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.

100 | 178 | 131 | 91 | 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 |

What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1 in the following scenarios? (Round your answers up the nearest whole number.)

(a) a preliminary estimate for *p* is 0.19

(b) there is no preliminary estimate for *p*

Answer #1

The statistical software output for this problem is :

(a)

x = 107.8

s = 31.1

(b)

Lower limit = 88.5

Upper limit = 127.0

Solution :

Given that,

margin of error = E = 0.1

Z_{/2}
= 1.96

(a)

= 0.19

1 - = 0.81

sample size = n = (Z_{
/ 2} / E)^{2} *
* (1 -
)

= (1.96 / 0.1)^{2} * 0.19 * 0.81

= 59.1

sample size = n = 60

(b)

= 0.5

1 - = 0.5

sample size = n = (Z_{
/ 2} / E)^{2} *
* (1 -
)

= (1.96 / 0.1)^{2} * 0.5 * 0.5

= 96.04

sample size = n = 97

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.
Do you want...

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 xvalues has an approximately normal
distribution.
91
177
134
91...

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
172
127...

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.
92
176
134...

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.
90
170
126...

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.
96
180
128...

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.
91
179
132...

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.
100 175 127...

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.
90
175
132...

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
178
135...

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