Question

An experiment was performed to compare the degradation of two different tools. Twelve samples of tool 1 were tested and ten samples of tool 2 were tested. In each case, the degradation was observed. The samples for tool 1 gave an average degradation of 15 units with a sample standard of 4, while the sample for tool 2 gave an average of 11 with a sample standard deviation of 5. Assume the population to be approximately normal. (a) Use a hypothesis test to determine if the population variances are equal considering a 0.10 level of significance. (b) Use hypothesis testing to determine if the degradation of tool 1 exceeds that of tool of tool 2 by more than 2 units considering a significance level of 0.05 You must use conclusion about the variance from part A to set up the problem in part B

Answer #1

a) Test for variances

n1, n2 | m1,m2 | s1,s2 | |

sample 1 | 12 | 15 | 4 |

sample 2 | 10 | 11 | 5 |

Perform an F test

F = variance of sample 2 / variance of sample 1 = 1.5625

F critical = 2.896 with (9 dof for numerator and 11 dof for denomiator) because dof = n - 1

Thus we fail to reject that the sample variances are equal.

b) Since the sample variances are equal, unknown but the samples are independent, we will use a pooled t test

null hypothesis is M(tool 1) - M(tool 2) >= 2

Sp2 = 20.05

T = -1.04

At 0.05 level of significance t critical = -2.528 approximately for a one-tailed test with 20 dof. Hence, we fail to reject the null hypothesis that the mean degradation from tool 1 exceeds the mean degradation from tool 2 by 2 units.

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