A computer manufacturing company claims…

Question

A computer manufacturing company claims that only 7.3% 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 a = 0.025. Kelly takes a sample of 245 computers and observes that 23 are returned. Assume a normal sampling distribution.

(a) What are the null and alternative hypotheses?

H₀: (a) (b0) (c0)

Н_A: (a) (b1) (c0)

((((a) Options: p / u(population mean) / p1-p2 / u1-u2 )

((b0) Options: = / < / > / ≠ )

((b1) Options: = / < / > / ≠ / (less than or equal) / (greater than or equal)

((c0) Options: 0.073 or 0.0939)))

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

(c) Using the statistical table, what is the p-value? (Round your answer to 4 decimal places, if needed.)

(d) Based on the p-value, Kelly should (fail to reject/reject) the null hypothesis. (Choose one)

(e) This data (does not provide/provides) sufficient evidence to conclude that the true proportion of computers is higher than claimed. (Choose one)

Answer 1

Ho: p = 0.073

Ha: p > 0.073

sample proportion phat = 23/245 = 0.094

z = (0.094 - 0.073)/sqrt(0.073 * 0.927/245) = 1.26

p-value = P(z > 1.26) = :P(z < -1.26) = 0.1038

since p-value is > alpha, then we fail to reject the null hypothesis

This data does not provide sufficient evidence to conclude that the true proportion of computers is higher than claimed.