Question

Doctors have reported that the temperatures of new born babies have a standard deviation of 2.58 degrees. A recent sample of 26 newborns showed a variance of 17 degrees. Test the claim with alpha equal to 0.10.

a) What type of test is this?

b) What is the CV(s)?

c) What is the TV?

d) What is the correct summary?

Answer 1

Solution:

Given :

Population Standard Deviation:

Sample Size = n = 26

Sample Variance = s2 = 17

Level of significance = 0.10

Claim: Doctors have reported that the temperatures of new born babies have a standard deviation of 2.58 degrees

Part a) What type of test is this?

We use Chi-square test of Variance( Standard Deviation) .

Thus hypothesis are:

Vs

Part b) What is the CV(s)?

We have to find critical values:

df = n -1 = 26 - 1 = 25

Since this two tailed test, find

Area =

and

Thus Chi-square critical values are: ( 14.611 , 37.652 )

Part c)  What is the TV?

Find test statistic value:

Part d) What is the correct summary?

Decision Rule:

Reject null hypothesis H0, if Chi square test statistic < Chi-square critical value = 14.611 or > 37.652 , otherwise we fail to reject H0.

Since > Chi-square critical value = 37.652, we reject null hypothesis H0.

Thus there is not sufficient evidence to support the Doctors claim that the temperatures of new born babies have a standard deviation of 2.58 degrees.

That is: the temperatures of new born babies is different from  a standard deviation of 2.58 degrees.