Question

A direct mail appeal for contributions from a university's alumni is considered effective if more than 15% of the alumni provide monetary contributions. To determine if a direct mail appeal is cost effective, the fundraising director sends the direct mail brochure to a simple random sample of 250 people on the alumni mailing list. He receives monetary contributions form 40 people. Which of the follow alternative hypothesis statements is correct ? Group of answer choices Ha: p > 0.15 Ha: phat > 0.15 Ha: phat > 0.16 Ha: p < 0.16

Answer 1

Answer:

We want to verify if the true proportion of the alumni provide monetary contributions is higher than 0.15 (Alternative hypothesis), the system of hypothesis are.:  

Null hypothesis:$p \leq 0.15$  

Alternative hypothesis:$p > 0.15$  

And the best answer for this case would be:

Ha: p > 0.15

Step-by-step explanation:

Information given

n=250 represent the random sample taken

X=40 represent the number of people on the alumni mailing list

$\hat p=\frac{40}{250}=0.16$ estimated proportion of people on the alumni mailing list  

$p_o=0.15$ is the value to verify

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to verify if the true proportion of the alumni provide monetary contributions is higher than 0.15 (Alternative hypothesis), the system of hypothesis are.:  

Null hypothesis:$p \leq 0.15$  

Alternative hypothesis:$p > 0.15$  

And the best answer for this case would be:

Ha: p > 0.15