A Machine Produces Pipes Used in Airplanes

question 29

Essay

A machine produces pipes used in airplanes. The average length of the pipe is 16 inches. The acceptable variance for the length is .3 inches. A sample of 25 pipes was taken. The average length in the sample was 15.95 inches with a variance of .4 inches.
a.Construct a 95% confidence interval for the population variance.
b.State the null and alternative hypotheses to be tested.
c.Compute the test statistic.
d.The null hypothesis is to be tested at the 5% level of significance. State the decision rule for the test using the critical value approach.
e.What do you conclude about the population variance?

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Definitions:

Range

The difference between the highest and lowest values in a set of numbers, indicating the spread or dispersion of the dataset.

Empirical Rule

The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two, and 99.7% within three.

Normal Curve

A symmetrical, bell-shaped curve that represents the distribution of values, deviations, or probabilities for a set of data in which most measurements cluster around the mean.

Bell-Shaped

A bell-shaped curve is a graph of a distribution that resembles the shape of a bell, typically representing a normal distribution in which the bulk of the values lie towards the center and taper off symmetrically towards the extremes.