Please help me answer all parts of this question. Please help me answer all part

Question

Please help me answer all parts of this question. Please help me answer all parts of this question. , Carol Products is interested in knowing if the variability of sales in its northern sales division is greater than the southern sales regions. A sample of 20 salespersons of $533.45. A sample of 10 salespersons alpha level of 0.01, can we conclude that the variability of sales in the northern region is greater than (20 points) from the northern region produced a standard deviation in sales produced a standard deviation of $498.33. At an from the southern region gion? Ho: HA: Critical Value and Decision Rule: Calculated Value: Conclusion:

Explanation / Answer

Solution:

Null hypothesis: H0: Variability in the northern region is same as southern region.

Alternative hypothesis: Ha: Variability in the northern region is greater than southern region.

H0: 12 = 22

Ha: 12 > 22

12 = Variance for northern region

22 = Variance for southern region

We are given

n1 = 20

n2 = 10

S1 = 533.45

S2 = 498.33

= 0.01

df1 = 20 – 1 = 19

df2 = 10 – 1 = 9

Upper critical value = 4.8327

(By using F-table or excel)

Decision rule:

Reject H0 if absolute value of F test statistic is greater than 4.8327

Test statistic value or calculated value is given as below:

F = S1^2/S2^2

F = 533.45^2 / 498.33^2

F = 284568.9/248332.8

F = 1.1459

Calculated value = 1.1459

Conclusion:

Calculated F value = 1.1459 is less than critical value = 4.8327

So, we do not reject the null hypothesis that the variability in the northern region is same as southern region.

There is insufficient evidence to conclude that Variability in the northern region is greater than southern region.

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