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A normal distribution has known population mean 50 and a variance of 4. Probabilities where the sample variance - S² is greater than or equal to 7.50, and less than or equal to 2.50 are given below for sample sizes 16, 32 and 48. n = 16 n= 32 n = 48 P(S²>= 7.50) 0.0953 0.0364 0.0148 P(S? <= 2.50) 0.0577 0.0092 0.0016 Compare the results for the probabilities that the sample variance is greater than or equal to 7.44 and less than or equal to 2.56, with increased sample size. O a. The probabilities increase as n increase. As n increases, the sample variances should approach the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance increases O b. The probabilities decrease as n increase. As n increases, the sample variances should deviate the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance decreases O . The probabilities decrease as n increase. As n increase, the sample variances should approach the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance decreases O d. The probabilities increase as n increase. As n increases, the sample variances should approach the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance decreases

A normal distribution has known population mean 50 and a variance of 4. Probabilities where the sample variance - S² is greater than or equal to 7.50, and less than or equal to 2.50 are given below for sample sizes 16, 32 and 48. n = 16 n= 32 n = 48 P(S²>= 7.50) 0.0953 0.0364 0.0148 P(S? <= 2.50) 0.0577 0.0092 0.0016 Compare the results for the probabilities that the sample variance is greater than or equal to 7.44 and less than or equal to 2.56, with increased sample size. O a. The probabilities increase as n increase. As n increases, the sample variances should approach the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance increases O b. The probabilities decrease as n increase. As n increases, the sample variances should deviate the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance decreases O . The probabilities decrease as n increase. As n increase, the sample variances should approach the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance decreases O d. The probabilities increase as n increase. As n increases, the sample variances should approach the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance decreases

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 13PPS
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A normal distribution has known population mean 50 and a variance of 4. Probabilities where the sample variance - S? is greater than or equal to 7.50, and less than or equal to 2.50 are given below for sample sizes 16, 32 and 48. n= 16 n= 32 n= 48 P(S²>= 7.50) 0.0953 0.0364 0.0148 P(S? <= 2.50) 0.0577 0.0092 0.0016 Compare the results for the probabilities that the sample variance is greater than or equal to 7.44 and less than or equal to 2.56, with increased sample size. a. The probabilities increase as n increase. As n increases, the sample variances should approach the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance increases O b. The probabilities decrease as n increase. As n increases, the sample variances should deviate the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance decreases O. The probabilities decrease as n increase. As n increase, the sample variances should approach the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance decreases O d. The probabilities increase as n increase. As n increases, the sample variances should approach the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance decreases
Transcribed Image Text:A normal distribution has known population mean 50 and a variance of 4. Probabilities where the sample variance - S? is greater than or equal to 7.50, and less than or equal to 2.50 are given below for sample sizes 16, 32 and 48. n= 16 n= 32 n= 48 P(S²>= 7.50) 0.0953 0.0364 0.0148 P(S? <= 2.50) 0.0577 0.0092 0.0016 Compare the results for the probabilities that the sample variance is greater than or equal to 7.44 and less than or equal to 2.56, with increased sample size. a. The probabilities increase as n increase. As n increases, the sample variances should approach the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance increases O b. The probabilities decrease as n increase. As n increases, the sample variances should deviate the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance decreases O. The probabilities decrease as n increase. As n increase, the sample variances should approach the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance decreases O d. The probabilities increase as n increase. As n increases, the sample variances should approach the population variance. Therefore, the likelihood of obtaining a sample variance greater or smaller than the population variance decreases
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