Answered: Problem 6 The compressive strength of…

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter29: Tolerance, Clearance, And Interference

Section: Chapter Questions

Problem 16A: Spacers are manufactured to the mean dimension and tolerance shown in Figure 29-12. An inspector...

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Problem 6

The compressive strength of concrete is being tested by a civil engineer. She tests 12 specimens and obtains the following data (in psi): 2213, 2256, 2247, 2203, 2225, 2304, 2289, 2287, 2312, 2252, 2274, 2295.

Part a

Assuming that the compressive strength is normally distributed, test the hypothesis that the mean strength is at least 2250 psi.

Part b

Refer to Problem 6. Now assume that the compressive strength is not normally distributed, and test the hypothesis that the median strength is at least 2250 psi. One way to do this is to notice that if the median is 2250 psi, then you can count how many of the samples have strengths above and below that value—i.e., the proportion of samples greater than 2250—compared to the proportion you would expect if the true median were indeed 2250 psi. If you view the data as being either above or below the median, you can calculate the related P-value.

Refer to Problem 6. Are the P-values from (a) and (b) similar? If not, can you explain why?

Problem 6
The compressive strength of concrete is being tested by a civil engineer. She tests 12 specimens and obtains
the following data (in psi): 2213, 2256, 2247, 2203, 2225, 2304, 2289, 2287, 2312, 2252, 2274, 2295.
Part a
Assuming that the compressive strength is normally distributed, test the hypothesis that the mean strength
is at least 2250 psi.

Part b
Refer to Problem 6. Now assume that the compressive strength is not normally distributed, and test the
hypothesis that the median strength is at least 2250 psi. One way to do this is to notice that if the median is
2250 psi, then you can count how many of the samples have strengths above and below that value i.e., the
proportion of samples greater than 2250-compared to the proportion you would expect if the true median
were indeed 2250 psi. If you view the data as being either above or below the median, you can calculate the
related P-value.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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