QUESTION 1 In a completely randomized design, 12 experimental units were used fo

Question

QUESTION 1

In a completely randomized design, 12 experimental units were used for the first treatment, 15 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance (to 2 decimals, if necessary).

At a .05 level of significance, is there a significant difference between the treatments?

The p-value is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 8

What is your conclusion?
SelectConclude not all treatment means are equalCannot reject the assumption all treatment means are equal

QUESTION 2

To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow.

Temperature 50°C: 33 29 26 23 30 60°C: 31 35 33 31 38 70°C: 22 33 31 26 34 Construct an analysis of variance table (to 2 decimals, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square F Treatments Error Total Use a .05 level of significance to test whether the temperature level has an effect on the mean yield of the process. Calculate the value of the test statistic (to 2 decimals).

QUESTION 3

The price drivers pay for gasoline often varies a great deal across regions throughout the United States. The following data show the price per gallon for regular gasoline for a random sample of gasoline service stations for three major brands of gasoline (Shell, BP, and Marathon) located in eleven metropolitan areas across the upper Midwest region (OhioGasPrices.com website, March 18, 2012).

Click on the webfile logo to reference the data.

Use  = .05 to test for any significant difference in the mean price of gasoline for the three brands. Round SS to 6 decimals, MS to 7 decimals, F to 2 decimals and p to 3 decimals, if necessary.

Source of Variation Sum of Squares Degrees of Freedom Mean Square F Treatments 1,100 Error Total 1,900

Explanation / Answer

Given k = 3 treatment conditions.

Total sample size N = n1 + n2 + n3 = 12 + 15 + 20 = 47

dfTreaments = k - 1 = 3 - 1 = 2

dfError = N - k = 47 - 3 = 44

SSError = SSTotal - SSbetween = 1900 - 1100 = 800

MSTreaments = SSTreaments /dfTreaments = 1100/2 = 550

MSError = SSError/dfError = 800/44 = 18.18

F = MSTreaments/MSError = 550/18.18 = 30.25

The correct option is:

For p-value, use excel formula =FDIST(30.25,2,44)

p-value = 0.0000

At a .05 level of significance, there is a significant difference between the treatments.

The p-value is less than .01.

SOURCE SS DF MS F Treatments 1100 2 550 30.25 Error 800 44 18.18 TOTAL 1900 46

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