Answered: Problem 6 The compressive strength of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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