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For independent samples of size 4 and 16, respectively, find the mean and standard deviation of x, - x. (Assume that the sampling is done with replacement or t the population is large enough.) e mean of x, -X, is pe an integer or a decimal. Do not round.) e standard deviation of x, -X, is und to four decimal places as needed.) Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Choose the correct answer below. A. No, the formulas for the mean and standard deviation of x, - x, hold regardless of the distributions of the variable on the two populations, as long as the sampling is done with replacement or that the population is large enough. B. No, the variable does not need to be normally distributed for the formulas for the mean and standard deviation of x, - x, to hold as long as the sample sizes are large enough, as long as the sampling is done with replacement. C. Yes, the variable must be approximately normally distributed on each of the two populations for the formulas for the mean and standard deviation of x, - x, to hold. D. No, the variable must be approximately normally distributed at least one of the two populations for the formulas for the mean and standard deviation of x, - x, to hold, as long as the sampling is done with replacement. Can you conclude that the variable x, - x, is normally distributed? Explain your answer. pose the correct answer below. A. Yes, x, -x, is always normally distributed because it is calculated using parameters. B. Yes, x, -X, is always normally distributed because of the central limit theorem. C. No. X, - Xa is normally distributed only if x is normally distributed on each of the two populations or if the sample sizes are large enough,

For independent samples of size 4 and 16, respectively, find the mean and standard deviation of x, - x. (Assume that the sampling is done with replacement or t the population is large enough.) e mean of x, -X, is pe an integer or a decimal. Do not round.) e standard deviation of x, -X, is und to four decimal places as needed.) Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Choose the correct answer below. A. No, the formulas for the mean and standard deviation of x, - x, hold regardless of the distributions of the variable on the two populations, as long as the sampling is done with replacement or that the population is large enough. B. No, the variable does not need to be normally distributed for the formulas for the mean and standard deviation of x, - x, to hold as long as the sample sizes are large enough, as long as the sampling is done with replacement. C. Yes, the variable must be approximately normally distributed on each of the two populations for the formulas for the mean and standard deviation of x, - x, to hold. D. No, the variable must be approximately normally distributed at least one of the two populations for the formulas for the mean and standard deviation of x, - x, to hold, as long as the sampling is done with replacement. Can you conclude that the variable x, - x, is normally distributed? Explain your answer. pose the correct answer below. A. Yes, x, -x, is always normally distributed because it is calculated using parameters. B. Yes, x, -X, is always normally distributed because of the central limit theorem. C. No. X, - Xa is normally distributed only if x is normally distributed on each of the two populations or if the sample sizes are large enough,

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 26PFA
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A variable of two populations has a mean of 60 and a standard deviation of 8 for one of the populations and a mean of 60 and a standard deviation of 12 for the other population. Complete parts (a) through (c). ..... a. For independent samples of size 4 and 16, respectively, find the mean and standard deviation of x, - x,. (Assume that the sampling is done with replacement or that the population is large enough.) The mean of X, - X, is. (Type an integer or a decimal. Do not round.) The standard deviation of x, – x, is (Round to four decimal places as needed.) b. Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Choose the correct answer below. O A. No, the formulas for the mean and standard deviation of x, - x, hold regardless of the distributions of the variable on the two populations, as long as the sampling is done with replacement or that the population is large enough. B. No, the variable does not need to be normally distributed for the formulas for the mean and standard deviation of x, – x, to hold as long as the sample sizes - are large enough, as long as the sampling is done with replacement. C. Yes, the variable must be approximately normally distributed on each of the two populations for the formulas for the mean and standard deviation of x, - X, to hold. D. No, the variable must be approximately normally distributed on at least one of the two populations for the formulas for the mean and standard deviation of X, - x, to hold, as long as the sampling is done with replacement. c. Can you conclude that the variable x, - X, is normally distributed? Explain your answer. Choose the correct answer below. A. Yes, x, - x, is always normally distributed because it is calculated using parameters. B. Yes, x, - X, is always normally distributed because of the central limit theorem. O C. No, x, – x, is normally distributed only if x is normally distributed on each of the two populations or if the sample sizes are large enough. O D. No, since x, - X, must be greater than or equal to 0, the distribution is right skewed, so cannot be normally distributed.
Transcribed Image Text:A variable of two populations has a mean of 60 and a standard deviation of 8 for one of the populations and a mean of 60 and a standard deviation of 12 for the other population. Complete parts (a) through (c). ..... a. For independent samples of size 4 and 16, respectively, find the mean and standard deviation of x, - x,. (Assume that the sampling is done with replacement or that the population is large enough.) The mean of X, - X, is. (Type an integer or a decimal. Do not round.) The standard deviation of x, – x, is (Round to four decimal places as needed.) b. Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Choose the correct answer below. O A. No, the formulas for the mean and standard deviation of x, - x, hold regardless of the distributions of the variable on the two populations, as long as the sampling is done with replacement or that the population is large enough. B. No, the variable does not need to be normally distributed for the formulas for the mean and standard deviation of x, – x, to hold as long as the sample sizes - are large enough, as long as the sampling is done with replacement. C. Yes, the variable must be approximately normally distributed on each of the two populations for the formulas for the mean and standard deviation of x, - X, to hold. D. No, the variable must be approximately normally distributed on at least one of the two populations for the formulas for the mean and standard deviation of X, - x, to hold, as long as the sampling is done with replacement. c. Can you conclude that the variable x, - X, is normally distributed? Explain your answer. Choose the correct answer below. A. Yes, x, - x, is always normally distributed because it is calculated using parameters. B. Yes, x, - X, is always normally distributed because of the central limit theorem. O C. No, x, – x, is normally distributed only if x is normally distributed on each of the two populations or if the sample sizes are large enough. O D. No, since x, - X, must be greater than or equal to 0, the distribution is right skewed, so cannot be normally distributed.
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