Question

A. Find the p-value of a 2 sided 95% confidence test of hypothesis if the value found for the sample mean was 14.53 the Null Hypothesis assumes that the population mean is Mu = 14, the population standard deviation is 3 and the sample size is 14

B. Find the p-value of a 2-sided 95% confidence test of hypothesis if the value found for the sample mean was 35.71 the Null Hypothesis assumes that the population mean is Mu = 32, the population standard deviation is 8 and the sample size is 6

C. Find the p-value of a test of hypothesis if the value found for the sample mean was 591.33 the Null Hypothesis assumes that the population mean is Mu = 538, the population standard deviation is 152 and the sample size is 13

PLEASE SHOW WORK.

Answer 1

A) The test statistic z = ()/()

= (14.53 - 14)/(3/)

= 0.66

P-value = 2 * P(Z > 0.66)

= 2 * (1 - P(Z < 0.66))

= 2 * (1 - 0.7454)

= 2 * 0.2546 = 0.5092

B) The test statistic z = ()/()

= (35.71 - 32)/(8/)

= 1.14

P-value = 2 * P(Z > 1.14)

= 2 * (1 - P(Z < 1.14))

= 2 * (1 - 0.8729)

= 2 * 0.1271 = 0.2542

C) The test statistic z = ()/()

= (591.33 - 538)/(152/)

= 1.27

P-value = 2 * P(Z > 1.27)

= 2 * (1 - P(Z < 1.27))

= 2 * (1 - 0.8980)

= 2 * 0.102 = 0.204