Question

The Historical average is 35 minutes with a population standard deviation of 8 minutes. A test of the new process on 10 random runs has a mean of 33 minutes. They are only testing for a reduction in the mean. What is the critical value for an Alpha level of 5%. Assume normality.

Answer 1

We need to conduct a hypothesis in order to check if the mean is lower than 35 min, the system of hypothesis would be:

Null hypothesis:
`\mu \geq 35`

Alternative hypothesis:
`\mu < 35`

For the critical value since we are conducting a left tailed test we neeed to find on the normal satandard distribution a quantile who accumulates 0.05 of the area in the left and we got:

`Z_(\alpha)= -1.64`

And if the statistic calculated is lower than the critical value we relect the null hypothesis otherwise we FAIL to reject the null hypothesis at the significance level given.

Explanation:

Data given and notation

`\bar X=33` represent the sample mean

`\sigma=8` represent the population standard deviation

`n=10` sample size

`\mu_o =35` represent the value that we want to test

`\alpha=0.05` represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is lower than 35 min, the system of hypothesis would be:

Null hypothesis:
`\mu \geq 35`

Alternative hypothesis:
`\mu < 35`

For the critical value since we are conducting a left tailed test we neeed to find on the normal satandard distribution a quantile who accumulates 0.05 of the area in the left and we got:

`Z_(\alpha)= -1.64`

And if the statistic calculated is lower than the critical value we relect the null hypothesis otherwise we FAIL to reject the null hypothesis at the significance level given.