Question

How much does a sleeping bag cost? Let's say you want a sleeping bag that should keep you warm in temperatures from 20°F to 45°F. A random sample of prices ($) for sleeping bags in this temperature range is given below. Assume that the population of x values has an approximately normal distribution.

55 | 105 | 110 | 115 | 100 | 50 | 30 | 23 | 100 | 110 |

105 | 95 | 105 | 60 | 110 | 120 | 95 | 90 | 60 | 70 |

(a) Use a calculator with mean and sample standard deviation
keys to find the sample mean price x and sample standard deviation
*s*. (Round your answers to two decimal places.)

x = | $ |

s = |
$ |

(b) Using the given data as representative of the population of prices of all summer sleeping bags, find a 90% confidence interval for the mean price μ of all summer sleeping bags. (Round your answers to two decimal places.)

lower limit | $ |

upper limit | $ |

Answer #1

Solution:

Part a

Xbar = 85.40

S = 29.33

(by using calculator or excel)

Part b

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 85.4

S = 29.32647448

n = 20

df = n – 1 = 19

Confidence level = 90%

Critical t value = 1.7291

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 85.4 ± 1.7291*29.32647448/sqrt(20)

Confidence interval = 85.4 ± 11.3390

Lower limit = 85.4 - 11.3390 = 74.06

Upper limit = 85.4 + 11.3390 = 96.74

Lower limit = 74.06

Upper limit = 96.74

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random sample of prices ($) for sleeping bags in this temperature
range is given below. Assume that the population of x values has an
approximately normal distribution.
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bag that should keep you warm in temperatures from 20°F to 45°F. A
random sample of prices ($) for sleeping bags in this temperature
range is given below. Assume that the population of x
values has an approximately normal distribution.
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110
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90
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bag that should keep you warm in temperatures from 20°F to 45°F. A
random sample of prices ($) for sleeping bags in this temperature
range is given below. Assume that the population of x
values has an approximately normal distribution.
110
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bag that should keep you warm in temperatures from 20°F to 45°F. A
random sample of prices ($) for sleeping bags in this temperature
range is given below. Assume that the population of x
values has an approximately normal distribution.
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random sample of prices ($) for sleeping bags in this temperature
range is given below. Assume that the population of x
values has an approximately normal distribution.
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