Question

Consider the following hypothesis test: H_0: µ <= 50 H_a: µ > 50

A sample of size 60 provided a sample mean of 51.8. The population standard deviation is 8.

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 = 50 versus Ha: µ > 50

This is an upper tailed test.

a) Compute the value of the test statistic.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 50

Xbar = 51.8

σ = 8

n = 60

α = 0.05

Critical value = 1.6449

(by using z-table or excel)

Z = (51.8 - 50)/[8/sqrt(60)]

Z = 1.7428

Test statistic = 1.74

b) What is the associated p-value?

P-value = 0.0407

(by using Z-table)

c) Using α = 0.05, what is your conclusion?

P-value < α = 0.05

So, we reject the null hypothesis