Question

Consider the following hypothesis test:

H₀: μ = 15

H_a: μ ≠ 15

A sample of 50 provided a sample mean of 14.18. The population standard deviation is 5.

a. Compute the value of the test statistic (to 2 decimals).

b. What is the p-value (to 4 decimals)?

c. Using α = .05, can it be concluded that the population mean is not equal to 15? SelectYesNo

Answer the next three questions using the critical value approach.

d. Using α = .05, what are the critical values for the test statistic? (+ or -)

e. State the rejection rule: Reject H₀ if z is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal to the lower critical value and is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal to the upper critical value.

f. Can it be concluded that the population mean is not equal to 15?
SelectYesNo

Answer 1

Answer)

As the population s.d is known here we can use standard normal z table to conduct the test

A)

Test statistics z = (sample mean - claimed mean)/(s.d/√n)

Z = (14.18 - 15)/(5/√50) = -1.16

B)

From z table, P(z<-1.16) = 0.123

As the test is two tailed

P-value = 2*0.123 = 0.246

C)

As the obtained p-value is > 0.05 given significance

We fail to reject the null hypothesis

So no it cannot be concluded that population mean is not equal to 15

D)

As the test is two tailed

First we need to divide the given alpha into two parts

0.05/2 = 0.025

From z table, P(z<-1.96) = P(z>1.96) = 0.025

So critical values are -1.96 and 1.96 respectively

E)

Reject Ho if test statistics is greater than 1.96 or less than -1.96

F)

As test statistics is -1.16 which is not less than -1.96

We fail to reject the null hypothesis

So No