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 ​$39​, with a standard deviation of ​$10. Complete parts a and b below. a. Construct a 90​% confidence interval estimate for the population​ one-time gift donation. nothingless than or equalsmuless than or equals nothing ​(Type integers or decimals rounded to two decimal places as​ needed.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = $39

sample standard deviation = s = $10

sample size = n = 50

Degrees of freedom = df = n - 1 = 50 - 1 = 49

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t _/2,df = t_0.05,49 = 1.677

Margin of error = E = t_/2,df * (s /n)

= 1.677 * (10 / 50)

= 2.37

The 90% confidence interval estimate of the population mean is,

- E < < + E

39 - 2.37 < < 39 + 2.37

36.63 < < 41.37

(36.63 , 41.37)