Question

Every year Green Community College contacts its alumni asking for donations. In the past, alumni have always been contacted by phone. Last year, 50% of the alumni contacted contributed with a donation. This year, under the administration of the newly elected president Leonard, the university has decided to try a new method and plans to contact its alumni by e-mail. The university has decided to randomly contact half of its 7000 alumni by phone and the other half by e-mail. In a random sample of 200 alumni who were contacted by phone, 55% agreed to contribute with a donation.

Part i) To test if the donation rate has increased since last year for alumni contacted by phone, what will be the null hypothesis?

A. The proportion of 3500 alumni who were contacted by phone and subsequently contributed a donation this year equals 0.5.
B. The proportion of 3500 alumni who were contacted by phone and subsequently contributed a donation this year equals 0.55.
C. The proportion of 200 alumni who were contacted by phone and subsequently contributed a donation this year equals 0.55.
D. The proportion of 200 alumni who were contacted by phone and subsequently contributed a donation this year is higher than 0.5.
E. The proportion of 200 alumni who were contacted by phone and subsequently contributed a donation this year equals 0.5.
F. The proportion of 3500 alumni who were contacted by phone and subsequently contributed a donation this year is higher than 0.5.

Part ii) For the test mentioned in the previous part, what is the alternative hypothesis?

A. The proportion of 3500 alumni who were contacted by phone and subsequently contributed a donation this year equals 0.55.
B. The proportion of 200 alumni who were contacted by phone and subsequently contributed a donation this year is higher than 0.5.
C. The proportion of 200 alumni who were contacted by phone and subsequently contributed a donation this year equals 0.55.
D. The proportion of 3500 alumni who were contacted by phone and subsequently contributed a donation this year is higher than 0.5.
E. The proportion of 3500 alumni who were contacted by phone and subsequently contributed a donation this year equals 0.5.
F. The proportion of 200 alumni who were contacted by phone and subsequently contributed a donation this year equals 0.5.

Part iii) What is the approximate null model for the sample proportion of the alumni who were contacted by phone and contributed a donation?

A. N(0.5,0.5(1−0.5)3500‾‾‾‾‾‾‾‾√)N(0.5,0.5(1−0.5)3500)
B. N(0.5,0.5(1−0.5)200‾‾‾‾‾‾‾‾√)N(0.5,0.5(1−0.5)200)
C. N(0.55,0.55(1−0.55)200‾‾‾‾‾‾‾‾‾‾√)N(0.55,0.55(1−0.55)200)
D. N(0.55,0.5(1−0.5)200‾‾‾‾‾‾‾‾√)N(0.55,0.5(1−0.5)200)
E. N(0.5,0.55(1−0.55)200‾‾‾‾‾‾‾‾‾‾√)N(0.5,0.55(1−0.55)200)
F. N(0.55,0.55(1−0.55)3500‾‾‾‾‾‾‾‾‾‾√)N(0.55,0.55(1−0.55)3500)

Part iv) Compute the P-value (your answer must be expressed as a proportion and rounded to 4 decimal places):

Part v) What is an appropriate conclusion to the hypothesis test?

A. The donation rate for alumni contacted by phone this year is significantly higher than last year's at the 5% significance level.
B. The donation rate for alumni contacted by phone this year is not significantly higher than last year's at the 5% significance level.
C. The donation rate for alumni contacted by phone this year is the same as last year's.
D. Both (B) and (C)

Answer 1

Solution:-

Given data:-

The alumni contacted contributed with a donation = 50%

Probability of the alumni contacted contributed with a donation = 0.5.

The alumni was randomly contact by the university = 7000

Random sample alumni contacted by phone = 200

Part i)

To test if the donation rate has increased since last year for alumni contacted by phone, what will be the null hypothesis?

The proportion of 3500 alumni who were contacted by phone and subsequently contributed a donation this year equals 0.5.

Option A is correct.

Part ii)

For the test mentioned in the previous part, what is the alternative hypothesis?

The proportion of 3500 alumni who were contacted by phone and subsequently contributed a donation this year is higher than 0.5.

So,option D is correct

Part iii)

What is the approximate null model for the sample proportion of the alumni who were contacted by phone and contributed a donation?

Probability of the alumni contacted contributed with a donation = 0.5

Random sample alumni contacted by phone = 200

N(0.5,0.5(1−0.5)200‾‾‾‾‾‾‾‾√)N(0.5,0.5(1−0.5)200)

So,option B is correct.

Part iv)

Compute the P-value.

p=0.55

P=0.5

n=200

By using P value calculator,One tailed test

P=0.078652

P=0.078652 >0.05 level of significance.

Therefore,the null hypothesis is rejected.

Part v)

What is an appropriate conclusion to the hypothesis test?

Conclusion:-

The donation rate for alumni contacted by phone this year is significantly higher than last year's at the 5% significance level.

So.option A is correct.