The data in the accompanying table represent the compressive strength, in thousands of pounds per square inch (psi), of 20 samples of concrete taken two and seven days after pouring. A. Determine the test statistic & the critical values. B. What assumption is necessary about the population distribution in order to perform this test? C. Determine the P-value Interpret the meaning of the p-value.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The data in the accompanying table represent the compressive strength, in thousands of pounds per square inch (psi), of 20 samples of concrete taken two and seven days after pouring.
A. Determine the test statistic & the critical values.
B. What assumption is necessary about the population distribution in order to perform this test?
C. Determine the P-value Interpret the meaning of the p-value.
Given data along with d values
| sample | two days X | Seven days Y | d = X-Y |
| 1 | 3.765 | 4.570 | -0.805 |
| 2 | 3.205 | 3.540 | -0.335 |
| 3 | 2.680 | 3.805 | -1.125 |
| 4 | 3.800 | 4.070 | -0.270 |
| 5 | 2.895 | 3.250 | -0.355 |
| 6 | 3.295 | 3.430 | -0.135 |
| 7 | 3.035 | 3.595 | -0.560 |
| 8 | 2.830 | 3.340 | -0.510 |
| 9 | 2.830 | 3.505 | -0.675 |
| 10 | 3.590 | 3.915 | -0.325 |
| 11 | 2.935 | 3.630 | -0.695 |
| 12 | 3.265 | 3.700 | -0.435 |
| 13 | 3.000 | 4.005 | -1.005 |
| 14 | 3.605 | 3.720 | -0.115 |
| 15 | 2.980 | 3.985 | -1.005 |
| 16 | 3.080 | 3.140 | -0.060 |
| 17 | 2.005 | 2.690 | -0.685 |
| 18 | 2.750 | 3.250 | -0.500 |
| 19 | 3.825 | 4.170 | -0.345 |
| 20 | 2.895 | 2.915 | -0.020 |
| Sum | -9.96000 | ||
| Average | -0.49800 | ||
| sample std dev | 0.32165 |
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