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.

96

173

130

92

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 ? for candy store franchises. (Round your answers to one decimal place.)

lower limit	thousand dollars
upper limit	thousand dollars

Answer 1

Solution:

Given that

a )The mean of sample is   

x/n = ( 96 + 173 + 130 +92 +75 +94 +116 +100+86/9 )

= 962 / 9

= 106.89

The sample mean is 106.89

Sample standard deviation is s

s = 1/(n-1)(x - )²

⁼  1/8 (96 - 106.89 )²+ (173 - 106.89 )²+ (130 - 106.89 )²+ (92- 106.89 )² +( 75 - 106.89 )²+ (94 - 106.89)² + (116 - 106.89 )²) + (100 - 106.89 )²) + (85 - 106.89 )²)

= 1/8 ( 118.59 +4370.53 +534.07 +221.71 + 1016.97 +166.15+82.99+47.47+479.17 )

= 6994.88 /8

= 874.36

= 29.57

Standard deviation s = 29.57:

b ) = 106.89

s = 29.57

n = 9

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

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t _/2,df = t_0.05,90 =1.860

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

= 1.860 * (29.57 / 9) = 18.33

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

- E < < + E

106.89 - 18.33 < < 106.89 + 18.33

88.56 < < 125.22

Lpwer limit = 88.6 = 88600

Upper limit = 125.2 = 125200