Question

Random samples of people ages 15−24 and of people ages 25−34 were asked about their preferred method of (remote) communication with friends. The respondents were asked to select one of the methods from the following list: cell phone, instant message, e-mail, other.

	Preferred Communication Method
Age	Cell Phone	Instant Message	Email	Other	Row Total
15-24	42	45	7	6	100
25-34	45	26	15	14	100
Column Total	87	71	22	20	200

(i) Make a cluster bar graph showing the percentages in each age group who selected each method. (In the graphs, cyan represents ages 15-24, and gray represents ages 25-34.)

(ii) Test whether the two populations share the same proportions of preferences for each type of communication method. Use α = 0.05.

(a) What is the level of significance?

0.05

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

Are all the expected frequencies greater than 5?

Yes

What sampling distribution will you use?

chi-square

What are the degrees of freedom?

(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

p-value > 0.100

0.050 < p-value < 0.100     

0.025 < p-value < 0.050

0.010 < p-value < 0.025

0.005 < p-value < 0.010

p-value < 0.005

Answer 1

The statistical software output for this problem is :

Level of significance = 0.05

chi-square statistic = 11.297

degrees of freedom = 3

0.010 < p-value < 0.025