Question

A computer manufacturing company claims that only 7.2% of their computers are returned. Kelly thinks that the company is misrepresenting the true proportion of computers that are returned, and that the true proportion is higher than they claim. She wants to test this using α = 0.05. Kelly takes a sample of 260 computers and observes that 23 are returned. Assume a normal sampling distribution.

What is the test statistic? (Round your answer to 2 decimal places, if needed.)

Answer 1

To test Kelly's claim, we need to perform a hypothesis test. The test statistic (z) is approximately -3.29.

Step-by-step explanation:

To test Kelly's claim, we need to perform a hypothesis test. Let's define the null and alternative hypotheses:

H0: p = 0.072 (The true proportion of computers returned is 7.2%)

H1: p > 0.072 (The true proportion of computers returned is greater than 7.2%)

Next, we need to calculate the test statistic using the formula:

z = (p - p') / sqrt(p'(1-p')/n)

where:

p' = x/n = 23/260 = 0.0885 (sample proportion)

n = 260 (sample size)

Substituting the values into the formula:

z = (0.072 - 0.0885) / sqrt(0.0885(1 - 0.0885)/260)

z = -0.0165 / sqrt(0.0885(0.9115)/260)

z ≈ -0.0165 / sqrt(0.0806/260)

z ≈ -0.0165 / 0.00501

z ≈ -3.29

Therefore, the test statistic (z) is approximately -3.29.