A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether the proportion of the population in favor of Candidate A is significantly more than 75%. The test statistic is
A) .8.
B) .75.
C) 1.15.
D) -1.25.

Question

Quizplus · Accepted Answer

We can use the formula for the test statistic for a one-sided hypothesis test for a proportion:
Z = (p - P) / sqrt(P(1-P)/n)
where:
p = proportion in the sample who favor Candidate A = 80/100 = 0.8
P = hypothesized proportion in the population who favor Candidate A = 0.75
n = sample size = 100

Plugging in the numbers, we get:
Z = (0.8 - 0.75) / sqrt(0.75(1-0.75)/100) = 1.15

Since we are interested in whether the proportion in favor of Candidate A is significantly more than 75%, we are doing a one-sided test with the alternative hypothesis of p > 0.75. The p-value for this test is the probability of getting a Z-score of 1.15 or higher, assuming the null hypothesis is true. Consulting a standard normal distribution table or using a calculator, we find that the p-value is approximately 0.1251.

Since the p-value is greater than the usual significance level of 0.05, we fail to reject the null hypothesis that the proportion in the population who favor Candidate A is 75%. This means that we do not have sufficient evidence to conclude that the proportion is significantly more than 75%.

A Random Sample of 100 People Was Taken