Question

# Do you want to own your own candy store? Wow! With some interest in running your...

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

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

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