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 changed? Complete parts (a) through (e) below. Player 1 5 6 7 8 9 10 Completion percentage (freshman) 2 3 4 67.9 62.6 56.5 61.0 64.3 50.0 59.0 62.6 54.8 59.5 Completion percentage (sophomorel 67.5 58.6 62.9 62.5 63.2 57.7 64.6 61.6 56.7 61.3 (b) Calculated and sd. Calculate d. d (Round to three decimal places as needed.) Calculate S- $=(Round to three decimal places as needed.) (c) Find the standardized test statistic t t= (Round to two decimal places as needed.) (d) Calculate the P-value. P-value= (Round three decimal places as needed.) (e) The rejection regions for this test would be t< -1.833 and t > 1.833, so the null hypothesis would not be rejected. Decide whether to reject or fail to reject the null hypothesis using the P-value. Interpret the decision the context of the orig claim. Are the results the same as the critical value approach? the results the same as using the critical value approach. the null hypothesis. There enough evidence to the claim that the pass completion percentages have
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 changed? Complete parts (a) through (e) below. Player 1 5 6 7 8 9 10 Completion percentage (freshman) 2 3 4 67.9 62.6 56.5 61.0 64.3 50.0 59.0 62.6 54.8 59.5 Completion percentage (sophomorel 67.5 58.6 62.9 62.5 63.2 57.7 64.6 61.6 56.7 61.3 (b) Calculated and sd. Calculate d. d (Round to three decimal places as needed.) Calculate S- $=(Round to three decimal places as needed.) (c) Find the standardized test statistic t t= (Round to two decimal places as needed.) (d) Calculate the P-value. P-value= (Round three decimal places as needed.) (e) The rejection regions for this test would be t< -1.833 and t > 1.833, so the null hypothesis would not be rejected. Decide whether to reject or fail to reject the null hypothesis using the P-value. Interpret the decision the context of the orig claim. Are the results the same as the critical value approach? the results the same as using the critical value approach. the null hypothesis. There enough evidence to the claim that the pass completion percentages have
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 11PPS
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Transcribed Image Text:### Pass Completion Percentages Analysis of College Football Quarterbacks
#### Given Data:
The pass completion percentages of 10 college football quarterbacks for their freshman and sophomore seasons are listed below. We are tasked with determining if there is statistically significant evidence to support the claim that the pass completion percentages have changed, using a significance level of α = 0.10.
#### Table: Completion Percentages by Player
| Player | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|--------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
| **Completion Percentage (Freshman)** | 67.9 | 62.6 | 56.5 | 61.0 | 64.3 | 50.0 | 59.0 | 62.6 | 54.8 | 59.5 |
| **Completion Percentage (Sophomore)** | 67.5 | 58.6 | 62.9 | 62.5 | 63.4 | 57.7 | 64.6 | 61.6 | 56.7 | 61.3 |
#### (a) Claim Identification and Hypothesis Statement
**Question: What is the claim?**
#### Claim Options:
- **A.** The pass completion percentages have increased.
- **B.** The pass completion percentages have decreased.
- **C.** The pass completion percentages have not changed.
- **D.** The pass completion percentages have changed.
**Answer Selection:**
For hypothesis testing, we need to evaluate if there is any change regardless of the direction (increase or decrease). The claim states:
**D.** The pass completion percentages have changed.
Next, we need to state the null hypothesis (H₀) and the alternative hypothesis (Hₐ). Let μd be the hypothesized mean of the differences in pass completion percentages (freshman – sophomore). Then \(\bar{d}\) is the sample mean of the differences.
#### Hypothesis Options:
- **A.**
- \( H_0: \mu_d \geq \bar{d} \)
- \( H_a: \mu_d < \bar{d} \)
- **B.**
- \( H_0: \mu
![The following table displays the pass completion percentages of 10 college football quarterbacks for their freshman and sophomore seasons. The objective is to determine if there's evidence, at a significance level of α = 0.10, to support the claim that the pass completion percentages have changed. You are tasked with completing parts (a) through (e) as outlined below.
| Player | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|--------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
| Completion percentage (freshman) | 67.9 | 62.6 | 65.5 | 61.0 | 64.3 | 50.0 | 59.0 | 62.6 | 54.8 | 59.5 |
| Completion percentage (sophomore) | 67.5 | 58.6 | 62.9 | 62.5 | 63.2 | 57.7 | 64.0 | 61.6 | 56.7 | 61.3 |
(b) **Calculate d and s_d:**
Calculate \( \overline{d} \).
\[ \overline{d} = \] (Round to three decimal places as needed.)
Calculate \( s_d \).
\[ s_d = \] (Round to three decimal places as needed.)
(c) Find the standardized test statistic t.
\[ t = \] (Round to two decimal places as needed.)
(d) Calculate the P-value.
\[ \text{P-value} = \] (Round to three decimal places as needed.)
(e) The rejection regions for this test would be \( t < -1.833 \) and \( t > 1.833 \), so the null hypothesis would not be rejected. Decide whether to reject or fail to reject the null hypothesis using the P-value. Interpret the decision in the context of the original claim. Are the results the same as the critical value approach?
\[ \begin{array}{|c|c|}
\hline
\text{the results} & \text{the same as using the critical value approach.} \\
\hline
\text{the null hypothesis} & \\
\hline
& \text{the null](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac4255ba-2787-4b8b-b63d-664d949df058%2F1673f6bf-6101-4feb-8dee-92eae4283232%2Fdggd5fu_processed.png&w=3840&q=75)
Transcribed Image Text:The following table displays the pass completion percentages of 10 college football quarterbacks for their freshman and sophomore seasons. The objective is to determine if there's evidence, at a significance level of α = 0.10, to support the claim that the pass completion percentages have changed. You are tasked with completing parts (a) through (e) as outlined below.
| Player | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|--------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
| Completion percentage (freshman) | 67.9 | 62.6 | 65.5 | 61.0 | 64.3 | 50.0 | 59.0 | 62.6 | 54.8 | 59.5 |
| Completion percentage (sophomore) | 67.5 | 58.6 | 62.9 | 62.5 | 63.2 | 57.7 | 64.0 | 61.6 | 56.7 | 61.3 |
(b) **Calculate d and s_d:**
Calculate \( \overline{d} \).
\[ \overline{d} = \] (Round to three decimal places as needed.)
Calculate \( s_d \).
\[ s_d = \] (Round to three decimal places as needed.)
(c) Find the standardized test statistic t.
\[ t = \] (Round to two decimal places as needed.)
(d) Calculate the P-value.
\[ \text{P-value} = \] (Round to three decimal places as needed.)
(e) The rejection regions for this test would be \( t < -1.833 \) and \( t > 1.833 \), so the null hypothesis would not be rejected. Decide whether to reject or fail to reject the null hypothesis using the P-value. Interpret the decision in the context of the original claim. Are the results the same as the critical value approach?
\[ \begin{array}{|c|c|}
\hline
\text{the results} & \text{the same as using the critical value approach.} \\
\hline
\text{the null hypothesis} & \\
\hline
& \text{the null
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