Question

10) A company is willing to renew its publishing contract with a popular statistics book author only if she can show that her book can sell to more than 20% of the entire statistics market. The publishing company contacts 2000 statistics professors at random and 448 professors were interested in the book. Should the company renew the contract? Support your recommendation with an appropriate test. Explain carefully what your P-value means in this context.

Answer 1

H0:Null Hypothesis: P $\leq$ 0.20 (Her book can sell to not more than 20% of the entire statistic market. She should not renew the contract)

HA: Alternative Hypothesis: P > 0.20 (Her book can sell to more than 20% of the entire statistic market. She should renew the contract) (claim)

n = 2000

$\hat{p}$ = 448/2000 = 0.224

Take $\alpha$ = 0.05

Test Statistic is given by:

$Z=\frac{0.224-0.20}{\sqrt{0.20\times (1-0.20)/2000}}=2.683$

By Technology,

P - value = 0.0036

Since P - value = 0.0036 is less than $\alpha$ = 0.05, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that her book can sell to more than 20% of the entire statistic market. She should renew the contract.

Gven the Null Hypothesis: "Her book can sell to not more than 20% of the entire statistic market. She should not renew the contract" is true, P - value = 0.0036 is the probability of getting a result as or more extreme than the sample result: 448 out of 2000 books by random chance alone.