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(solution) The director of manufacturing at a textile mill needs to

The director of manufacturing at a textile mill needs to determine whether a new machine is producing a particular type of cloth according to the manufacturer's specifications, which indicate that the cloth should have a mean breaking strength of 40 kgs. The standard deviation is known to be 4 kgs. A sample of 49 pieces of cloth reveals a mean breaking strength of 39.1 kgs.

Is there evidence that the mean breaking strength is less than 40 kgs? Use a 1% test.

The population parameter of interest is | Answer 1Choose...? < 40reject H0µ ? 400.01z_stat is greater than 2.3263the mean breaking strength of all cloth0.11420.10do not reject H0z_stat is less than -2.3263 or z_stat is greater than 2.3263insufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgsµ ? 40z_stat is less than -2.3263-1.58sufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgs0.05? > 400.05711.58 |

The null hypothesis is | Answer 2Choose...? < 40reject H0µ ? 400.01z_stat is greater than 2.3263the mean breaking strength of all cloth0.11420.10do not reject H0z_stat is less than -2.3263 or z_stat is greater than 2.3263insufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgsµ ? 40z_stat is less than -2.3263-1.58sufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgs0.05? > 400.05711.58 |

The alternative hypothesis is | Answer 3Choose...? < 40reject H0µ ? 400.01z_stat is greater than 2.3263the mean breaking strength of all cloth0.11420.10do not reject H0z_stat is less than -2.3263 or z_stat is greater than 2.3263insufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgsµ ? 40z_stat is less than -2.3263-1.58sufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgs0.05? > 400.05711.58 |

The level of significance is | Answer 4Choose...? < 40reject H0µ ? 400.01z_stat is greater than 2.3263the mean breaking strength of all cloth0.11420.10do not reject H0z_stat is less than -2.3263 or z_stat is greater than 2.3263insufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgsµ ? 40z_stat is less than -2.3263-1.58sufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgs0.05? > 400.05711.58 |

H0 will be rejected if | Answer 5Choose...? < 40reject H0µ ? 400.01z_stat is greater than 2.3263the mean breaking strength of all cloth0.11420.10do not reject H0z_stat is less than -2.3263 or z_stat is greater than 2.3263insufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgsµ ? 40z_stat is less than -2.3263-1.58sufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgs0.05? > 400.05711.58 |

The test statistic is | Answer 6Choose...? < 40reject H0µ ? 400.01z_stat is greater than 2.3263the mean breaking strength of all cloth0.11420.10do not reject H0z_stat is less than -2.3263 or z_stat is greater than 2.3263insufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgsµ ? 40z_stat is less than -2.3263-1.58sufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgs0.05? > 400.05711.58 |

The p-value is | Answer 7Choose...? < 40reject H0µ ? 400.01z_stat is greater than 2.3263the mean breaking strength of all cloth0.11420.10do not reject H0z_stat is less than -2.3263 or z_stat is greater than 2.3263insufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgsµ ? 40z_stat is less than -2.3263-1.58sufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgs0.05? > 400.05711.58 |

The decision is | Answer 8Choose...? < 40reject H0µ ? 400.01z_stat is greater than 2.3263the mean breaking strength of all cloth0.11420.10do not reject H0z_stat is less than -2.3263 or z_stat is greater than 2.3263insufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgsµ ? 40z_stat is less than -2.3263-1.58sufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgs0.05? > 400.05711.58 |

Based on the sample, there is | Answer 9 |

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