Question

We randomly select 263 individuals from Rutherford county and ask them whether they approve or disapprove of the President. The sample proportion of people who approve is equal to .64. We want to test the President has an approval rating of something other than 60 percent. Let alpha be equal to .05. What are the hypotheses equal to? What is the test statistic and p value?

Answer 1

For the given test scenario, the null and alternative hypotheses are given as below:

Null hypothesis: H₀: President has an approval rating of 60 percent.

Alternative hypothesis: H_a: President has an approval rating of something other than 60 percent.

H₀: p = 0.60

H_a: p ≠ 0.60

This is a two tailed test.

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 = 263

p̂ = x/n = 0.64

p = 0.60

q = 1 - p = 0.40

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.64 - 0.60)/sqrt(0.60*0.40/263)

Z = 1.3241

Test statistic = 1.3241

P-value = 0.1855

(by using z-table or excel)