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?
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.
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(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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