Question

Consider the following hypotheses.

Upper H0​: p=0.41

Upper H1​: p≠0.41

Given that p overbar=0.31​, n=100​, and alphaαequals=0.10​, answer the following questions.

a. Determine the critical​ value(s) of the test statistic.

b. calculate the test statistic

c. choose whether to reject or do not reject.

Answer 1

a. Determine the critical​ value(s) of the test statistic.

For the given test, we have

α = 0.10

Test is two tailed.

So, required critical values by using z-table are given as below:

Critical values = - 1.6449 and 1.6449

b. calculate the test statistic

Test statistic formula for this test is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

n = sample size = 100

p̂ = x/n = 0.31

p = 0.41

q = 1 - p = 0.59

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.31 – 0.41)/sqrt(0.41*0.59/100)

Z = -2.0332

Test statistic = -2.0332

c. choose whether to reject or do not reject.

We have

Critical values = - 1.6449 and 1.6449

Test statistic = -2.0332

Test statistic value is not lies between critical values, so we reject the null hypothesis

Answer: Reject the null hypothesis