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. 100 170 133 93 75 94 116 100 85

(a) The sample mean startup cost is 107.3 thousand dollars.

    The sample mean startup cost is 107.3 thousand dollars.

(b) The 90% confidence interval for the population average startup costs  for candy store franchises is ($89.4, $125.2) thousand.

Step-by-step explanation:

The questions asked related to the data are:

(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

Solution:

The data provided is:

X = {100, 170, 133, 93, 75, 94, 116, 100, 85}

(a)

Compute the sample mean as follows:

The sample mean startup cost is 107.3 thousand dollars.

Compute the sample standard deviation as follows:

The sample standard deviation of startup cost is 28.9 thousand dollars.

(b)

As the population standard deviation is not known we will use a t-interval.

The critical value of t for 90% confidence level and (n - 1) = 8 degrees of freedom is:

*Use a t-table for the value.

Compute the 90% confidence interval for population mean as follows:

Thus, the 90% confidence interval for the population average startup costs  for candy store franchises is ($89.4, $125.2) thousand.

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step-by-step explanation:

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