Question

A simple random sample of 60 items resulted in a sample mean of 89. The population standard deviation is 18.

a. Compute the 95% confidence interval for the population mean

b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean

c. What is the effect of a larger sample size on the margin of error?

-increase - decrease -same - cannot determine

Answer #1

a)

sample mean 'x̄= | 89.000 |

sample size n= | 60.00 |

std deviation σ= | 18.000 |

std error ='σx=σ/√n= | 2.3238 |

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

margin of error E=z*std error = | 4.55 | ||

lower bound=sample mean-E= | 84.4455 | ||

Upper bound=sample mean+E= | 93.5545 |

from above 95% confidence interval for population mean
=(84.45,93.55) |

b)

sample size n= | 120.00 |

std deviation σ= | 18.000 |

std error ='σx=σ/√n= | 1.6432 |

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

margin of error E=z*std error = | 3.22 | |

lower bound=sample mean-E= | 85.7795 | |

Upper bound=sample mean+E= | 92.2205 |

from above 95% confidence interval for population mean
=(85.78,92.22) |

c)

**effect of a larger sample size on the margin of error :
decrease**

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