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Although the Canadian and U.S. one-cent coins have slightly different - Canadian () Us. @ dimensions and alloy compositions, the two types of pennies have : 5 . similar masses. The table below lists the masses of individual pennies ! : 2551 2.508 2.499 from each country measured using the same balance. Compare the two sets of one-cent coins by determining , . eq- Refer to the table of Student's values as necessary. Assume that the population standard deviation (o) for each data set is the same. 2.561 2.522 2.492 2.541 2.531 2.336 2512 Are the masses of the Canadian and U.S. one-cent coins Lcalculuted = significantly different at the 98% confidence level? () The difference is not significant. () The difference is significant. 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 f value to compare these two data sets. For the second set of measurements, is there a significant fcaleulaied = difference in the masses of the two types of coins at the 98% confidence level? {::- The difference is significant. {::- The difference is not significant. 'For the final project of an analytical chemistry laboratory course, the students were asked to quantify the lead (Ph*) content in a drinking water sample. To receive a passing grade for the project, the students must produce a result (Ph** concentration) that agrees with the result obtained by the course professor, who was using the same method, at the 95% confidence level. The mean (x), standard deviation (s,) and number of replicate measurements (n) are shown for the data obtained by the professor (p) and one student (s) chosen at random. Student: xz = 4.220 ppb 55 = 0.229 ppb n, =0 Professor: x, = 4.870 ppb sp = 0.140 ppb np =16 Calculate the F value. ca]c - :} Are the standard deviations from the professor's and student's data sets significantly different from each other at the 95% confidence level? The value of F,;, can be found in the table of critical F values. () no O yes Calculate the value of , to compare the data sets from the student and the professor at the 95% confidence level. leale = Did the student receive a passing grade for the final project? A list of values can be found in the Student's table. O yes ) no The rare earth element gadolinium is often used as a contrasting agent for MRIs. The concentration of gadolinium was measured in the discharge from a wastewater treatment plant near a large medical facility. Eight measurements were obtained: 1.341 ppm, 1.346 ppm, 1.339 ppm, 1.331 ppm, 1.901 ppm, 1.336 ppm, 1.348 ppm, 1.334 ppm. Use the Grubbs test to determine if one of these values is an outlier. What 1s the value of Gege? Should this potential outlier be rejected with 95% Geate = |:I confidence? Critical values of & can be found in this table. () The potential outlier should be kept. () The potential outlier should be rejected. Based on the outcome of the Grubbs test, calculate the mean (x), standard deviation (s), and 99% confidence interval for the results. A list of values can be found in the Student's lable. condcncc imterval: ii : ppm You are checking the accuracy of a volumetric flask marked 10.00 mL. To Measurement Yolume (mL) calculate the volume of water contained in the flask, you first measure the mass of 1 10.046 the empty flask and the mass of the flask filled with water and take the difference. 2 10.060 Then. you correct for the buoyancy factor and divide by the density of the water. 3 10.021 The result of 8 such measurements is given in the table. 4 10.062 Calculate the mean and the 95% confidence interval for these measurements. 5 10.008 6 10.012 7 10.053 8 10.021 Can you, with 95% confidence, say that the nominal value of 10.00 mL can be the true volume of the flask? O no O yes