To compare the effectiveness of three different types of phosphorescent coatings

Question

To compare the effectiveness of three different types of phosphorescent coatings on airplane instrument dials, eight dials each are coated with the three types. Then the dials are illuminated by an ultraviolet light, and the following are the number of minutes each glowed after the light source was shut off: Type 1: 52.9. 62.1. 57.4. 50.0. 59.3. 61.2. 60.8. 53.1 Type 2: 58.4. 55.0. 59.8. 62.5. 64.7. 59.9. 54.7. 58.4 Type 3: 71.3. 66.6. 63.4. 64.7. 75.8. 65.6. 72.9. 67.3 Test the null hypothesis that there is no difference in the effectiveness of the three coatings at the 0.01 level of significance. At the end of your analysis, present your findings in a table like the one shown below, which is taken from in Example 15.1 on page 429 of Miller and Miller's book. (You will get different numbers for your table.)

Explanation / Answer

Here there are three different types of phosphorescent coating.

Here we have to test the hypothesis that,

H0 : mu1 = mu2 = mu3

H1 : Atleast one of the mean is differ than 0.

Assume alpha = level of significance = 0.01

EXCEL steps :

Enter data in EXCEL sheet --> Data --> Data Analysis --> Anova : Single Factor --> Input : select all the data columns --> Grouped by : columns --> Alpha : 0.01 --> Output Range : select one empty cell --> ok

The test statistic is F = 17.04458

P-value = 4E-05 = 0.00004

P-value < alpha

Reject H0 at 1% level of significance.

Conclusion : At least one of the mean is differ than 0.

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