ADP SUPPORT POR... SSA Employer W-2 Filin... O Rental Campervans. O New Zealand Travel... G Google Add to MyRegistry O Mail - sgorham@a... Is the lottery fair? Powerball is a multistate lottery in which players try to guess the numbers that will turn up in a drawing of numbered balls. One of the balls drawn is the "Powerball." Matching the number drawn on the Powerball increases one's winnings. In a 17 month period, the Powerball was drawn from a collection of 35 balls numbered 1 through 35. A total of 147 drawings were made. For the purpose of this exercise, we grouped the numbers in to five categories: 1-7, 8-14, and so on. If the lottery is fair, then the winning number is equally likely to occur in any category. Following are the observed frequencies. Test the hypothesis that each of the categories is equally likely. Use the 0.05 level of significance and the critical value method with the table. Category 1-7 8-14 15-21 22-28 29-35 Observed 33 22 35 31 26 Send data to Excel Part: 0 /7 Part 1 of 7 Compute the expected frequencies. Category 1-7 8-14 15-21 22-28 29-35 Expected frequency

A First Course in Probability (10th Edition)
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**Is the lottery fair?**

Powerball is a multistate lottery where players try to guess the numbers from a drawing of numbered balls. One of these balls is the "Powerball." Matching the number drawn on the Powerball increases winnings. Over a period of 17 months, the Powerball was drawn from a set of 35 balls numbered 1 through 35, resulting in 147 drawings.

For this exercise, numbers are grouped into five categories: 1-7, 8-14, 15-21, 22-28, and 29-35. If the lottery is fair, the winning number will be equally likely to occur in any category. Below are the observed frequencies for each category. The task is to test the hypothesis that each category has an equal likelihood using a 0.05 level of significance and the critical value method.

| Category   | 1-7 | 8-14 | 15-21 | 22-28 | 29-35 |
|------------|-----|------|-------|-------|-------|
| Observed   | 33  | 22   | 35    | 31    | 26    |

**Part: 0 / 7**

**Part 1 of 7**

Compute the expected frequencies.

| Category           | 1-7 | 8-14 | 15-21 | 22-28 | 29-35 |
|--------------------|-----|------|-------|-------|-------|
| Expected frequency |     |      |       |       |       |

---

To calculate the expected frequency for each category, assume each category is equally likely to occur. Divide the total number of drawings (147) equally among the five categories to obtain the expected frequency.

*Submit your assignment using the interface provided.*
Transcribed Image Text:**Is the lottery fair?** Powerball is a multistate lottery where players try to guess the numbers from a drawing of numbered balls. One of these balls is the "Powerball." Matching the number drawn on the Powerball increases winnings. Over a period of 17 months, the Powerball was drawn from a set of 35 balls numbered 1 through 35, resulting in 147 drawings. For this exercise, numbers are grouped into five categories: 1-7, 8-14, 15-21, 22-28, and 29-35. If the lottery is fair, the winning number will be equally likely to occur in any category. Below are the observed frequencies for each category. The task is to test the hypothesis that each category has an equal likelihood using a 0.05 level of significance and the critical value method. | Category | 1-7 | 8-14 | 15-21 | 22-28 | 29-35 | |------------|-----|------|-------|-------|-------| | Observed | 33 | 22 | 35 | 31 | 26 | **Part: 0 / 7** **Part 1 of 7** Compute the expected frequencies. | Category | 1-7 | 8-14 | 15-21 | 22-28 | 29-35 | |--------------------|-----|------|-------|-------|-------| | Expected frequency | | | | | | --- To calculate the expected frequency for each category, assume each category is equally likely to occur. Divide the total number of drawings (147) equally among the five categories to obtain the expected frequency. *Submit your assignment using the interface provided.*
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