SOLUTION: Question 1 Consider the following results from a survey of small businesses: SECTOR Retail Manufact. Financial Services Mean number of Employees 4.1 11.7 7.2 Standard devi

Question 75809: Question 1
Consider the following results from a survey of small businesses:
SECTOR
Retail Manufact. Financial Services
Mean number of Employees 4.1 11.7 7.2
Standard deviation 3.3 3.9 3.7
No. of businesses with cash flow problems 17 32 11
No. with no cash flow problems 13 18 9
Total number in sample 30 50 20
In connection with the above data, answer the following questions:
(a) Does the proportion of businesses having cash flow problems vary from one sector to another?
(b) Is there a significant difference between the average number of employees in the retail and manufacturing sectors?
(c) Given that it is quite a small sample, what would you expect the average number of employees over all small businesses in the manufacturing sector to be?
(d) In a survey of retail businesses done last year, about 50% admitted to having cash flow problems. Has this proportion increased significantly?

NOTE : DO NOT USE A T- CALCULATOR . SHOW ALL YOUR MANUAL WORKINGS .
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Question 1
Consider the following results from a survey of small businesses:
SECTOR
Retail Manufact. Financial Services
Mean number of Employees 4.1 11.7 7.2
Standard deviation 3.3 3.9 3.7
No. of businesses with cash flow problems 17 32 11
No. with no cash flow problems 13 18 9
Total number in sample 30 50 20
In connection with the above data, answer the following questions:
(a) Does the proportion of businesses having cash flow problems vary from one sector to another?
Retail proportion= 17/30=57%
Manufacture prop = 32/50=64%
Fin Services prop= 11/20=55%
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(b) Is there a significant difference between the average number of employees in the retail and manufacturing sectors?
4.1 vs 11.7
Ho: u1-u2=0
Ha: u1-u2 is not zero
z(11.7-4.1)=(4.6-0)/sqrt(0.3^2/30 + 3.9^2/50)=8.99
Reject Ho:
Such a high z-score guarantees there is a significant difference.
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(c) Given that it is quite a small sample, what would you expect the average number of employees over all small businesses in the manufacturing sector to be?
Mean is 11.7 employees for a sample of 50 firms.
-------------------------------
(d) In a survey of retail businesses done last year, about 50% admitted to having cash flow problems. Has this proportion increased significantly?
Current percent is 17/30 = 56.7% ; Last year percent= 50%
Ho:p1-p2=0
Ha:p1-p2<0
z(0.567-0.500)= 0.517549
p value of 0.517549= 0.57
Conclusion: Fail to reject Ho; the proportions have not increased significantly.
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Cheers,
Stan H.
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