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 age and type of movie preferred are independent at the 0.05 level. movie preferred. A random sample of 93 adults revealed the following data. Test whether Person's A s Age 18-23 yr 24-29 yr 30-35 yr Movie Drama Science Fiction Comedy Column Total Row Total 6. 11 17 11 34 30 10 27 10 29 93 34 32

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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
24-29 yr
Movie
18-23 yr
30-35 yr
Row Total
Drama
17
11
34
Science Fiction
11
8
11
30
29
Comedy
Column Total
10
9.
10
27
34
32
93
A USE SALT
(a) What is the level of significance?
State the null and alternate hypotheses.
O Ho: Age and movie preference are not independent.
H,: Age and movie preference are independent.
O Ho: Age and movie preference are independent.
H,: Age and movie preference are independent.
O Ho: Age and movie preference are independent.
H,: Age and movie preference are not independent.
O Ho: Age and movie preference are not independent.
H,: Age and movie preference are not independent.
(b) Find the value of the çhi-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?
O Yes
O No
What sampling distribution will you use?
O binomial
O uniform
O chi-square
normal
O Student'st
What are the degrees of freedom?
(c) Find or estimate the P-value of the sample test statistic.
Transcribed Image Text: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 24-29 yr Movie 18-23 yr 30-35 yr Row Total Drama 17 11 34 Science Fiction 11 8 11 30 29 Comedy Column Total 10 9. 10 27 34 32 93 A USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Ho: Age and movie preference are not independent. H,: Age and movie preference are independent. O Ho: Age and movie preference are independent. H,: Age and movie preference are independent. O Ho: Age and movie preference are independent. H,: Age and movie preference are not independent. O Ho: Age and movie preference are not independent. H,: Age and movie preference are not independent. (b) Find the value of the çhi-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? O Yes O No What sampling distribution will you use? O binomial O uniform O chi-square normal O Student'st What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic.
H: 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?
O Yes
O No
What sampling distribution will you use?
O binomial
O uniform
O chi-square
O normal
O Student's t
What are the degrees of freedom?
(c) Find or estimate the P-value of the sample test statistic.
O P-value > 0.100
O 0.050 < P-value < 0.100
O 0.025 < P-value < 0.050
O 0.010 < P-value < 0.025
O 0.005 < P-value < 0.010
O 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?
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 < a, we reject the null hypothesis.
O Since the P-value < a, 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 age of young adult and movie preference are not independent.
O At the 5% level of significance, there is insufficient evidence to conclude that age of young adult and movie preference are not independent.
Transcribed Image Text:H: 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? O Yes O No What sampling distribution will you use? O binomial O uniform O chi-square O normal O Student's t What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic. O P-value > 0.100 O 0.050 < P-value < 0.100 O 0.025 < P-value < 0.050 O 0.010 < P-value < 0.025 O 0.005 < P-value < 0.010 O 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? 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 < a, we reject the null hypothesis. O Since the P-value < a, 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 age of young adult and movie preference are not independent. O 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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