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Question 1 2 pts

(CO6) From a random sample of 55 businesses, it is found that the mean time that employees spend on personal issues each week is 4.9 hours with a standard deviation of 0.35 hours. What is the 95% confidence interval for the amount of time spent on personal issues?

(4.84, 4.96) |

(4.83, 4.97) |

(4.81, 4.99) |

(4.82, 4.98) |

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Question 2 2 pts

(CO6) If a confidence interval is given from 8.54 to 10.21 and the mean is known to be 9.375, what is the margin of error?

8.540 |

0.835 |

1.670 |

0.418 |

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Question 3 2 pts

(CO6) Which of the following is most likely to lead to a small margin of error?

small standard deviation |

large margin of error |

small mean |

large sample size |

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Question 4 2 pts

(CO6) From a random sample of 41 teens, it is found that on average they spend 31.8 hours each week online with a standard deviation of 5.91 hours. What is the 90% confidence interval for the amount of time they spend online each week?

(30.62, 32.99) |

(25.89, 37.71) |

(29.99, 33.61) |

(30.28, 33.32) |

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Question 5 2 pts

(CO6) A company making refrigerators strives for the internal temperature to have a mean of 37.5 degrees with a standard deviation of 0.6 degrees, based on samples of 100. A sample of 100 refrigerators have an average temperature of 37.70 degrees. Are the refrigerators within the 90% confidence interval?

No, the temperature is outside the confidence interval of (36.90, 38.10) |

No, the temperature is outside the confidence interval of (37.40, 37.60) |

Yes, the temperature is within the confidence interval of (37.40, 37.60) |

Yes, the temperature is within the confidence interval of (36.90, 38.10) |

Answer #1

1)

Solution :

Given that,

Point estimate = sample mean = = 4.9

Population standard deviation = = 0.35

Sample size = n = 55

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_{/2}
= Z_{0.025} = 1.96

Margin of error = E = Z_{/2}*
(
/n)

= 1.96 * (0.35 / 55)

= 0.09

At 95% confidence interval estimate of the population mean is,

- E < < + E

4.9 - 0.09 < < 4.9 + 0.09

4.81 < < 4.99

(4.81 , 4.99 )

2)

Given that,

Lower confidence interval = 8.54

Upper confidence interval = 10.21

= 9.375

Margin of error = E = Upper confidence interval - = 10.21 - 9.375 = 0.835

Margin of error = 0.835

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