Thirty men in college were taught a method of finger tapping. They were randomly assigned to three groups of ten, with each receiving one of three doses of caffeine: $0mg$, $100mg$, $200mg$. This is approximately the amount in no, one, or two cups of coffee. Two hours after ingesting the caffeine, the men had the rate of finger tapping per minute recorded. The experiment was double blind, so neither the recorders nor the students knew which group they were in. Does caffeine affect the rate of tapping, and if so how?

Here are the data:

$0mg$	$100mg$	$200mg$	$0mg$	$100mg$	200 mg
$242$	$248$	$246$	$245$	$246$	$248$
$244$	$245$	$250$	$248$	$247$	$252$
$247$	$248$	$248$	$248$	$250$	$250$
$242$	$247$	$246$	244	$246$	$248$
$246$	$243$	$245$	$242$	$244$	$250$

Given in the question that the table,

Consider the data provided in the table $13.36$to determine the caffeine effect on three groups.

Consider the null hypothesis that there is no significance difference between the variances of three groups. For this use Ti83 calculator, click on STAT $\to$ENTER, and then put the data into the list $L1,L2$and L3.The screenshot is given as below:

Now again press STAT $\to$arrow over the TESTS $\to$arrow down to 2 sample F-test $\to$Select data and press then select1 and press var then select 3 in list 1 and list 2 . And select the hypothesis as ${\sigma }_1\ne {\sigma }_2$. The screen shot is given as below:

The screenshot of the obtained output is qiven as below:

Use the above results to solve the below given subparts.

a.

The null hypothesis that the no difference between the variance of the $0\mathrm{mg}$caffeine and $200\mathrm{mg}$caffeine is given as below:

$H_0:{\sigma }_1={\sigma }_2$

b.

The alternate hypothesis is given as below:

$H_1:{\sigma }_1\ne {\sigma }_2$

C.

The degree of freedom in the numerator is $9$, and the degree of freedom in the denominator is $9$.

d.

The$F_{(9,9)}$distribution is used for the test of two variances.

e.

The value of the test statistic is $0.81$.

f.

The $P$-value for the test is $\mathbf{0}\mathbf{.}\mathbf{81}$.

g.

The graph of the distribution is given as below:

h.

a. Level of significance$\alpha$is $0.05$.

b.

Decision: Null hypothesis will be accepted.

C.

Reason for decision: $P$-value is $0.81$which is greater than the $0.05$level of significance.

d.

There is evidence that there is no difference between the variance of $0\mathrm{mg}$and $200\mathrm{mg}$caffeine doses .