The home run percentage is the number of home runs per 100 times at bat. A rando
ID: 3359030 • Letter: T
Question
The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages.
(a) Use a calculator with mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)
(b) Compute a 90% confidence interval for the population mean of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (Round your answers to two decimal places.)
(c) Compute a 99% confidence interval for the population mean of home run percentages for all professional baseball players. (Round your answers to two decimal places.)
(d) The home run percentages for three professional players are below.
Examine your confidence intervals and describe how the home run percentages for these players compare to the population average.
We can say Player A falls close to the average, Player B is above average, and Player C is below average.We can say Player A falls close to the average, Player B is below average, and Player C is above average. We can say Player A and Player B fall close to the average, while Player C is above average.We can say Player A and Player B fall close to the average, while Player C is below average.
(e) In previous problems, we assumed the x distribution was normal or approximately normal. Do we need to make such an assumption in this problem? Why or why not? Hint: Use the central limit theorem.
Yes. According to the central limit theorem, when n 30, the x distribution is approximately normal.Yes. According to the central limit theorem, when n 30, the x distribution is approximately normal. No. According to the central limit theorem, when n 30, the x distribution is approximately normal.No. According to the central limit theorem, when n 30, the x distribution is approximately normal.
1.6 2.4 1.2 6.6 2.3 0.0 1.8 2.5 6.5 1.8 2.7 2.0 1.9 1.3 2.7 1.7 1.3 2.1 2.8 1.4 3.8 2.1 3.4 1.3 1.5 2.9 2.6 0.0 4.1 2.9 1.9 2.4 0.0 1.8 3.1 3.8 3.2 1.6 4.2 0.0 1.2 1.8 2.4 The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages 1.6 2.4 1.2 6.6 2.3 0.0 1.8 2.5 6.5 1.8 2.7 2.0 1.9 1.3 2.7 1.7 1.3 2.1 2.8 1.4 3.8 2.1 3.4 13 1.5 2.9 2.6 0.0 4.1 2.9 1.9 2.4 0.0 1.8 3.1 3.8 3.2 1.6 4.2 0.0 1.2 1.8 2.4 (a) Use a calculator with mean and standard deviation keys to find X and s. (Round your answers to two decimal places.) b Compute a 90% confidence interval or the population mean home run percentages or all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (Round your answers to two decimal places.) lower limit upper limit (c Compute a 99% confidence in eval or he population mean 1 o home run percentages or all pro essional baseball players. Round your answers u wo dec"rial places. lower limit upper limit (d) The home run percentages for three professional players are below Player A, 2.5 Player B, 2.1 Player C, 3.8 Examine your confidence intervals and describe how the home run percentages for these players compare to the population average We can say Player A falls close lo lhe average, Player B is above average, and Player C is below average. We can say Player A falls close to the average, Player B is below average, and Player C is ahove average we can say Player A and Player B fall close to the average, while Player C ls above average , we can say Player A and Player B fall close to the average, while Player C is below average (e) In previous problerns, we assumed the x distribution was nomal or approximately mal. Do we need to make such an assumption in this problem? Why or why not? Hint: Use the central limit theorem Yes. According to the central limit theorem, when n 2 30, the x distribution is approximately normal. Yes. According to the central limit theorem, when n 30, the x distribution is approximately normal No. According to the central limit theorem, when n 2 30, the x distribution is approximately normal Nu. According lo the central limit theorem, when 30, the x distribution is approximately nulmalExplanation / Answer
solution=
(a) Use a calculator with mean and standard deviation keys to find x and s.
mean = 2.29 standard deviation = 1.40
(B) Compute a 90% CI for the population mean of home run percentages for all professional baseball players
E = 1.64 = 1.64 *0.2145 = 0.35178... rounded to 5 places
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90% CI: (2.29-E < u < 2.29+E)
= (1.93822. < 2.64178)
(C)Compute a 99% CI for the population mean of home run percentages for all professional baseball players
E = 2.575 = 2.575*0.2145 = 0.54976... rounded to 5 places
99% CI: (2.29-E < u < 2.29+E)
= (1.74024.. < 2.83976)
(d) The home run percentages for three professional players are: Tim Huelett, 2.5, HerbHunter, 2.0, and Jackie Jensen, 3.8. Examine your confidence intervals and describe how thehome run percentages for these players compare to the population average
A: Huilett and Hunter are in the 99% CI range; Jensen is above the range
(e) In previous problems, we assumed the x distribution was normal or approximately normal.Do we need to make such an assumption in this problem? Why or why not?
A: By the central limit theorem, when n is large, the x distribution is approximately normal. Ingeneral, n>(or equal) to 30 which is considered large
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