Andrew and Bob are inspecting the quality of two types of bolts which are going to be used to replace current bolts in two different parts of an aircraft.
Andrew is inspecting the replacements for Bolt A, which are used to help secure a compartment in the cabin containing the pilot’s snacks. They should have a diameter of 1 cm. He takes a sample of 32 replacement bolts and produces a report about their suitability.
Bob is inspecting the replacements for Bolt B, which are used to help secure the engines to the wings. They should have a diameter of 8 cm. He takes a sample of 32 replacement bolts and produces a report about their suitability.
Bolt A (Andrew’ report)
Unbiased estimate of mean: 0.995 cm
Unbiased estimate of the variance: 0.012 cm2
Using a 99% confidence interval I found that the interval was entirely below 1 cm, so I have decided that Bolt A has FAILED.
Bolt B (Bob’s report)
Unbiased estimate of mean: 7.99 cm
Unbiased estimate of the variance: 0.052 cm2
Using an 80% confidence interval I found that the interval contained the value 8 cm, so I have decided that Bolt B has PASSED.
Find the confidence intervals, correct to 4 decimal places, that Andrew and Bob used.