Question

The purchasing director wants to compare the daily food expenses of the collection team. Collected the following sample information (dollar amount).
Collection ($) 130 102 129 143 149 120 139
At the significance level of 0.05, can it be concluded that the deviation of the daily expenses of the sales team is less than 16? Use a hypothesis test for variance to test it.

Answer 1

Solution:

Level of significance = 0.05

We have to test if  the deviation of the daily expenses of the sales team is less than 16.

Step 1) State H0 and H1:

Vs

Left tailed test.

Step 2) Test statistic:

where

thus

x	x2
130	16900
102	10404
129	16641
143	20449
149	22201
120	14400
139	19321

Thus

Thus

Step 3) Find Chi-square critical value:

df = n - 1 = 7 - 1 = 6

Level of significance = 0.05

Since this is left tailed test, find Area = 1 - 0.05 = 0.95

Chi-square critical value = 1.635

Step 4) Decision Rule:

Reject null hypothesis H0, if Chi square test statistic < Chi-square critical value =1.635, otherwise we fail to reject H0.
Since Chi square test statistic = > Chi-square critical value =1.635, we fail to reject H0.

Step 5) Conclusion:

At 0.05 level of significance, there is not sufficient evidence to conclude that the deviation of the daily expenses of the sales team is less than 16.