Question

Is the variance for the amount of money, in dollars, that shoppers spend on Saturdays at the mall the same as the variance for the amount of money that shoppers spend on Sundays at the mall? Suppose that the Table 13.33 shows the results of a study

Saturday	Sunday	Saturday	Sunday
$75$	$44$	$62$	$137$
$18$	$58$	$0$	$82$
$150$	$61$	$124$	$39$
$94$	$19$	$50$	$127$
62	$99$	$31$	$141$
$73$	$60$	$118$	$73$
	$80$

Short answer

There is evidence that variance for the amount of money that shoppers spend on Saturday is same as shoppers spend on Sunday.

Step-by-step solution

Given information,

Given in the question that the table,

Saturday	Sunday	Saturday	Sunday
$75$	$44$	$62$	$137$
$18$	$58$	$0$	$82$
$150$	$61$	$124$	39
$94$	$19$	$50$	$127$
$62$	$99$	$31$	$141$
73	60	$118$	$73$
	80

Explanation

Consider the data provided in the table $13.34$to determine the variance for the amount of money that shoppers spend on Saturday is same as shoppers spend on Sunday.

Consider the null hypothesis that there is no significance difference between the variances. For this use Ti-83 calculator, click on STAT $\to$ENTER, and then put the data into the list $L1$, and $L2$. The screenshot is given as below:

Now again press STAT $\to$arrow over the $\mathrm{TESTS}\to$arrow down to 2 sample F-test $\to$Select data and press then select1 and press var then select 2 in list 1 and list$2.$

And select the hypothesis as ${\sigma }_1\ne {\sigma }_2$. The screen shot is given as below:

Screenshot of output

The screenshot of the obtained output is given as below:

Use the above results to solve the below given subparts.

a.

The null hypothesis is given as below:

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

b.

The alternate hypothesis is given as below:

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

Subparts

c.

The degree of freedom in the numerator is 11 , and the degree of freedom in the denominator is$12.$

d.

The$F_{(1,12)}$distribution is used for the test of three different means.

e. The value of the test statistic is $1.35$.

f. The $P$-value for the test is $\mathbf{0}\mathbf{.}\mathbf{60}$.

Graph

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 $0.60$which is greater than the $0.05$level of significance.

d.

There is evidence that variance for the amount of money that shoppers spend on Saturday is same as shoppers spend on Sunday.