Although the Canadian and U.S. one-cent coins have slightly different dimensions and alloy compositions, the two types of pennies have similar masses. The table below lists the masses of individual pennies from each country measured using the same balance. Compare the two sets of one-cent coins by determining ?calculatedtcalculated. Refer to the table of Student's ?t values as necessary. Assume that the population standard deviation (σ) for each data set is the same. Find t-calculated. Are the masses of the Canadian and U.S. one-cent coins significantly different at the 98% confidence level? Suppose the number of replicate measurements and the average mass of an individual penny remain the same, but the standard deviation of each data set is three times greater than its original value. Calculate the t value to compare these two data sets. For the second set of measurements, is there a significant difference in the masses of the two types of coins at the 98% confidence level? Canadian (g) U.S. (g) 1 2.346 2.552 2 2.379 2.501 3 2.295 2.497 4 2.321 2.560 5 2.364 2.521 6 2.312 2.489 7 2.353 2.548 8 2.338 2.532 9 2.306 2.533 10 2.5
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.
Although the Canadian and U.S. one-cent coins have slightly different dimensions and alloy compositions, the two types of pennies have similar masses. The table below lists the masses of individual pennies from each country measured using the same balance. Compare the two sets of one-cent coins by determining ?calculatedtcalculated. Refer to the table of Student's ?t values as necessary. Assume that the population standard deviation (σ) for each data set is the same.
Find t-calculated.
Are the masses of the Canadian and U.S. one-cent coins significantly different at the 98% confidence level?
Suppose the number of replicate measurements and the average mass of an individual penny remain the same, but the standard deviation of each data set is three times greater than its original value. Calculate the t value to compare these two data sets.
For the second set of measurements, is there a significant difference in the masses of the two types of coins at the 98% confidence level?
| Canadian (g) | U.S. (g) | |
|---|---|---|
| 1 | 2.346 | 2.552 |
| 2 | 2.379 | 2.501 |
| 3 | 2.295 | 2.497 |
| 4 | 2.321 | 2.560 |
| 5 | 2.364 | 2.521 |
| 6 | 2.312 | 2.489 |
| 7 | 2.353 | 2.548 |
| 8 | 2.338 | 2.532 |
| 9 | 2.306 | 2.533 |
| 10 | 2.5 |
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