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 46 43 5 6 100 25-34 39 30 15 16 100 Column Total 85 73 20 22 200 (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 ? = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. H0: Same proportion of communication preference for each age group. H1: Different proportion of communication preference for each age group.H0: Same proportion of communication preference for each age group. H1: Same proportion of communication preference for each age group. H0: Different proportion of communication preference for each age group. H1: Different proportion of communication preference for each age group.H0: Different 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? YesNo What sampling distribution will you use? uniformnormal chi-squarebinomialStudent's t 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 > 0.1000.050 < p-value < 0.100 0.025 < p-value < 0.0500.010 < p-value < 0.0250.005 < p-value < 0.010p-value < 0.005 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? Since the P-value > ?, we fail to reject the null hypothesis.Since the P-value > ?, we reject the null hypothesis. Since the P-value ≤ ?, we reject the null hypothesis.Since the P-value ≤ ?, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. 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.

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 46 43 5 6 100 25-34 39 30 15 16 100 Column Total 85 73 20 22 200 (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 ? = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. H0: Same proportion of communication preference for each age group. H1: Different proportion of communication preference for each age group.H0: Same proportion of communication preference for each age group. H1: Same proportion of communication preference for each age group. H0: Different proportion of communication preference for each age group. H1: Different proportion of communication preference for each age group.H0: Different 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? YesNo What sampling distribution will you use? uniformnormal chi-squarebinomialStudent's t 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 > 0.1000.050 < p-value < 0.100 0.025 < p-value < 0.0500.010 < p-value < 0.0250.005 < p-value < 0.010p-value < 0.005 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? Since the P-value > ?, we fail to reject the null hypothesis.Since the P-value > ?, we reject the null hypothesis. Since the P-value ≤ ?, we reject the null hypothesis.Since the P-value ≤ ?, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. 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.

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Description: 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,

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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	Preferred Communication Method
Age	Cell Phone	Instant Message	Email	Other	Row Total
15-24	46	43	5	6	100
25-34	39	30	15	16	100
Column Total	85	73	20	22	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 ? = 0.05.

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: Same proportion of communication preference for each age group.
H₁: Different proportion of communication preference for each age group.H₀: Same proportion of communication preference for each age group.
H₁: Same proportion of communication preference for each age group. H₀: Different proportion of communication preference for each age group.
H₁: Different proportion of communication preference for each age group.H₀: Different 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?

YesNo

What sampling distribution will you use?

uniformnormal chi-squarebinomialStudent's t

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 > 0.1000.050 < p-value < 0.100 0.025 < p-value < 0.0500.010 < p-value < 0.0250.005 < p-value < 0.010p-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > ?, we fail to reject the null hypothesis.Since the P-value > ?, we reject the null hypothesis. Since the P-value ≤ ?, we reject the null hypothesis.Since the P-value ≤ ?, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

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.

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