Effects of two different catalysts and two different temperatures on the rate of a chemical reaction

  1. (2.5 points) A biochemist is interested in the effects of two different catalysts and two different temperatures on the rate of a chemical reaction.  She performs six replicates of a 22 design, making the runs in random order.  Analyze the rate of chemical reaction data that follow and draw appropriate conclusions.

 

Catalyst
Temperature 1 2
31 32 35 36
350 K 33 38 34 35
30 36 39 37
47 49 41 44
360 K 48 48 49 43
45 46 40 45

(2.5 points) An engineer suspects that the surface finish of a metal part is influenced by the feed rate and the depth of cut.  She selects three feed rates and four depths of cut.  She then conducts a factorial experiment and obtains the following data:

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Depth of Cut (in)
Feed Rate (in/min) 0.15 0.18 0.20 0.25
79 84 87 104
0.20 69 73 93 109
65 78 97 101
97 103 104 109
0.25 91 109 113 115
93 93 100 104
104 109 113 119
0.30 103 104 115 116
107 100 104 112

 

  1. Analyze the data and conclusions.  Use á = 0.05.
  2. (2.5 points) the effect of three different grades of gasoline on fuel economy in car engines is being studied.  Fuel economy is measured using brake-specific fuel consumption after the engine has been running for 15 minutes.  Five different car engines are available for the study, and the experimenters conduct the following randomized complete block design.
Car
Gasoline grade 1 2 3 4 5
1 0.545 0.685 0.530 0.445 0.550
2 0.510 0.644 0.497 0.339 0.522
3 0.523 0.605 0.498 0.410 0.520

 

  • Analyze the data from this experiment.

(b) Use the Bonferroni correction method to make comparisons among the three grades of gasoline to determine specifically which grades differ in brake-specific fuel consumption.

  1. (2.5 points) suppose that we are testing H0: µ = µ0 versus H1: µµ0.  Calculate the P-value for the following observed values of the test statistic:

(a) Z0 = 4.9

  • Z0 = -3
  • Z0 = 4.3
  • Z0 = 3.9
  • Z0 = -0.5

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