Question

Do you want your own candy store? Wow! With some interest in running your own buisness and a decent credit rating, you can probably get a band loan on startup cosrs 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.

90 170 134 94 75 94 116 100 85

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean startip cost x and sample standard deviation s.

x=

s=

(b) Find a 90% confidence interval for the population average startup costs for candy store franchises

lower limit=

upper limit=

Answer 1

Part a

The sample size is n=9. The provided sample data along with the data required to compute the sample mean Xbar and sample variance s² are shown in the table below:

	X	X2
	90	8100
	170	28900
	134	17956
	94	8836
	75	5625
	94	8836
	116	13456
	100	10000
	85	7225
Sum =	958	108934

The sample mean Xbar is computed as follows:

Part b

The provided sample mean is Xbar=106.44 and the sample standard deviation is s=24.496. The size of the sample is n=9 and the required confidence level is 90%.

The number of degrees of freedom is 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 f=8 degrees of freedom is tc​=1.86.

The critical value is calculated using the standard normal distribution table

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

lower limit = 91.256

upper limit = 121.624