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A variable of two populations has a mean of 50 and a standard deviation of 12 for one of the populations and a mean of 50 and a standard deviation of 15 for the other population. Complete parts (a) through (c). a. For independent samples of size 9 and 25, respectively, find the mean and standard deviation of x₁-x₂. (Assume that the sampling is done with replacement or that the population is large enough.) The mean of x₁-X2 is. (Type an integer or a decimal. Do not round.) The standard deviation of X₁ -X₂ 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 variable does not need to be normally distributed for the formulas for the mean and standard deviation of X₁ X₂ to hold as long as the sample sizes are large enough, as long as the sampling is done with replacement. OB. Yes, the variable must be approximately normally distributed on each of the two populations for the formulas for the mean and standard deviation of x₁-x₂ to hold. OC. 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 x₁-x₂ to hold, as long as the sampling is done with replacement.

A variable of two populations has a mean of 50 and a standard deviation of 12 for one of the populations and a mean of 50 and a standard deviation of 15 for the other population. Complete parts (a) through (c). a. For independent samples of size 9 and 25, respectively, find the mean and standard deviation of x₁-x₂. (Assume that the sampling is done with replacement or that the population is large enough.) The mean of x₁-X2 is. (Type an integer or a decimal. Do not round.) The standard deviation of X₁ -X₂ 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 variable does not need to be normally distributed for the formulas for the mean and standard deviation of X₁ X₂ to hold as long as the sample sizes are large enough, as long as the sampling is done with replacement. OB. Yes, the variable must be approximately normally distributed on each of the two populations for the formulas for the mean and standard deviation of x₁-x₂ to hold. OC. 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 x₁-x₂ to hold, as long as the sampling is done with replacement.

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
Section10.5: Comparing Sets Of Data
Problem 14PPS
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c. Can you conclude that the variable x₁-x₂ is normally distributed? Explain your answer. Choose the correct answer below. O A. Yes, X₁ -X₂ is always normally distributed because it is calculated using parameters. O B. Yes, X₁ -X₂ is always normally distributed because of the central limit theorem. O C. No, X₁ -X₂ 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 x₁ - x₂ must be greater than or equal to 0, the distribution is right skewed, so cannot be normally distributed.
Transcribed Image Text:c. Can you conclude that the variable x₁-x₂ is normally distributed? Explain your answer. Choose the correct answer below. O A. Yes, X₁ -X₂ is always normally distributed because it is calculated using parameters. O B. Yes, X₁ -X₂ is always normally distributed because of the central limit theorem. O C. No, X₁ -X₂ 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 x₁ - x₂ must be greater than or equal to 0, the distribution is right skewed, so cannot be normally distributed.
A variable of two populations has a mean of 50 and a standard deviation of 12 for one of the populations and a mean of 50 and a standard deviation of 15 for the other population. Complete parts (a) through (c). a. For independent samples of size 9 and 25, respectively, find the mean and standard deviation of X₁ -X₂. (Assume that the sampling is done with replacement or that the population is large enough.) The mean of X₁ -X₂ is. (Type an integer or a decimal. Do not round.) The standard deviation of X₁-X₂ 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 variable does not need to be normally distributed for the formulas for the mean and standard deviation of X₁ X₂ to hold as long as the sample sizes are large enough, as long as the sampling is done with replacement. O B. Yes, the variable must be approximately normally distributed on each of the two populations for the formulas for the mean and standard deviation of x₁ - x₂ to hold. O C. 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 x₁ - x₂ to hold, as long as the sampling is done with replacement.
Transcribed Image Text:A variable of two populations has a mean of 50 and a standard deviation of 12 for one of the populations and a mean of 50 and a standard deviation of 15 for the other population. Complete parts (a) through (c). a. For independent samples of size 9 and 25, respectively, find the mean and standard deviation of X₁ -X₂. (Assume that the sampling is done with replacement or that the population is large enough.) The mean of X₁ -X₂ is. (Type an integer or a decimal. Do not round.) The standard deviation of X₁-X₂ 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 variable does not need to be normally distributed for the formulas for the mean and standard deviation of X₁ X₂ to hold as long as the sample sizes are large enough, as long as the sampling is done with replacement. O B. Yes, the variable must be approximately normally distributed on each of the two populations for the formulas for the mean and standard deviation of x₁ - x₂ to hold. O C. 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 x₁ - x₂ to hold, as long as the sampling is done with replacement.
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