Question

You decide to study an important question of the average height of the ASU student body. The answer to this question is essential to your future, so we need to study it correctly. You decide to sample 64 students. You set up the following test: H_o: HYB Average height ≥ 59 inches H_a: Average height < 59 inches.

1) Draw the table that shows the 4 possible scenarios of Reality vs. Experimental Outcome. What are the types of errors? Which ones can we control? Let's call that possible error ɑ.

2) What type of distribution will we use to test this hypothesis (z-test or t-test)? Why? If a t-test, how many degrees of freedom?

3) Is this a lower tail, upper tail, or two-tailed test? Draw a graph to help show what we are doing and when we will reject and accept the null hypothesis.

4) Should we worry about the error we are trying to control if the actual average height is less than 59 inches? Why?

5) What about if the actual average height is greater than 59 inches? Why?

Answer 1

Solution:-

Given that,

Sample size is n=64

1)

The Table is as shown in below:

	Null Hypothesis is true	Null Hypothesis is false
Reject null hypothesis	Less than 59 inches	Greater Than or equal to 59 inches
Fail to reject Null Hypothesis	Greater Than or equal to 59 inches	Less than 59 inches

The Typeof errors are type1 error represdewnted by Reject null hypothesis when null hypothesis is true and Type2 error represented by Fail when null hypotehsis is False.

We can control type1 error by setting the level of significance.

2)

We will use t0distribution to test the given hypothesis and the

degrees of freedom are

=n-1

64-1=63

3)

This is a lower tail test.

The graph as shown below:

4)

Yes,because if the null hypothesis is rejected then we wil have to find the reason behind why the average is less than 59 inches and whatwe can do to improve it.

5)

No,because we will able to believe in the null hypothesis.