Question

A hair salon in Cambridge, Massachusetts, reports that on seven
randomly selected weekdays, the number of customers who visited the
salon were 72, 55, 49, 35, 39, 23, and 77. It can be assumed that
weekday customer visits follow a normal distribution. **[You
may find it useful to reference the t table.]**

**a.** Construct the 90% confidence interval for
the average number of customers who visit the salon on weekdays.
**(Round intermediate calculations to** **at
least** **4 decimal places, "sample mean" and "sample
standard deviation" to 2 decimal places****.**
**Round " t" value to 3 decimal places and final
answers to 2 decimal places.)**

**b.** Construct the 99% confidence interval for
the average number of customers who visit the salon on weekdays.
**(Round intermediate calculations to** **at
least** **4 decimal places, "sample mean" and "sample
standard deviation" to 2 decimal places****.**
**Round " t" value to 3 decimal places and final
answers to 2 decimal places.)**

**c.** What happens to the width of the interval as
the confidence level increases?

A: As the confidence level increases, the interval becomes narrower and less precise.

Or

B: As the confidence level increases, the interval becomes wider and less precise.

Answer #1

Values ( X ) | ||

72 | 484 | |

55 | 25 | |

49 | 1 | |

35 | 225 | |

39 | 121 | |

23 | 729 | |

77 | 729 | |

Total | 350 | 2314 |

Mean

Standard deviation

Part a)

Confidence Interval

Lower Limit =

Lower Limit = 35.5765

Upper Limit =

Upper Limit = 64.4235

90% Confidence interval is ( 35.58 , 64.42 )

Width of CI = 64.42 - 35.58 = 25.84

part b)

Confidence Interval

Lower Limit =

Lower Limit = 22.4812

Upper Limit =

Upper Limit = 77.5188

99% Confidence interval is ( 22.48 , 77.52 )

Width of CI = 77.52 - 22.48 = 55.04

part c)

B: As the confidence level increases, the interval becomes wider and less precise.

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