Question

Was wondering if why one would reject the null hypothesis in this situation could be explained, thanks!

Answer 1

Solution:

For the given scenario, we have to use one sample z test for the population mean. We use z test instead of t test because we know the value of population standard deviation.

H₀: µ ≥ 70 versus H_a: µ < 70

This is a one tailed test.

This is a lower tailed or left tailed test.

We are given

Test statistic = Z = -2.10

So, p-value is given as below:

P-value = P(Z<-2.10) (Because test is lower tailed)

P-value = 0.0179

(by using z-table)

We are given

Level of significance = α = 0.05

We reject the null hypothesis when p-value is less than alpha value or level of significance, otherwise we do not reject the null hypothesis.

For this test, we have

P-value = 0.0179 < α = 0.05

So, we reject the null hypothesis

Answer:

The p-value of the test is 0.0179 and we will decide to reject the null hypothesis if α = 0.05 is used.