# A bolt manufacturer wants to  investigate the machine that produces  bolts with a diameter of 0.27 centimeter.  if the variance of the diameters is equal to  0.025,  then the machine is working as expected. a random sample of 11 bolts has a standard deviation of 0.3199.  does the manufacturer have evidence at the a =0.025 level that this variance of the bolt diemeters is more than required?assum the population is normally distributed.1.state the null and alternative hypothesis. round to 4 decimal places when necessary.2.determine the critical value of the test statistic.  If the test is two tailed, separate the values with a comma. Round to 3 decimal places.3.determine the value of the test statistic.  Round to 3 decimals.4. Make the decision to reject or fail hypothesis. 5. What is the conclusion?

Question

A bolt manufacturer wants to  investigate the machine that produces  bolts with a diameter of 0.27 centimeter.  if the variance of the diameters is equal to  0.025,  then the machine is working as expected. a random sample of 11 bolts has a standard deviation of 0.3199.  does the manufacturer have evidence at the a =0.025 level that this variance of the bolt diemeters is more than required?assum the population is normally distributed.

1.state the null and alternative hypothesis. round to 4 decimal places when necessary.

2.determine the critical value of the test statistic.  If the test is two tailed, separate the values with a comma. Round to 3 decimal places.

3.determine the value of the test statistic.  Round to 3 decimals.

4. Make the decision to reject or fail hypothesis.

5. What is the conclusion?

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Step 1

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Step 2

1.

Hypotheses:

Let σ be the true population standard deviation of the diameters of the bolts. The aim is to check whether the variance of the bolt diameters is more than required or not. The null and the alternative hypothesis is,

H0 : σ2 = 0.025

That is, the diameter is 0.025.

H1 : σ2 > 0.025.

That is, the diameter is more than 0.025.

Step 3

2.

Critical value:

For testing this, Chi-square test can be used.

The level of significance is α = 0.0...

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### Hypothesis Testing 