7.2 Estimating when is not known Key concepts: Use the steps below to find any c

Question

7.2 Estimating when is not known Key concepts: Use the steps below to find any confidence interval. Exploration 7.2.2. (Problem 16, page 365) Franchise: candy store Do you want to own your own candy store? With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for a franchise that specializes in candy sales. Startup costs (in thousands of dollars) for a random sample of candy stores is given below: 95, 173, 129,95,75,94, 116, 100, 85. (a) Compute the sample mean and the sample standard deviation s. Introduce the data in list Li. (b) Find a 90% confidence interval for the population average startup costs for candy store franchises Step 1. The confidence level: c- Step 2.1s known? YES or NO Step 3 . If is NOT known, then one needs to use Student's t distribution with df= (If is known one skips this step and uses z-critical values in Step 4) Step 4. The critical value is: tc- Step 5. The margin of error is: 2

Explanation / Answer

(a) sample mean x = 107.89

sample standard deviation s = 29.4425

(b) 90% confidence interval = x +- tdf,0.10 (s/n)

Step 1 : The confidence level : c = 0.10

Step 2 : Is known? - NO

Step 3 : dF = 9-1 = 8

Step 4 : Critical value tc for alpha = 0.10

tcritical = 1.8595

Step 5 : Margin of Error

MoE = tc . s/ n = 1.8595 * 29.4425/9 = 18.2494

Step 6 : 90% confidence interval = x +- tdf,0.10 (s/n)

= 107.8889 +- 1.8595 * (29.4425/9)

= (88.6390, 125.1388)

(c)

(d) Here CI means in this context of this problem that there is around 90% probability when we take samples of size 9 that if we take sample mean will be in the given confidence interval.

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