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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 x values has an approximately normal distribution. 92 177 129 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 ? for candy store franchises. (Round your answers to one decimal place.) lower limit thousand dollars upper limit thousand dollars

Respuesta :

Answer: Lower limit = 88.1

Upper limit = 126.1

Explanation:

Given :

Sample mean = [tex]\overline{x}[/tex] = 107.1

Sample standard deviation = s = 30.7

Sample size = n = 9

∴ Degree of freedom = [tex]d_{f}[/tex] = n - 1  = 8

∝ = 1 - confidence interval = 1 - 0.90 = 0.10

[tex]\frac{\alpha}{2}[/tex] = 0.05

From t-distribution table;

[tex]t_{0.05}[/tex] = 1.860

∴ Margin of error(MOE) = [tex]t_{0.05}[/tex]×[tex]\frac{30.7 }{\sqrt{9} }[/tex]

= 1.860×[tex]\frac{30.7 }{\sqrt{9} }[/tex]

=19.03

∴ Lower Limit = 107.1 - 19.03 = 88.1

Upper limit = 107.1 + 19.03 = 126.1

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