Although the Canadian and U.S. one-cent coins have slightly different dimensions

Question

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 leaktated. Are the masses of the Canadian and US. one-cent coins significantly different at the 98% confidence level? The table of Student's t values can be found here. Assume that the population standard deviation () for each data set is the same. Masses of individual pennies Canadian U.S O The difference is significant. Number The difference is not significant. 12.347 talculated 2.552 2.504 2493 2.371 2299 Suppose the number of replicate measurements and the average mass of an individual penny remain the same, but the standard deviation o each data set is three times greater than its original value. Calculate the t value to compare these two data sets. For these sets of measurements 2.557 2.521 2.486 2544 2.526 4 2.326 2.369 2.30i there a significant difference in the masses of the two types of coins at the 98% confidence level? 2.354 8 2.337 Number The difference is significant. 92.305 2.538 The difference is not significant 10 2.515 O

Explanation / Answer

The average mass of Canadian pennies (x) = 2.3362 g

The average mass of U.S. pennies(x) = 2.5236 g

Now, the tcalculated = 2.326

The 98% confidence level = x ± (ts/n1/2), where s = standard deviation and n = no. of observations

Here, the 's' value is the same for both the data sets.

Since, the x values are nearly same for both the data sets, the difference is not significant.

If the standard deviation of each data set is 3 times greater than its original value, i.e. 4*s

Now, the tcalculated = 2.326

Here also, the 's' value is the same for both the data sets (i.e. 4*s).

Since, the x values are nearly same for both the data sets, the difference is not significant.

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