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case that the pete for four seasons in each sport. Due to the maturing of bodies and skill set, and more experi playing time of student athletes increases from their first year of participation until their fourth year of participation. Suppose population 1 is all female volleyball players in their fourth year of competition, and population 2 is all female volleyball players in their first year of competition. Of interest is to estimate the difference in the mean number of sets played by all female volleyball players in their fourth year of competition and the mean number of sets played by all female volleyball players in their first year of competition. A simple random sample of 8 female volleyball players in their fourth year of competition is selected, and the number of sets they played in their fourth year and the number of sets they played in their first year were recorded. The data is as follows. It is known that the population of differences in the number of sets played in the fourth and first years is normally distributed. If appropriate, use this information to test the hypotheses stated in question 8 at the a = .05 level of significance. 12 6 Standard Deviation 69 48 21 Student Fourth year First year Difference 61 54 23 51 38 3 3 83 48 35 49455 34 15 5 92 75 17 7 72 17 55 8 96 84 12 Mean 72.00 47.50 24.50 17.24 23.34 16.90

case that the pete for four seasons in each sport. Due to the maturing of bodies and skill set, and more experi playing time of student athletes increases from their first year of participation until their fourth year of participation. Suppose population 1 is all female volleyball players in their fourth year of competition, and population 2 is all female volleyball players in their first year of competition. Of interest is to estimate the difference in the mean number of sets played by all female volleyball players in their fourth year of competition and the mean number of sets played by all female volleyball players in their first year of competition. A simple random sample of 8 female volleyball players in their fourth year of competition is selected, and the number of sets they played in their fourth year and the number of sets they played in their first year were recorded. The data is as follows. It is known that the population of differences in the number of sets played in the fourth and first years is normally distributed. If appropriate, use this information to test the hypotheses stated in question 8 at the a = .05 level of significance. 12 6 Standard Deviation 69 48 21 Student Fourth year First year Difference 61 54 23 51 38 3 3 83 48 35 49455 34 15 5 92 75 17 7 72 17 55 8 96 84 12 Mean 72.00 47.50 24.50 17.24 23.34 16.90

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Question

Are the sample sizes large enough for the central limit theorem?
A) Yes because on sample sizes of 40 are needed
B) Yes because on sample sizes of 15 are needed
C) Yes since it is normally distributed any sample size will work
D) No because the sample is small for the central limit theorem to apply

While in college student athletes can compete for four seasons in each sport. Due to the maturing of bodies and skill set, and more experience, it is often the case that the playing time of student athletes increases from their first year of participation until their fourth year of participation. Suppose population 1 is all female volleyball players in their fourth year of competition, and population 2 is all female volleyball players in their first year of competition. Of interest is to estimate the difference in the mean number of sets played by all female volleyball players in their fourth year of competition and the mean number of sets played by all female volleyball players in their first year of competition. A simple random sample of 8 female volleyball players in their fourth year of competition is selected, and the number of sets they played in their fourth year and the number of sets they played in their first year were recorded. The data is as follows. It is known that the population of differences in the number of sets played in the fourth and first years is normally distributed. If appropriate, use this information to test the hypotheses stated in question 8 at the a = .05 level of significance. Standard Deviation Student Fourth year First year Difference 1 2 61 54 23 51 38 3 3 83 48 35 4 49 34 15 5 92 75 17 6 69 48 21 7 72 17 55 8 96 84 12 Mean 72.00 47.50 24.50 17.24 23.34 16.90
Transcribed Image Text:While in college student athletes can compete for four seasons in each sport. Due to the maturing of bodies and skill set, and more experience, it is often the case that the playing time of student athletes increases from their first year of participation until their fourth year of participation. Suppose population 1 is all female volleyball players in their fourth year of competition, and population 2 is all female volleyball players in their first year of competition. Of interest is to estimate the difference in the mean number of sets played by all female volleyball players in their fourth year of competition and the mean number of sets played by all female volleyball players in their first year of competition. A simple random sample of 8 female volleyball players in their fourth year of competition is selected, and the number of sets they played in their fourth year and the number of sets they played in their first year were recorded. The data is as follows. It is known that the population of differences in the number of sets played in the fourth and first years is normally distributed. If appropriate, use this information to test the hypotheses stated in question 8 at the a = .05 level of significance. Standard Deviation Student Fourth year First year Difference 1 2 61 54 23 51 38 3 3 83 48 35 4 49 34 15 5 92 75 17 6 69 48 21 7 72 17 55 8 96 84 12 Mean 72.00 47.50 24.50 17.24 23.34 16.90
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Follow-up Question

Are there 2 independent simple random samples?

a) Yes

b) No

 

Are the sample sizes large enough for the central limit theorem?

a) Yes because on sample sizes of 40 are needed

b) No because the sample is small for the central limit theorem to apply

c) Yes because on sample sizes of 15 are needed

 d) Yes since it is normally distributed any sample size will work

While in college student athletes can compete for four seasons in each sport. Due to the maturing of bodies and skill set, and more experience, it is often the case that the playing time of student athletes increases from their first year of participation until their fourth year of participation. Suppose population 1 is all female volleyball players in their fourth year of competition, and population 2 is all female volleyball players in their first year of competition. Of interest is to estimate the difference in the mean number of sets played by all female volleyball players in their fourth year of competition and the mean number of sets played by all female volleyball players in their first year of competition. A simple random sample of 8 female volleyball players in their fourth year of competition is selected, and the number of sets they played in their fourth year and the number of sets they played in their first year were recorded. The data is as follows. It is known that the population of differences in the number of sets played in the fourth and first years is normally distributed. If appropriate, use this information to test the hypotheses stated in question 8 at the a- .05 level of significance S 6 Standard Deviation 92 69 Student Fourth year First year Difference 3 61 54 83 48 35 23 38 2443 4945 49 34 15 75 48 17 21 7 72 17. 55 8 96 84 12 Mean 72.00 47.50 24.50 17.24 23.34 16.90
Transcribed Image Text:While in college student athletes can compete for four seasons in each sport. Due to the maturing of bodies and skill set, and more experience, it is often the case that the playing time of student athletes increases from their first year of participation until their fourth year of participation. Suppose population 1 is all female volleyball players in their fourth year of competition, and population 2 is all female volleyball players in their first year of competition. Of interest is to estimate the difference in the mean number of sets played by all female volleyball players in their fourth year of competition and the mean number of sets played by all female volleyball players in their first year of competition. A simple random sample of 8 female volleyball players in their fourth year of competition is selected, and the number of sets they played in their fourth year and the number of sets they played in their first year were recorded. The data is as follows. It is known that the population of differences in the number of sets played in the fourth and first years is normally distributed. If appropriate, use this information to test the hypotheses stated in question 8 at the a- .05 level of significance S 6 Standard Deviation 92 69 Student Fourth year First year Difference 3 61 54 83 48 35 23 38 2443 4945 49 34 15 75 48 17 21 7 72 17. 55 8 96 84 12 Mean 72.00 47.50 24.50 17.24 23.34 16.90
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