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.
92 | 174 | 126 | 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:
a)
Given data,
92 , 174 , 126 , 96 , 75 , 94 , 116 , 100 , 85
Mean = x / n
= (92 + 174 + 126 + 96 + 75 + 94 + 116 + 100 + 85)/9
= 958/9
= 106.44
xbar = 106.44
Standard deviation = sqrt(((x-xbar)^2/(n-1)))
substitute values & then we get
= 29.58
s = 29.58
b)
Here for 90% CI, alpha = 0.1, degree of freedom = n - 1 = 9 - 1 = 8
t(alpha/2,df) = t(0.05 , 8) = 1.859547 = 1.86
Interval = xbar +/- t*s/sqrt(n)
substitute values
= 106.44 +/- 1.86*29.58/sqrt(9)
= 106.44 +/- 18.3396
= (88.1 , 124.8)
upper limit = 124.8
lower limit = 88.1
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