A production manager is interested in comparing the precision of two brands of stamping machines. From a random sample o

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A production manager is interested in comparing the precision of
two brands of stamping machines. From a random sample of 12 units
of output from the Brand A machine, a standard deviation of 15.2 is
reported for a quality characteristic. For the Brand B machine, in
a sample of 20 units of output, there is a standard deviation of
10.1. Is there sufficient evidence at the 5% significance level to
conclude that Brand B machines have a lower variance in quality?
Assume that the quality characteristic of both machines follows a
normal distribution.
1. Select the most appropriate hypothesis test that the
null hypothesis.
A) H_0: σ2 in A = σ2 in B; H_1: σ2 in A > σ2 in B
B) H_0: σ2 in A = σ2 in B; H_1: σ2 in A ≥ σ2 in B
C) H_0: σ2 in A < σ2 in B; H_1: σ2 in A > σ2 in B
D) H_0: σ2 in A ≤ σ2 in B; H_1: σ2 in A < σ2 in B
2. Select the most appropriate the form of the decision
rule where Fcalc and Fcrit are the test statistic and the critical
values
A) Reject if F_calc>F_crit
B) Reject if F_calc<F_crit
C) Reject if F_calc≤F_crit
D) Reject if F_calc=F_crit
3. What is the critical value?
4. What is the test statistics?
5. Select the most appropriate test results
A) Reject H_0 at the 1% level.
B) Reject H_0 at the 5% level
C) Reject H_0 at the 10% level
D) Failed to reject H_0 at the 10% level.