The pass completion percentages of 10 college football quarterbacks for their freshman and sophomore seasons are shown in the table below. At a=0.10, is there enough evidence to support the claim that the pass completion percentages have changed? Complete parts (a) through (e) below. Player 3 4 5 6 7 8 9 10 Completion percentage (freshman) 68.3 62.1 56.3 59.0 62.1 51.0 58.0 62.6 54.9 57.1 Completion percentage (sophomore) 67.9 57.1 62.6 59.6 60.8 59.2 63.8 61.6 56.0 58.2 OD. The pass completion percentages have not changed. Let Ho be the hypothesized mean of the differences in the pass completion percentages (freshman - sophomore). Then d is the sample mean of the differences. What are Ho and H₂? B. Ho: Hd=0 OA. Ho: Hd 20 Ha: Hd <0 OC. Ho: Hd #0 H₂: Hd=0 Ha: Hd #0 OD. Ho: Hd zd OE. Ho: Hasd H₂: Hg>d OF. Ho: Hd ≤0 Ha: Hd>0 H₂: H

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The pass completion percentages of 10 college football quarterbacks for their freshman and sophomore seasons are shown in the table below. At \(\alpha = 0.10\), is there enough evidence to support the claim that the pass completion percentages have changed? Complete parts (a) through (b) below.

### Player Data

| Player                      | 1     | 2     | 3     | 4     | 5     | 6     | 7     | 8     | 9     | 10    |
|-----------------------------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------|
| Completion percentage (freshman) | 68.3  | 62.1  | 56.3  | 59.0  | 62.1  | 51.0  | 60.8  | 54.9  | 57.1  | -     |
| Completion percentage (sophomore)| 67.9  | 57.1  | 62.6  | 59.6  | 60.8  | 59.2  | 63.8  | 61.6  | 56.0  | 58.2  |

#### (a) Null and Alternative Hypotheses:

- The pass completion percentages have not changed.
- Let \(\mu_d\) be the hypothesized mean of the differences in the pass completion percentages (freshman - sophomore).
  
Determine the hypotheses:

- A. \( H_0: \mu_d \ge 0 \)
     \( H_a: \mu_d < 0 \)
- B. \( H_0: \mu_d = 0 \)
     \( H_a: \mu_d \ne 0 \)
- C. \( H_0: \mu_d \ne 0 \)
     \( H_a: \mu_d = 0 \)
- D. \( H_0: \mu_d \ge d \)
     \( H_a: \mu_d < d \)
- E. \( H_0: \mu_d \le d \)
     \( H_a: \mu_d > d \)
- F. \( H_0: \mu_d \le 0 \)
     \( H_a: \mu_d > 0 \)

Correct answer: **B.
Transcribed Image Text:The pass completion percentages of 10 college football quarterbacks for their freshman and sophomore seasons are shown in the table below. At \(\alpha = 0.10\), is there enough evidence to support the claim that the pass completion percentages have changed? Complete parts (a) through (b) below. ### Player Data | Player | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |-----------------------------|-------|-------|-------|-------|-------|-------|-------|-------|-------|-------| | Completion percentage (freshman) | 68.3 | 62.1 | 56.3 | 59.0 | 62.1 | 51.0 | 60.8 | 54.9 | 57.1 | - | | Completion percentage (sophomore)| 67.9 | 57.1 | 62.6 | 59.6 | 60.8 | 59.2 | 63.8 | 61.6 | 56.0 | 58.2 | #### (a) Null and Alternative Hypotheses: - The pass completion percentages have not changed. - Let \(\mu_d\) be the hypothesized mean of the differences in the pass completion percentages (freshman - sophomore). Determine the hypotheses: - A. \( H_0: \mu_d \ge 0 \) \( H_a: \mu_d < 0 \) - B. \( H_0: \mu_d = 0 \) \( H_a: \mu_d \ne 0 \) - C. \( H_0: \mu_d \ne 0 \) \( H_a: \mu_d = 0 \) - D. \( H_0: \mu_d \ge d \) \( H_a: \mu_d < d \) - E. \( H_0: \mu_d \le d \) \( H_a: \mu_d > d \) - F. \( H_0: \mu_d \le 0 \) \( H_a: \mu_d > 0 \) Correct answer: **B.
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