Answered: (a) What is the level of significance?…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 4BGP

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Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Test whether age and type of movie preferred are independent at the 0.05 level.

	Person's Age
Movie	18-23 yr	24-29 yr	30-35 yr	Row Total
Drama	8	16	10	34
Science Fiction	10	8	12	30
Comedy	11	8	10	29
Column Total	29	32	32	93

(a) What is the level of significance?

State the null and alternate hypotheses.

H₀: Age and movie preference are not independent.
H₁: Age and movie preference are independent.H₀: Age and movie preference are independent.
H₁: Age and movie preference are independent. H₀: Age and movie preference are not independent.
H₁: Age and movie preference are not independent.H₀: Age and movie preference are independent.
H₁: Age and movie preference are not independent.

(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?

Student's normal

chi-square

binomial

uniform

What are the degrees of freedom?

(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.1000

.050 < P-value < 0.100

0.025 < P-value < 0.0500

.010 < P-value < 0.0250.

005 < P-value < 0.010

P-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 age of young adult and movie preference are not independent.At the

5% level of significance, there is insufficient evidence to conclude that age of young adult and movie preference are not independent.

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