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. Age 15-24 25-34 Column Total Preferred Communication Method Cell Phone Instant Message Email Other Row Total 54 43 97 36 5 5 100 30 66 12 17 15 20 100 200 (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.) 60 27 % 50 40 22% Percentage 30- 20 10 18% 15% 8% 6% 3% 3% 0 Cell phone Inst message E-mail Other Comm Communication Preference 60 50 40 36% 30% Percentage 30- 54 % 43 % 60 54 % 50 43 % 40 36% 30% Percentage 30- 20 10 60 50 15% 12% 5% 5% Cell phone Inst message E-mail Communication Preference Other Comm 27 % 22 % 40 18 % 15% Percentage 30 20 15% 12% 10 5% 5% 20 8% 10 3% 3% Cell phone Inst message E-mail Other Comm O Cell phone Inst message E-mail Other Comm (ii) Test whether the two populations share the same proportions of preferences for each type of communication method. Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. ○ H₁: Different proportion of communication preference for each age group. H₁: Different proportion of communication preference for each age group. O Ho: Same proportion of communication preference for each age group. H₁: Different proportion of communication preference for each age group. ○ Ho: Different proportion of communication preference for each age group. H₁: Same proportion of communication preference for each age group. O Ho: Same proportion of communication preference for each age group. H₁: Same proportion of communication preference for each age group. (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 ○ No What sampling distribution will you use? ○ Student's t O uniform O chi-square O normal O binomial 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.) (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? O Since the P-value> a, we fail to reject the null hypothesis. O Since the P-value> a, we reject the null hypothesis. O Since the P-value sa, we reject the null hypothesis. O Since the P-value sa, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O At the 5% level of significance, there is sufficient evidence to conclude that the proportion of age groups within each communication preference is not the same. ○ At the 5% level of significance, there is insufficient evidence to conclude that the proportion of age groups within each communication preference is not the same.