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 xvalues has an approximately normal distribution.10017913194759411610085(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 dollarss = 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 dollarsupper limit     thousand dollars

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Asked Jul 28, 2019
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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 xvalues has an approximately normal distribution.

100 179 131 94 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
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Expert Answer

Step 1

(a) Computation of sample mean and sample standard deviation:

Here, the sample size, n = 9. Using calculator, the sample mean is calculated as 108.2 and sample standard deviation is calculated as 31.2, from the calculations given below.

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n 100 179131+94 75 +94 116 +100 85 9 974 9 =108.2 S= n-1 (100-108.22)+(179 -108.22)+(131-108.22)+(94-108.22)+(75-108.22) (94-108.22)+(116 -108.22)+(100-108.22)+(85 -108.22) (9-1) 31.2 Il

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Step 2

(b) Confidence interval when population standard deviation is not known:

The formula of confidence interval for the population mean when population standard deviation is not given is as follows.

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S Confidence interval = 3tt. / 2 S S <μ< x +14) where, x Sample mean, S ta/2 Margin of error vn S = Lower limit of the mean n S Upper limit of the mean 2

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Step 3

Computation of 90% confidence interval for population mean:

Here, the sample mean (x-bar) is 108.2.

The sample standard deviation (s) is 31.2.

The confidence level is 0.90.

Thus, the level of significance, α is 0.10 (= 1 – 0.90).

The degrees of freedom (n − 1) is 8 (=9 − 1).

For 90% confidence interval, the cr...

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| 108.2-|1.86 x >12 μ< 1 108.22+| 1.86 x- 31.2 (108.22-19.34) < μ < (108.22 + 19.34) 88.3<μ< 127.5

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