Question

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.

94

171

126

98

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 1

The sample size is n = 9 . The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:

	X	X2
	94	8836
	171	29241
	126	15876
	98	9604
	75	5625
	94	8836
	116	13456
	100	10000
	85	7225
Sum =	959	108699

The sample mean is computed as follows:

x = 106.5

Also, the sample variance is

Therefore, the sample standard deviation s is

s = 28.5

the required confidence level is 90%.

The number of degrees of freedom are df = 9 - 1 = 8 , and the significance level is α=0.1.

Based on the provided information, the critical t-value for α=0.1 and df = 8 degrees of freedom is t_c = 1.86

The 90% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 90 % confidence for the population mean μ is

CI = (88.9, 124.2)

which completes the calculation.