Question

Instructions: Round all your math steps to two decimal places just like I have been doing in class.

Consider the following hypothesis test:

H₀: µ = 15

H_a: µ ≠ 15

A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3.

a. Compute the value of the test statistic. (Round to two decimal places). Answer

b. What is the p-value? (Round to four decimal places). Answer

c. At α=0.05, what is your conclusion? Choices - (Reject the null hypothesis) or (do not reject the null hypothesis)

Answer 1

(A) test statistics is z =

it is given that population mean = 15, sample mean = 14.15, population standard deviation = 3 and sample size n = 50

this implies

= -0.85/0.4243

= -2.00

(B) using z distribution table, check -2.0 in the first left column and 0.00 in the first row, then select the intersecting cell

p value = 0.0455

(C) Since the p value is less than significance level of 0.05, rejecting the null hypothesis because the result is significant