Question

1. A machine cuts steel to length for nails. The mean length of a nail is 43 millimeters. There is concern that the settings of the machine producing the nails have changed. To test the claim, 12 nails (n = 12) were sampled and given in the following table.

43.2

43.1

44

42.2

42.6

42

43.3

44.2

41.8

41.9

43

43.2

Required:

1. Develop the 99% confidence interval for the population mean length of the nail.

2. To decide if the sample data support the claim that the mean length is 43 millimeters, state your decision in terms

of the null hypothesis. Use a 0.05 level of significance.

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Answer 1

a)
sample mean, xbar = 42.88
sample standard deviation, s = 0.791
sample size, n = 12
degrees of freedom, df = n - 1 = 11

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, tc = t(α/2, df) = 3.106

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (42.88 - 3.106 * 0.791/sqrt(12) , 42.88 + 3.106 * 0.791/sqrt(12))
CI = (42.17 , 43.59)

b)
As CI includes 43, we fail to reject the null hypothesis

Evidence that the  mean length of a nail is 43 millimeters.