Question

Cameron is a writer for an online consumer advocacy publication and is investigating people who are looking to unload their timeshares. He recently heard a claim that 40% of people who own a timeshare want to unload it and thinks the percentage is too low. Cameron tests whether more than 40% of timeshare owners want to unload their timeshare. He randomly selects and surveys 91 timeshare owners and finds that 44 of them want to unload their timeshare. What are the null and alternative hypotheses for this hypothesis test?

A. {H0:p=0.4/ Ha:p>0.4

B. {H0:p=0.4/ Ha:p<0.4

C. {H0:p=0.4/ Ha:p≠0.4

D. {H0:p≠0.4/ Ha:p=0.4

Answer 1

Solution:

From given ,

Hypothetical value of proportion is p₀ = 40% = 0.4

Claim: More than 40% of timeshare owners want to unload their timeshare.

i.e. more than 0.4

Valid signs in null hypothesis H₀ are = , and

Valid signs in alternative hypothesis H_A   are , < and >

So , required null and alternative hypothesis are

A. {H0: p = 0.4/ Ha:p > 0.4