Question

A bolt manufacturer wants to investigate the machine that produces bolts with a diameter of 0.28 centimeters. If the variance of the diameters is equal to 0.03, then the machine is working as expected. A random sample of 14 bolts has a standard deviation of 0.1741. Does the manufacturer have evidence at the α=0.01 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)

Ho : σ² = 0.03

Ha : σ² > 0.03

step 2)

Level of Significance , α = 0.01

Sample Size , n = 14

degree of freedom, DF=n-1 = 13

Upper Critical Value = 27.688

3)

sample Variance, s² = 0.1741^2 = 0.0303

Sample Size , n = 14

Chi-Square Statistic X² = (n-1)s²/σ² =
13.135

4)

test value < critical value, Do not reject the null
hypothesis

5)

we do not enough evidence to conclude that the variance of the
bolt diameters is more than required at α=0.01

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