Problem 3. (5166) A study was conducted to determine whether the age of customers is related to the type of movie he or she watches. A sample is shown in the following table. Age 12-20 21-40 41 and over (b) Documentary 33 45 43 Comedy 29 46 60 Mystery 28 69 57 (a) Given that the total sample size n = 410 is fixed, what is the distribution of the nine categories? What are the mean value and variance of each cell frequency? Run a chi-square test of independence and draw your conclusion. Use a = 0.05. Note: A small chi-square table may be found on page 6. Run a chi-square test of "Comedy" versus "Mystery". Use a = 0.05.

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### Problem 3. (5166)

A study was conducted to determine whether the age of customers is related to the type of movie he or she watches. A sample is shown in the following table:

| Age          | Documentary | Comedy | Mystery |
|--------------|-------------|--------|---------|
| 12-20        | 33          | 29     | 28      |
| 21-40        | 45          | 46     | 69      |
| 41 and over  | 43          | 60     | 57      |

(a) Given that the total sample size \( n = 410 \) is fixed, what is the distribution of the nine categories? What are the mean value and variance of each cell frequency? Run a chi-square test of independence and draw your conclusion. Use \(\alpha = 0.05\).

**Note:** A small chi-square table may be found on page 6.

(b) Run a chi-square test of “Comedy” versus “Mystery”. Use \(\alpha = 0.05\).
Transcribed Image Text:### Problem 3. (5166) A study was conducted to determine whether the age of customers is related to the type of movie he or she watches. A sample is shown in the following table: | Age | Documentary | Comedy | Mystery | |--------------|-------------|--------|---------| | 12-20 | 33 | 29 | 28 | | 21-40 | 45 | 46 | 69 | | 41 and over | 43 | 60 | 57 | (a) Given that the total sample size \( n = 410 \) is fixed, what is the distribution of the nine categories? What are the mean value and variance of each cell frequency? Run a chi-square test of independence and draw your conclusion. Use \(\alpha = 0.05\). **Note:** A small chi-square table may be found on page 6. (b) Run a chi-square test of “Comedy” versus “Mystery”. Use \(\alpha = 0.05\).
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