Question

A popular charity used 29% of its donations on expenses. An organizer for a rival charity wanted to quickly provide a donor with evidence that the popular charity has expenses that are higher than other similar charities. The organizer randomly selected 20 similar charities and examined their donations.

The charity conducts a one-mean hypothesis at the 5% significance level, to test whether the mean is less than 29%.

(a) H0:μ=0.29; Ha:μ<0.29, which is a left-tailed test.

(b) The percentages of the donations that those 20 charities spend on expenses are given below.

Use Excel to test whether the mean is less than 29%. Identify the test statistic, t, rounding to two decimal places, and p-value, rounding to three decimal places from the Excel output.

21
9
24
14
25
31
23
37
19
25
31
20
41
32
26
32
27
35
5
25

Test Statistic= P-value=

Answer 1

First we calculate the mean and sample standard deviation using excel using the formula: =average() and stdev.s()

The calculations can also be done as follows :

Now we perform a t test as follows:

The p-value is calculated using the formula in excel as:

=T.DIST(-1.938,19,1)

The critical t-value is given in excel as:

=T.INV(0.05,19)

The test statistic is given as:-1.938=-1.94

p-value =0.0338=0.034