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.

100

178

131

91

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

What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1 in the following scenarios? (Round your answers up the nearest whole number.)

(a) a preliminary estimate for p is 0.19


(b) there is no preliminary estimate for p

Answer 1

The statistical software output for this problem is :

(a)

x = 107.8

s = 31.1

(b)

Lower limit = 88.5

Upper limit = 127.0

Solution :

Given that,

margin of error = E = 0.1

Z_/2 = 1.96

(a)

= 0.19

1 - = 0.81

sample size = n = (Z _{/ 2} / E)² * * (1 - )

= (1.96 / 0.1)² * 0.19 * 0.81

= 59.1

sample size = n = 60

(b)

= 0.5

1 - = 0.5

sample size = n = (Z _{/ 2} / E)² * * (1 - )

= (1.96 / 0.1)² * 0.5 * 0.5

= 96.04

sample size = n = 97