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Chapter 8: Q. R8.5 (page 548)

Engine parts A random sample of 16 of the more than 200auto engine crankshafts produced in one day was selected. Here are measurements (in millimeters) of a critical component on these crankshafts:

a. Construct and interpret a 95%confidence interval for the mean length of this component on all the crankshafts produced on that day.

b. The mean length is supposed to be μ=224mm but can drift away from this target during production. Does your interval from part (a) suggest that the mean has drifted from 224mm? Explain your answer.

Short Answer

Expert verified

Part a) The confidence interval is (223.971,224.0.33)

Part b) No, it has not drifted from24mm

Step by step solution

01

Part a) Step 1: Given information

The data set is

02

Part a) Step 2: The objective is to find out the 95%confidence interval for the mean length of the component.

We know,

The formula to compute the t- confidence interval for the population mean is:

CI=x¯±tα/2,df×sn

Because the population standard deviation is unknown, the t-confidence interval should be used.

The obtained excel output is:

Therefore, the required confidence interval is(223.971,224.033)

03

Part b) Step 1: The objective is to explain whether the mean has drifted from 224 mm 

The confidence interval is known from the preceding(223.971,224.033) Since the upper limit is224.033, which is greater than224. As a result, the mean cannot be said to have deviated from 224mm

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