8/4/2019 Chem 27.1 Homework 2 Hypothesis Testing

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Chem 27.1Homework No. 2: Hypothesis Testing

1. Before determining the amount of Na 2CO3 in an unknown sample, a student decides to check her procedure by analyzing asample known to contain 98.76% Na 2CO3. Five replicate determinations of the %w/w Na 2CO3 in the standard were madewith the following results: 98.71%, 98.59%, 98.26%, 98.44, 98.58%. Is the mean for these five trials significantly differentfrom the accepted value at the 95% confidence level?

2. A manufacturer s process for analyzing aspirin tablets has a known variance of 25. A sample of ten aspirin tablets is selected

and analyzed for the amount of aspirin, yielding the following results: 254, 249, 252, 252, 249, 249, 250, 247, 251, 252.Determine whether there is any evidence that the measurement process is not under statistical control at = 0.05.

3. Tables 1 and 2 show results for two separate experiments to determine the mass of a circulating 25-centavo coin.Determine: a) whether there is a difference in the means of these analyses at = 0.05; b) whether there is a difference inthe precisions of these analyses at = 0.05.

4. Marecek and colleagues developed a new electrochemical method for the rapid quantitative analysis of the antibioticmonensin in the fermentation vats used during its production. The standard method for the analysis, which is based on atest for microbiological activity, is both difficult and time-consuming. As part of the study, samples were taken at differenttimes from a fermentation production vat were analyzed for the concentration of monensin using both the electrochemicaland microbiological procedures. The results, in parts per thousand (ppt), are reported in Table 3. Determine whether thereis a significant difference between the methods at = 0.05.

5. The following masses, in grams, were recorded in an experiment to determine the average mass of a 25-centavo coin.3.067 3.049 2.514 3.048 3.079 3.094 3.109 3.102

Determine if there are any outlier(s) at = 0.05.

Table 1. Results for a determination of themass of a 25-centavo coin in circulation

Coin Mass (g)1 3.080

2 3.0943 3.1074 3.0565 3.1126 3.1747 3.198

Table 2. Results for a second determinationof the mass of a 25-centavo coin in circulation

Coin Mass (g)1 3.0522 3.1413 3.0834 3.0835 3.048

Table 3. Quantitative analysis of monensin in fermentation vats usingtwo methods

Sample Microbiological Electrochemical1 129.5 132.3

2 89.6 91.03 76.6 73.64 52.2 58.25 110.8 104.26 50.4 49.97 72.4 82.18 141.4 154.19 75.0 73.410 34.1 38.111 60.3 60.1