Question

the same brand/model. The university supplier has three different models. The lab manager has borrowed one of each of the three models for a week in order to test which one is the most reliable before deciding to do the purchase. A co-op student who works in the lab is assigned to test each pH meter seven times with a solution that has a known pH of 7. The plot below is the result of the pH analysis (of the solution) using the three different models of pH meter. Box and Whisker Chart of pH Analysis 7.6 I 7.4 7.2 I X Х 7- O Model 1 рн 6.8 O Model 2 6.6 O Model 3 6.4 6.2 pH Analyzer The collected data for two of the models (that were used to produce the plots) are presented in the table below, but the Model numbers of pH meters are missing!! pH Row 1 Model ? 7.2 6.6 6.8 7.0 7.4 6.5 7.5 Row 2 Model ? 6.3 6.7 7.4 7.3 7.4 7.5 7.0 a) Can you tell which pH meter model (box plot) do these rows of data belong to? You should calculate 3 appropriate parameters for each row that can justify your answer of what model each row belongs to. (6 marks) b) It is given that the actual standard deviation of the Model 1 is 0.16. Based on that and the collected sample, how confident can we be that the error of estimating true mean is less than 0.1? (3 marks) c) Based on the given plots and data set only, which pH meter model do you think is the most reasonable to purchase? Why? (2 marks)

Answer 1

Sol:

	Row 1	Row 2
	Model ?	Model ?
	7.2	6.3
	6.6	6.7
	6.8	7.4
	7	7.3
	7.4	7.4
	6.5	7.5
	7.5	7
Median	7	7.3
Quartile 1	6.6	6.7
Quartile 3	7.4	7.4

From the above data and the Box Plot, it is evident that Row 1 belongs to Model 3

From the above data and the Box Plot, it is evident that Row 2 belongs to Model 2

The mean standard deviation is  

0/Vn = 0.16/V1 = 0.0033

So We will be 1 - 0.0033 = 0.997 or 99.7% confident

From the given sample data the best model to purchase is model 1, since the values are evebly distributed, less inter-quartile range. So the readings will be consistent

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