Question

Assume that a researcher wants to use sample data to test the claim that the sample is from a population with a standard deviation less than 1.8 min. The researcher will use a 0.05 significance level to test that claim. If the researcher wants to use the confidence interval method of testing​ hypotheses, what level of confidence should be used for the confidence​ interval? Will the conclusion based on the confidence interval be the same as the conclusion based on a hypothesis test that uses the​ P-value method or the critical value​ method?

Answer 1

Answer:

Step-by-step explanation:

Hello!

First, let me remind you that the hypothesis test is made to the parameter of known distributions. To say it easy, the population deviation, σ, is no parameter of a distribution bu the population variance, σ², is. So when you want to study the population standard deviation, you have to study the population variance. Any decision made for the σ² may be applied to the σ.

So if the experimental hypothesis is that the standard deviation of the population is 1.8 min, since you cannot test it statistically, you will test that the population variance is (1.8)² min².

Your study hypothesis is:

H₀: σ² = 3.24

H₁: σ² < 3.24

α: 0.05

> To take a decision using a Confidence Interval you have to remember that, of course, the interval should be for the same parameter (σ²) and with a complementary confidence level. So if you make the test using a level of significance α: 0.05, the confidence level should be constructed with a confidence level of 1 - α= 0.95

There are 3 methods you can use to decide on a hypothesis test.

> With the critical value against the calculated statistic value

> p-value vs α

> Confidence interval (with complementary confidence level)

You may apply the three methods and should obtain the same decision, of course, this applies only when you use the same sample data for the three of them.

It only makes sense to compare the decisions made with all three methods if the same sample was used. Remember that different samples, even if they are from the same population, do not always give the same results.

I hope it helps!