 11/87 = 0.126
Sample proportion of suburban residents subscribing to Sporting News (p2): 19/95 = 0.199
Step 2: Calculate the pooled sample proportion (P):
P = (n1 * p1 + n2 * p2) / (n1 + n2)
P = (87 * 0.126 + 95 * 0.199) / (87 + 95)
P = 0.167
Step 3: Calculate the standard error of the difference in proportions:
SE(p1 - p2) = sqrt(P * (1 - P) * (1 / n1 + 1 / n2))
SE(p1 - p2) = sqrt(0.167 * (1 - 0.167) * (1 / 87 + 1 / 95))
SE(p1 - p2) = 0.065
Step 4: Calculate the sample test statistic:
z = (p1 - p2) / SE(p1 - p2)
z = (0.199 - 0.126) / 0.065
z = 1.12
Step 5: Find the P-value:
The P-value is the probability of observing a test statistic as extreme as or more extreme than the calculated value, assuming the null hypothesis is true (i.e., there is no difference in the population proportions).
Since we are testing for a one-tailed difference (suburban proportion > urban proportion), we need to find the area to the right of the calculated z-value in the standard normal distribution table.
Looking up the z-value of 1.12 in the standard normal distribution table, we find the corresponding area to be 0.1314.
Therefore, the P-value = 0.1314.
Complete 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 87 urban residents showed that 11 subscribed, and a random sample of 95 suburban residents showed that 19 subscribed. Does this indicate that a higher proportion of suburban residents subscribe to Sporting News. Find (or estimate) the P-value. (Round your answer to four decimal places.)