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.
STATISTICAL ANALYSIS (No long explanation needed. Rate will be given and write the complete solutions.)
Choose the correct answer.
CI on the Mean, Variance Known
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.
b. 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
c. 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
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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