Question

A survey of nonprofit organizations showed that online fundraising has increased in the past year. Based on a random sample of

50

​nonprofits, the mean​ one-time gift donation in the past year was

​$28​,

with a standard deviation of

​$10.

Complete parts a and b below.

a. Construct a

95​%

confidence interval estimate for the population​ one-time gift donation.

Answer 1

= Solution :

Given that,

Point estimate = sample mean =     =28

Population standard deviation =    = 10

Sample size n =50

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)

= 1.96 * ( 10 / 50 )

=2.77

95% confidence interval estimate for the population​ one-time gift donation
is,

- E < < + E

28 - 2.77 <   <28 + 2.77

25.23 <   < 30.77

(25.23, 30.77)