Question

A random sample of 100 students produced the following results concerning movie preferences:

	Horror	Comedy	Romance
Kids (<15yr old)	15	25	10
Adults (not kids)	17	15	18

At the 0.05 level, test the claim that genre preference is independent of age category. (Round test statistic chi-squared to three decimal places. This problem requires claim, hypothesis setup, test statistic, reject null or not, and a conclusion )

A) Step 1: What is the claim?

B) Step 2: What is the Hypothesis set up?

C) Is the claim related to the null hypothesis, or the alternate hypothesis?

D) In relation to the Observed values "15, 25, 10, 17, 15, 18"; what are the Expected values?

E) Step 3: What is the Test Statistic X²-score?

F) You only need one of these answers: What is the P-value or Critical Z value?

G) Step 4: Do we "Reject Ho" or "Fail to reject the null hypothesis"?

H) Step 5: State the conclusion (must include 3 parts as discussed in lecture)

  

Answer 1

A) Claim : Genre preference is independent of age category.

B)

H0 : The variables Genre preference is independent of age category.

Ha: The variables Genre preference is dependent of age category.

C)  The claim related to the null pothhyesis

D) Observed frequency table :

We need to find expected frequency.

Expected frequency =

E( Kids and Horror ) = (32*50)/100 = 16

Expected frequency table :

E) Now we need to find chi square statistic:

   =                     ; O is observed and E is expected.

   = 4.91

F) Critical value:  α = 0.05 ,

Degrees of freedom (df) = (r-1)(c-1)           r is type of genre  and c is categories of age

r = 3 and c = 2

df = (3-1)*(2-1) = 2

Therefore critical value (0.05,2) = 5.991 -------- ( From chi square table )

G) Decision : As test statistic   is less than 5.991

We fail to reject null hypothesis H0

H) Conclusion: We do not have significant evidence that the variables Genre preference is dependent of age category.