Question

A random sample of 100 observations from a population with standard deviation 76 yielded a sample mean of 114. Complete parts a through c below. a. Test the null hypothesis that u = 100 against the alternative hypothesis that u > 100, using a = 0.05. Interpret the results of the test. What is the value of the test statistic? und to two decimal places as needed.) Find the p-value. p-value = (Round to three decimal places as needed.) State and interpret the results of the test. O A. Reject Ho. There is sufficient evidence to indicate that the true population mean is greater than 100 at a = 0.05. OB. Reject Ho. There is insufficient evidence to indicate that the true population mean is greater than 100 at a = 0.05. O C. Do not reject Ho. There is sufficient evidence to indicate that the true population mean is greater than 100 at a = 0.05. O D. Do not reject Ho. There is insufficient evidence to indicate that the true population mean is greater than 100 at a= 0.05.

Answer 1

a)
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (114 - 100)/(76/sqrt(100))
z = 1.84

P-value = 0.033

Reject H0
Option A

b)
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (114 - 100)/(76/sqrt(100))
z = 1.84

P-value = 0.066

do not reject H0
option B

c)
option C