A student team in a business statistics course performed a factorial experiment

Question

A student team in a business statistics course performed a factorial experiment to investigate the time required for pain-relief tablets to dissolve in a glass of water. The two factors of interest were brand name (Equate, Kroger, or Alka-Seltzer) and water tempearture (hot or cold). The experiment consisted of four replicates for each of the six factor combinations. The data (PainRelief.xlsx) show the time a tablet took to dissolve (in seconds) for the 24 tablets used in the experiment.

(a) At the 0.05 level of significance, is there an interaction between brand of pain reliever and water temperature?

(b) At the 0.05 level of significance, is there an effect due to brand?

(c) At the 0.05 level of significance, is there an effect due to water temperature?

Temperature Equate Kroger Alka-Seltzer Cold 85.87 75.98 100.11 Cold 78.69 87.66 99.65 Cold 76.42 85.71 100.83 Cold 74.43 86.31 94.16 Hot 21.53 24.10 23.80 Hot 26.26 25.83 21.29 Hot 24.95 26.32 20.82 Hot 21.52 22.91 23.21

Explanation / Answer

Here the summary table for Cold and Hot temeprature

Here below is the given excel output here to know the significance here

So we will use the table to solve these questions here

(a) Here for Interaction the F value = 20.7167 which gives us p - value = 2.14 x 10-5 that means there is significant interaction  between brand of pain reliever and water temperature

(b) Here for Brand, the F - value = 14.5666 which gives us p - value = 0.000173 < 0.05 so that also shows that there is significant effect due to different types of brand

(c) Here for Water temeprature, the F - value = 1986.507 that gives us p - value is very less 0.000000 < 0.05 so that there is very significant effect due to water temperature.

SUMMARY Equate Kroger Alka-Seltzer Total Cold Count 4 4 4 12 Sum 315.41 335.66 394.75 1045.82 Average 78.8525 83.915 98.6875 87.15167 Variance 24.91575833 28.6491 9.346158 94.40396 Hot Count 4 4 4 12 Sum 94.26 99.16 89.12 282.54 Average 23.565 24.79 22.28 23.545 Variance 5.834833333 2.477667 2.095667 3.984282

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