Question

The yields for the last six batches from a chemical reactor
are:

61.84, 61.18, 64.71, 62.83, 62.66, 62.47.

**Assuming that these yields form a random sample from a
normal population, but sample size is too SMALL to assume
s ≈ σ, construct a 99% confidence interval for the true
mean yield.**

t-values for tail area α | |||||
---|---|---|---|---|---|

ν | 0.100 | 0.050 | 0.025 | 0.010 | 0.005 |

1 | 3.078 | 6.314 | 12.706 | 31.821 | 63.657 |

2 | 1.886 | 2.920 | 4.303 | 6.965 | 9.925 |

3 | 1.638 | 2.353 | 3.182 | 4.541 | 5.841 |

4 | 1.533 | 2.132 | 2.776 | 3.747 | 4.604 |

5 | 1.476 | 2.015 | 2.571 | 3.365 | 4.032 |

6 | 1.440 | 1.943 | 2.447 | 3.143 | 3.707 |

7 | 1.415 | 1.895 | 2.365 | 2.998 | 3.499 |

8 | 1.397 | 1.860 | 2.306 | 2.896 | 3.355 |

9 | 1.383 | 1.833 | 2.262 | 2.821 | 3.250 |

10 | 1.372 | 1.812 | 2.228 | 2.764 | 3.169 |

Your answers can be rounded to three decimal digit accuracy when
entered.

Lower limit is = | Upper limit is = |

Answer #1

A polymer mixing process must be run until the blending is
complete. A random sample of nine runs measuring the time to
complete blending, were recorded as (in hours):
14.82, 13.16, 12.86, 12.4, 12.98, 12.88, 13.86, 13, 13.1.
Assuming blending times are normally distributed but sample
size is too SMALL to assume s ≈ σ, construct a 90%
confidence interval for the true mean blending time.
t-values for tail area α
ν
0.100
0.050
0.025
0.010
0.005
1
3.078
6.314...

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A simple random sample of size n is drawn. The sample mean, x
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(a) Construct a 95% confidence interval about mu if the
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Lower bound: ________;
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