Question

Consider the following hypothesis test: H_0: µ <= 25 H_a: µ > 25

A sample of size 40 provided a sample mean of 26.4. The population standard deviation is 6.

a) Compute the value of the test statistic, rounding all calculations to 2 decimal places.

b) What is the associated p-value?

c) Using α = 0.05, what is your conclusion? Enter either "reject" or "fail to reject" without the quotes for what to do with the null hypothesis.

Answer 1

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

H₀: µ = 25 versus H_a: µ > 25

This is an upper tailed test.

Part a

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 25

Xbar = 26.4

σ = 6

n = 40

α = 0.05

Critical value = 1.6449

(by using z-table or excel)

Z = (26.4 - 25)/[6/sqrt(40)]

Z = 1.4757

Test statistic = 1.48

Part b

P-value = 0.0694

(by using Z-table)

Part c

P-value > α = 0.05

So, we do not reject the null hypothesis