Question

A bolt manufacturer wants to investigate the machine that produces bolts with a diameter of 0.23 centimeters. If the variance of the diameters is equal to 0.025. then the machine is working as expected. A random sample of 26 bolts has a standard deviation of 0.2318. Does the manufacturer have evidence at the α=0.1 level that the variance of the bolt diameters is more than required? Assume the population is normally distributed

Step 1 of 5: State the null and alternative hypotheses. Round to four decimal places when necessary.

Step 2 of 5: Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.

Step 3 of 5: Determine the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Make the decision

Step 5 of 5: What is the conclusion?

Answer #1

step 1:

Null hypothesis: Ho:
σ^{2} |
= | 0.025 |

Alternate hypothesis: Ha:
σ^{2} |
> | 0.025 |

Step 2 of 5:

for 10 % level and given df critical values of X2 = | 21.064 |

Step 3 of 5:

test statistic χ2=(n-1)s^{2}/σ^{2}= |
53.731 |

Step 4 of 5: since test statistic is higher than critical value , we reject null hypothesis

Step 5 of 5: we can conclude that the variance of the bolt diameters is more than required

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