Question

Asked Jul 28, 2019

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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 | 179 | 131 | 94 | 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.)

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

Step 1

**(a) Computation of sample mean and sample standard deviation:**

Here, the sample size, *n =* 9. Using calculator, the sample mean is calculated as **108.2** and sample standard deviation is calculated as **31.2**, from the calculations given below.

Step 2

**(b) Confidence interval when population standard deviation is not known:**

The formula of confidence interval for the population mean when population standard deviation is not given is as follows.

Step 3

**Computation of 90% confidence interval for population mean:**

Here, the sample mean (*x-*bar) is 108.2.

The sample standard deviation (*s*) is 31.2.

The confidence level is 0.90.

Thus, the level of significance, *α* is 0.10 (= 1 – 0.90).

The degrees of freedom (*n* − 1) is 8 (=9 − 1).

For 90% confidence interval, the cr...

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