Question

1. Use per diemsheet to answer this question.   

Suppose a company from the United States does considerable business in the city of Johannesburg, South Africa, and wishes to establish a per diem rate for employee travel to that city. The company researcher is assigned this task, and in an effort to determine this figure, she obtains a random sample of 14 business travelers staying in Johannesburg.  The result is the data presented in per diemsheet. Use these data to construct a 98% confidence interval to estimate the average per diem expense for business people traveling to Johannesburg. Assume per diem rates for any locale are approximately normally distributed. Round your answer to 2 decimal places. Interpret your findings.

142.59
159.09
148.48
156.32
159.63
142.49
171.93
129.28
146.9
151.56
168.87
132.87
141.94
178.34

Answer 1

Below is table of calculation made to find the x-bar & (x- x-bar)^2

X	(x-x-bar)^2
142.59	91.6532699
159.09	47.97541276
148.48	13.56869847
156.32	17.27589847
159.63	55.74755561
142.49	93.57798418
171.93	390.7116985
129.28	523.6578413
146.9	27.70518418
151.56	0.364298469
168.87	279.1047556
132.87	372.2418985
141.94	104.5214128
178.34	685.2054128
152.1636	2703.311321
X-bar	Sum of (x - xbar)^2

xbar = 152.1636

S = (Sum of (x - xbar)^2/(n-1))^(1/2)

S = (2703.311321/13)^(1/2)

S = 14.42037

Degree of Freedom = 13

Significance Level = 1-98% = 0.02

Critical Value = 2.650 (From t table, for 13 df & 0.02 significance level (two tail))

Margin of Error E = Critical Value*S/(n)^(1/2)

E = 2.650*14.42037/(14)^0.5

E = 10.21312

Lower limit = xbar - E

Lower Limit = 152.1636 - 10.21312

Lower Limit = 141.9505 = 141.95

Upper limit = xbar + E

Upper Limit = 152.1636 + 10.21312

Upper Limit = 162.3767 = 162.38

98% Confidence Interval = (141.95,162.38)