Question

A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x overbar, is found to be 105, and the sample standard deviation, s, is found to be 10. (a) Construct a 90% confidence interval about mu if the sample size, n, is 24. (b) Construct a 90% confidence interval about mu if the sample size, n, is 20. (c) Construct an 80% confidence interval about mu if the sample size, n, is 24. (d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed? LOADING... Click the icon to view the table of areas under the t-distribution. (a) Construct a 90% confidence interval about mu if the sample size, n, is 24. Lower bound: nothing; Upper bound: nothing (Use ascending order. Round to one decimal place as needed.)

Answer #1

a)

sample mean 'x̄= | 105.000 |

sample size n= | 24.00 |

sample std deviation s= | 10.000 |

std error 'sx=s/√n= | 2.0412 |

for 90% CI; and 23 df, value of t= | 1.714 | |

margin of error E=t*std error = | 3.50 | |

lower bound=sample mean-E = | 101.50 | |

Upper bound=sample mean+E = | 108.50 | |

from above 90% confidence interval for population mean =(101.5, 108.5 ) |

b)

90% confidence interval for population mean =(101.1 , 108.9 )

c)

80% confidence interval for population mean =(102.3 , 107.7 )

d)

No since sample size is less than 30 , we Could not have computed the confidence intervals

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is normally distributed. The sample mean, x overbar, is found to
be 105, and the sample standard deviation, s, is found to be 10.
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simple random sample of size n is drawn from a population that
is normally distributed. The sample mean, x overbar, is found to
be 112, and the sample standard deviation, s, is found to be
10.
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sample size, n, is 19.
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and the sample standard deviation, s, is found to be 10.
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is normally distributed. The sample mean, x overbar, is found to
be 109, and the sample standard deviation, s, is found to be
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a
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is normally distributed. The sample mean, x overbar, is found to
be 111, and the sample standard deviation, s, is found to be 10.
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