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.

97 180 127 90 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 start up costs μ for candy store franchises. (Round your answers to one decimal place.)
lower limit thousand dollars
upper limit thousand dollars
x = 107.1
s = 31.5

I have 90.8 & 123.4

are they correct?

I was wrong! I got the correct answers... 87.6 & 126.6

To find the sample mean startup cost (x) and sample standard deviation (s), you need to calculate the mean and standard deviation of the given values.

(a) To find the sample mean startup cost (x):
1. Add up all the startup costs: 97 + 180 + 127 + 90 + 75 + 94 + 116 + 100 + 85 = 964.
2. Divide the sum by the number of values in the sample (9 in this case): 964 / 9 = 107.1.

So, the sample mean startup cost (x) is 107.1 thousand dollars.

To find the sample standard deviation (s):
1. Subtract the sample mean (107.1) from each value in the sample and square the differences:
(97 - 107.1)^2 + (180 - 107.1)^2 + (127 - 107.1)^2 + (90 - 107.1)^2 + (75 - 107.1)^2 + (94 - 107.1)^2 + (116 - 107.1)^2 + (100 - 107.1)^2 + (85 - 107.1)^2 = 4736.6.
2. Divide the sum of the squared differences by (n-1) (n is the number of values in the sample), which in this case would be 8: 4736.6 / 8 = 592.075.
3. Take the square root of the result from step 2: sqrt(592.075) ≈ 24.4.

So, the sample standard deviation (s) is approximately 24.4 thousand dollars.

(b) To find a 90% confidence interval for the population average startup costs (μ):
1. Since the sample size is small (n < 30), we can use a t-distribution.
2. The critical value (t*) for a 90% confidence interval with (n-1) degrees of freedom (df) can be found from a t-distribution table or a calculator. For a sample size of 9, the critical value is approximately 1.83.
3. Calculate the margin of error (E) using the formula: E = t* * (s / sqrt(n)), where t* is the critical value, s is the sample standard deviation, and n is the sample size. In this case, E = 1.83 * (24.4 / sqrt(9)) ≈ 18.2.
4. To find the lower and upper limits of the confidence interval, subtract and add the margin of error to the sample mean: lower limit = x - E and upper limit = x + E.
lower limit = 107.1 - 18.2 ≈ 88.9 thousand dollars
upper limit = 107.1 + 18.2 ≈ 125.3 thousand dollars

So, the 90% confidence interval for the population average startup costs (μ) is approximately 88.9 thousand dollars to 125.3 thousand dollars.

Based on the calculations provided, your values of 90.8 and 123.4 are incorrect. The correct values for the 90% confidence interval are 88.9 and 125.3 thousand dollars.