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

170

125

99

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

Given that,

96

170

125

99

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.)

Sample mean startup cost x = x / n = (96+170+125+99+75+94+116+100+85) / 9 = 960/9 = 106.66

x = 106.7  thousand dollars (Rounded answers to one decimal place.)

sample standard deviation s = sqrt ( (x - Sample mean)^2 / (n-1))

=sqrt(((96-106.7)^2+(170-106.7)^2+(125-106.7)^2+(99-106.7)^2+(75-106.7)^2+(94-106.7)^2+(116-106.7)^2+(100-106.7)^2+(85-106.7)^2) / (9-1))

= sqrt(6284.01/8)

=28.02679521

s = 28.0 thousand dollars (Rounded answers to one decimal place.)

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

c = 90% = 90/100 = 0.90

= 1-c = 1-0.90 = 0.1

/2 = 0.1/2 = 0.05

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

Critical value = = = 1.859547

90% CI = Sample mean   * (s/sqrt(n))

90% CI = 106.7 1.859547* (28.0 /sqrt(9))

90% CI = 106.7 17.355772

Lower limit = 106.7-17.355772= 89.344228 = 89.3 (Rounded to one decimal place)

Upper limit = 106+17.355772= 123.355772 = 123.4(Rounded to one decimal place)

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