Question

You are given the sample mean and the population standard
deviation. Use this information to construct the 90% and 95%
confidence intervals for the population mean. Interpret the results
and compare the widths of the confidence intervals. From a random
sample of 72 dates, the mean record high daily temperature in a
certain city has a mean of 82.80^{0}F. Assume the
population standard deviation is 15.25^{0}F.

The 90% confidence interval is ( , ). (Round to two decimal places as needed.)

The 95% confidence interval is ( , ). (Round to two decimal places as needed.)

Which interval is wider? Choose the correct answer below. The 90% confidence interval The 95% confidence interval Interpret the results.

A. You can be certain that the population mean record high temperature is either between the lower bounds of the 90% and 95% confidence intervals or the upper bounds of the 90% and 95% confidence intervals.

B. You can be 90% confident that the population mean record high temperature is outside the bounds of the 90% confidence interval, and 95% confident for the 95% interval. C. You can be 90% confident that the population mean record high temperature is between the bounds of the 90% confidence interval, and 95% confident for the 95% interval.

D. You can be certain that the mean record high temperature was within the 90% confidence interval for approximately 65 of the 72 days, and was within the 95% confidence interval for approximately 68 of the 72 days.

Answer #1

1)

sample mean 'x̄= | 82.800 | |

sample size n= | 72 | |

std deviation σ= | 15.250 | |

std error ='σx=σ/√n=15.25/√72= | 1.7972 |

for 90 % CI value of z= | 1.645 | |

margin of error E=z*std error = | 2.956 | |

lower bound=sample mean-E= | 79.844 | |

Upper bound=sample mean+E= | 85.756 | |

from above
90% confidence interval for population mean
=(79.84,85.76) |

as above:

95% confidence interval for population mean
=(79.28,86.32) |

**C. You can be 90% confident that the population mean
record high temperature is between the bounds of the 90%
confidence interval, and 95% confident for the 95%
interval.**

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