Mr. Acosta, a sociologist, is doing a study to see if there is arelationship between the age of a young adult (18 to 35 years old)and the type of movie preferred. A random sample of 93 adultsrevealed the following data. Test whether age and type of moviepreferred are independent at the 0.05 level.
| Person'sAge | |
| Movie | 18-23yr | 24-29yr | 30-35yr | RowTotal |
| Drama | 8 | 17 | 9 | 34 |
| Science Fiction | 14 | 11 | 5 | 30 |
| Comedy | 8 | 10 | 11 | 29 |
| ColumnTotal | 30 | 38 | 25 | 93 |
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: Age and movie preference are notindependent.
H1: Age and movie preference areindependent.H0: Age and movie preference areindependent.
H1: Age and movie preference are notindependent.    H0: Age andmovie preference are not independent.
H1: Age and movie preference are notindependent.H0: Age and movie preference areindependent.
H1: Age and movie preference areindependent.
(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   Â
What sampling distribution will you use?
binomialnormal    uniformchi-squareStudent'st
What are the degrees of freedom?
(c) Find or estimate the P-value of the sample teststatistic.
P-value > 0.1000.050 < P-value <0.100Â Â Â Â 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 orfail to reject the null hypothesis of independence?
Since the P-value > α, we fail to rejectthe null hypothesis.Since the P-value > α, wereject the null hypothesis.    Since theP-value ≤ α, we reject the null hypothesis.Sincethe P-value ≤ α, we fail to reject the nullhypothesis.
(e) Interpret your conclusion in the context of theapplication.
At the 5% level of significance, there is sufficient evidence toconclude that age of young adult and movie preference are notindependent.At the 5% level of significance, there is insufficientevidence to conclude that age of young adult and movie preferenceare not independent.
