Question

A researcher obtains the following sample from people who like to read comic books about how many movies they saw last month.

Sample: 5, 0, 4, 7, 3, 7, 8, 2, 9, 3.

The average number of movies people in the general population see in a month is 2.

On the basis of this sample, is the average number of movies seen by comic book fans significantly different from the general population? Use a two-tailed test with α = 0.05. Make sure you show all your steps.        (6 points)

Answer 1

Here claim is that mean is 2

vs

For the given sample mean is

For standard deviation

Create the following table.

data	data-mean	(data - mean)2
5	0.2	0.04
0	-4.8	23.04
4	-0.8	0.64
7	2.2	4.84
3	-1.8	3.24
7	2.2	4.84
8	3.2	10.24
2	-2.8	7.84
9	4.2	17.64
3	-1.8	3.24

Find the sum of numbers in the last column to get

So

So test statistics is

The t-critical values for a two-tailed test, for a significance level of α=0.05 are

tc​=−2.262 and tc​=2.262

Graphically

As t statistics falls in the rejection region we reject the null hypothesis.

Hence we conclude that the average number of movies seen by comic book fans significantly different from the general population