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
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 23PFA
Related questions
Question
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 a = 0.05. (Use μ₁ for the population mean for Alex Smith and μ for the population mean for Joe Flacco.)
State the null and alternative hypotheses.
O Ho: (M₁M₂) #0 versus H₂: (μ₁ −μ₂) = 0
O Ho: (M₁M₂) = 0 versus H₂: (M₁-H₂) = 0
O H₁: (M₁ M₂) = 0 versus H₂: (μ₁ −µ₂) >0
O Ho: (M₁M₂) = 0 versus H₂: (M₁ - H₂) < 0
O Ho: (M₁M₂) < 0 versus Ha: (M₁ - H₂) > O
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.)
State the conclusion.
O Ho is rejected. There is insufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.
O Ho is rejected. There is sufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.
O Ho is not rejected. There is sufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.
O Ho 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-value =
(d) Use the information provided along with the pooled variance, s² = 39.4115 to construct a 95% confidence interval for the difference in the average number of completed passes for the two quarterbacks. (Round your answers to three decimal places.)
passes to
passes
Does the confidence interval confirm your conclusion in part (b)? Explain.
O Yes, since (μ₁ −μ₂) = 0 is in the interval, there is sufficient evidence to indicate that there is a difference in the means.
O Yes, since (μ₁ - ₂) = 0 is not in the interval, there is sufficient evidence to indicate that there is a difference in the means.
O No, since (μ₁ −μ₂) = 0 is in the interval, there is sufficient evidence to indicate that there is a difference in the means.
O Yes, since (μ₁ −μ₂) = 0 is in the interval, there is insufficient evidence to indicate that there is a difference in the means.
O No, since (μ₁ −μ₂) = 0 is not in the interval, there is sufficient evidence to indicate that there is a difference in the means.](/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 a = 0.05. (Use μ₁ for the population mean for Alex Smith and μ for the population mean for Joe Flacco.)
State the null and alternative hypotheses.
O Ho: (M₁M₂) #0 versus H₂: (μ₁ −μ₂) = 0
O Ho: (M₁M₂) = 0 versus H₂: (M₁-H₂) = 0
O H₁: (M₁ M₂) = 0 versus H₂: (μ₁ −µ₂) >0
O Ho: (M₁M₂) = 0 versus H₂: (M₁ - H₂) < 0
O Ho: (M₁M₂) < 0 versus Ha: (M₁ - H₂) > O
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.)
State the conclusion.
O Ho is rejected. There is insufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.
O Ho is rejected. There is sufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.
O Ho is not rejected. There is sufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.
O Ho 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-value =
(d) Use the information provided along with the pooled variance, s² = 39.4115 to construct a 95% confidence interval for the difference in the average number of completed passes for the two quarterbacks. (Round your answers to three decimal places.)
passes to
passes
Does the confidence interval confirm your conclusion in part (b)? Explain.
O Yes, since (μ₁ −μ₂) = 0 is in the interval, there is sufficient evidence to indicate that there is a difference in the means.
O Yes, since (μ₁ - ₂) = 0 is not in the interval, there is sufficient evidence to indicate that there is a difference in the means.
O No, since (μ₁ −μ₂) = 0 is in the interval, there is sufficient evidence to indicate that there is a difference in the means.
O Yes, since (μ₁ −μ₂) = 0 is in the interval, there is insufficient evidence to indicate that there is a difference in the means.
O No, since (μ₁ −μ₂) = 0 is not in the interval, there is sufficient evidence to indicate that there is a difference in the means.
![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.
t
Alex Smith
25 27 29
23 25 27
23
Joe Flacco
19
25 22
20 14 16 26 10 8
28
19 25 21 20 27 25
29 34 31
19
23 24 9
20
2-SampTTest
H₁ H₂
#
t = 0.3250234901
p= 0.7474965338
df = 29
x1 = 22.73333333
x2 = 22
Sx1 = 4.463609473
Sx2= 7.589466384
(a) The TI-84 Plus analysis uses the pooled estimate of o2. Is the assumption of equal variances reasonable? Why or why not?
O Yes, because the ratio of the larger variance to smaller variance is less than 3.
O 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.
O No, because the ratio of the larger variance to smaller variance is less than 3.
O No, because the ratio of the larger variance to smaller variance is more than 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9175f245-2e1a-4def-805b-da74e3897838%2F4e2b9d99-0f7f-4f61-94a9-eae7a0dc2c7a%2Fd1zaqwe_processed.png&w=3840&q=75)
Transcribed Image Text: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.
t
Alex Smith
25 27 29
23 25 27
23
Joe Flacco
19
25 22
20 14 16 26 10 8
28
19 25 21 20 27 25
29 34 31
19
23 24 9
20
2-SampTTest
H₁ H₂
#
t = 0.3250234901
p= 0.7474965338
df = 29
x1 = 22.73333333
x2 = 22
Sx1 = 4.463609473
Sx2= 7.589466384
(a) The TI-84 Plus analysis uses the pooled estimate of o2. Is the assumption of equal variances reasonable? Why or why not?
O Yes, because the ratio of the larger variance to smaller variance is less than 3.
O 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.
O No, because the ratio of the larger variance to smaller variance is less than 3.
O No, because the ratio of the larger variance to smaller variance is more than 3.
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