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. if convenient, use technology to construct the confidence intervals.

a random sample of 55 home theater systems has a mean price of $113.00. Assume the population standard deviation is $16.50

Answer #1

1)for 90% CI:

sample mean 'x̄= | 113.000 |

sample size n= | 55.00 |

std deviation σ= | 16.500 |

std error ='σx=σ/√n= | 2.2249 |

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

margin of error E=z*std error = | 3.660 | |

lower bound=sample mean-E= | 109.34 | |

Upper bound=sample mean+E= | 116.66 | |

from above 90% confidence interval for population mean
=(109.34,116.66) |

above interval gives 90% confidence to contain true value of population mean |

for 95% CI:

for 95 % CI value of z= | 1.960 | |

margin of error E=z*std error = | 4.361 | |

lower bound=sample mean-E= | 108.64 | |

Upper bound=sample mean+E= | 117.36 | |

95%
confidence interval for population mean
=(108.64,117.36) |
||

above interval gives 95% confidence to contain true value of population mean |

95% confidence interval has larger width.

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