Question

Do you want to own your own candy store? Wow! With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. Startup costs (in thousands of dollars) for a random sample of candy stores are given below. Assume that the population of x values has an approximately normal distribution.

93

176

128

96

75

94

116

100

85

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost x and sample standard deviation s. (Round your answers to one decimal place.)

x =	thousand dollars
s =	thousand dollars

(b) Find a 90% confidence interval for the population average startup costs μ for candy store franchises. (Round your answers to one decimal place.)

lower limit	thousand dollars
upper limit	thousand dollars

Answer 1

Solution:

x	x2
93	8649
176	30976
128	16384
96	9216
75	5625
94	8836
116	13456
100	10000
85	7225
x=963	x2=110367

The sample mean is

Mean     = (x / n) )

=93+176+128+96+75+94+116+100+85 /9

=963/9

=107

The sample standard is S

  S =( x² ) - (( x)² / n ) n -1

=110367-(963)298

=110367-1030418

=73268

=915.75

=30.2614

Degrees of freedom = df = n - 1 = 9 - 1 = 8

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,8 =1.859

Margin of error = E = t_/2,df * (s /n)

= 1.859 * (30.3 / 9)

= 18.8

Margin of error = 18.8

The 90% confidence interval estimate of the population mean is,

- E < < + E

107 - 18.8 < < 107 + 18.8

88.2 < < 125.8

lower limit = 88.2

upper limit =125.8