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