Question

A study based on a random sample of 17 reported a sample mean of 65 with a sample standard deviation of 4.

- Calculate a 95% Confidence interval.

- What is the margin of error?

- If we calculated a 90% confidence interval, as compared to your answer in part b, would your margin of error increase: (choose one)

- increase
- decrease
- stay the same

- If we increase the sample size to 50 persons, but the reported sample mean and sample standard deviation stayed the same as in part a, would the 95% confidence interval get: (choose one)

- wider
- narrower
- stay the same

Answer #1

1)

sample mean 'x̄= | 65.000 |

sample size n= | 17.00 |

sample std deviation s= | 4.000 |

std error 'sx=s/√n= | 0.9701 |

for 95% CI; and 16 df, value of t= | 2.120 |

margin of error E=t*std error = | 2.057 |

lower bound=sample mean-E = | 62.9434 |

Upper bound=sample mean+E = | 67.0566 |

from above 95% confidence
interval for population mean =(62.94,67.06) |

2)

margin of error =2.057 ~ 2.06

3)margin of error

decrease

4)

95% confidence interval get narrower

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