Question

In a random sample of 37 criminals convicted of a certain crime, it was determined that the mean length of sentencing was 57 months, with a standard deviation of 12 months. Construct and interpret a 90% confidence interval for the mean length of sentencing for this crime. Select the correct choice below and fill in the answer boxes to complete your choice. (Use ascending order. Round to one decimal place as needed.)

A. There is a 90% probability that the mean length of sentencing for the crime is between nothing and nothing months.

B.We can be 90% confident that the mean length of sentencing for the crime is between nothing and nothing months.

C.90% of the sentences for the crime are between nothing and nothing months.

Answer #1

sample mean 'x̄= | 57.000 | |

sample size n= | 37 | |

std deviation s= | 12.000 | |

std error ='sx=s/√n=12/√37= | 1.9728 |

for 90% CI; and 36 df, value of t= | 1.6883 | |

margin of error E=t*std error = | 3.3307 | |

lower bound=sample mean-E = | 53.669 | |

Upper bound=sample mean+E = | 60.331 | |

from above
90% confidence interval for population mean
=(53.7<μ<60.3) |

**B.We can be 90% confident that the mean length of
sentencing for the crime is between 53.7 and 60.3
months.**

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