Question

We learned in Chapter 13, Exercise 35 that the Paralyzed Veterans of America recently sent letters to a random sample of 100,000 potential donors and received 4781 donations. They’ve had a contribution rate of 5% in past campaigns, but a staff member worries that the rate is lower now that they’ve redesigned their letter. Is there evidence that the 4.78% they received is evidence of a real drop in the contribution rate?

Answer 1

Explanation:

given that the Paralyzed Veterans of America recently sent letters to a random sample of 100,000 potential donors and received 4781 donations

`H_0: p = 0.05\\H_a: p <0.05`

(left tailed test)

Sample proportion =
`(4781)/(100000) \\=0.04781`

p difference = -0.00219

Assuming H0 to be true, std error of proportion

=
`\sqrt{(pq)/(n) } \\=0.00158`

Test statistic Z = p diff/std error = -1.38641

p value = 0.0828

since p value >0.05 our significance level

we accept null hypothesis

There is no statistical evidence of a real drop in the contribution rate.