How does Alex Smith, quarterback for the Kansas City Chiefs, compare to Joe Flacco, quarterback for the Baltimore Ravens? The following table shows the number of completed passes for each athlete during the 2017 NFL football season. Alex Smith 25 27 29 25 22 19 23 25 27 29 34 31 20 14 16 26 10 8 19 25 21 20 27 25 t Joe Flacco 23 19 28 23 24 9 20 2-SampTTest -0.3250234901 p0.7474965338 df - 29 x122.73333333 x2 = 22 Sx1 = 4.463609473 Sx27.589466384
How does Alex Smith, quarterback for the Kansas City Chiefs, compare to Joe Flacco, quarterback for the Baltimore Ravens? The following table shows the number of completed passes for each athlete during the 2017 NFL football season. Alex Smith 25 27 29 25 22 19 23 25 27 29 34 31 20 14 16 26 10 8 19 25 21 20 27 25 t Joe Flacco 23 19 28 23 24 9 20 2-SampTTest -0.3250234901 p0.7474965338 df - 29 x122.73333333 x2 = 22 Sx1 = 4.463609473 Sx27.589466384
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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I need help with all parts of this question 9
![(b) Do the data indicate that there is a difference in the average number of completed passes for the two quarterbacks? Test using \( \alpha = 0.05 \). (Use \( \mu_1 \) for the population mean for Alex Smith and \( \mu_2 \) for the population mean for Joe Flacco.)
State the null and alternative hypotheses.
- \( H_0: (\mu_1 - \mu_2) \neq 0 \) versus \( H_a: (\mu_1 - \mu_2) = 0 \)
- \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) > 0 \)
- \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) < 0 \)
- \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) \neq 0 \)
State the test statistic. (Round your answer to three decimal places.)
\( t = \) [ ]
State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)
\( t > \) [ ]
\( t < \) [ ]
State the conclusion.
- \( H_0 \) is rejected. There is insufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.
- \( H_0 \) is rejected. There is sufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.
- \( H_0 \) is not rejected. There is sufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.
- \( H_0 \) is not rejected. There is insufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.
(c) What is the p-value for the test? (Round your answer to three decimal places.)
\( p\text{-value} = \)
(d) Use the information provided along with the pooled variance, \( s^2 = 39.4115 \) to](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9175f245-2e1a-4def-805b-da74e3897838%2F4e2b9d99-0f7f-4f61-94a9-eae7a0dc2c7a%2Ffzs4dac_processed.png&w=3840&q=75)
Transcribed Image Text:(b) Do the data indicate that there is a difference in the average number of completed passes for the two quarterbacks? Test using \( \alpha = 0.05 \). (Use \( \mu_1 \) for the population mean for Alex Smith and \( \mu_2 \) for the population mean for Joe Flacco.)
State the null and alternative hypotheses.
- \( H_0: (\mu_1 - \mu_2) \neq 0 \) versus \( H_a: (\mu_1 - \mu_2) = 0 \)
- \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) > 0 \)
- \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) < 0 \)
- \( H_0: (\mu_1 - \mu_2) = 0 \) versus \( H_a: (\mu_1 - \mu_2) \neq 0 \)
State the test statistic. (Round your answer to three decimal places.)
\( t = \) [ ]
State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)
\( t > \) [ ]
\( t < \) [ ]
State the conclusion.
- \( H_0 \) is rejected. There is insufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.
- \( H_0 \) is rejected. There is sufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.
- \( H_0 \) is not rejected. There is sufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.
- \( H_0 \) is not rejected. There is insufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.
(c) What is the p-value for the test? (Round your answer to three decimal places.)
\( p\text{-value} = \)
(d) Use the information provided along with the pooled variance, \( s^2 = 39.4115 \) to
Transcribed Image Text:### Comparison of Quarterbacks: Alex Smith vs. Joe Flacco
#### Table: Completed Passes (2017 NFL Season)
| | Alex Smith | Joe Flacco |
|-------|------------|------------|
| Week 1 | 25 | 27 |
| Week 2 | 27 | 25 |
| Week 3 | 29 | 29 |
| Week 4 | 25 | 22 |
| Week 5 | 23 | 19 |
| Week 6 | 27 | 19 |
| Week 7 | 25 | 23 |
| Week 8 | 19 | 20 |
| Week 9 | 25 | 29 |
| Week 10| 20 | 19 |
| Week 11| 23 | 22 |
| Week 12| 22 | 24 |
| Week 13| 19 | 26 |
#### Analysis using TI-84 Plus Calculations
- **2-SampTTest Results:**
- Alternative Hypothesis (\(H_1\)): \(\mu_1 \neq \mu_2\)
- t-value: 0.3250234901
- p-value: 0.7497465338
- Degrees of freedom (df): 29
- Mean of Group 1 (\(\bar{x}_1\)): 22.73333333
- Mean of Group 2 (\(\bar{x}_2\)): 23.23076923
- Standard deviation of Group 1 (\(s_{x1}\)): 4.66304973
- Standard deviation of Group 2 (\(s_{x2}\)): 7.589466384
#### Question:
(a) The TI-84 Plus analysis uses the pooled estimate of \(\sigma^2\). Is the assumption of equal variances reasonable? Why or why not?
- Answer Choices:
- ○ Yes, because the ratio of the larger variance to smaller variance is less than 3.
- ○ Yes, because the ratio of the larger variance to smaller variance is more than 3.
- ○ No, because the ratio of the larger variance to smaller variance is not equal to 1.
- ○ No, because the ratio of the larger
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