Question

In a study to compare the visibility of paints used on highways, four different types of paint were tested at three different locations. It is to be expected that paint wear will differ depending on the quantity and type of traffic on the road, so Highway was used as a blocking factor. The following table gives the amount of visibility of paint after a set period of exposure to traffic and weather; visibility was measured on a standard scale, with larger values indicating greater visibility.

Paint Type	1	2	3	4
Highway A	10	11.3	10.3	11.8
Highway B	6.2	9.2	9.2	?
Highway C	7.6	9.9	9.8	?
	7.93	10.13	9.77	11.3

Noting that two of the data points have not been shown, carry out calculations for the following questions using only a calculator and appropriate summary statistics. The overall data standard deviation is 1.607. A partial ANOVA table is given below. Compute the values needed to fill in the blanks.

Source	DF	SS	MS	F
Paint Type
Highway			4.73
Error
Total

Compute the value of the Paint Type degrees of freedom. 3 [1 pt(s)]

Compute the value of the Highway degrees of freedom. 2 [1 pt(s)]

Compute the value of the Error degrees of freedom. 6 [1 pt(s)]

Incorrect.

Tries 1/3

Previous Tries

Compute the value of the Paint Type sum of squares.  [2 pt(s)]

Compute the value of the Highway sum of squares.  [1 pt(s)]

Compute the value of the Total sum of squares.  [1 pt(s)]

Compute the value of the Error sum of squares.  [1 pt(s)]

Compute the value of the Paint Type mean sum of squares.  [1 pt(s)]

Compute the value of MSE.  [1 pt(s)]

What are the numerator degrees of freedom for the main factor F-statistic?  [1 pt(s)]Compute the value of the main factor (Paint Type) F-statistic.  [3 pt(s)]

What are the denominator degrees of freedom for the main factor F-statistic?  [1 pt(s)]

Which interval in the table contains the p-value for the test? (Use the table on the course site.)
p-value ≤ 0.001
0.001 < p-value ≤ 0.01
0.01 < p-value ≤ 0.05
0.05 < p-value ≤ 0.1
0.1 < p-value ≤ 0.25
p-value > 0.25
[1 pt(s)]

Compute the value of the block (Highway) F-statistic.  [3 pt(s)]

What are the numerator degrees of freedom for the block F-statistic?  [1 pt(s)]

What are the denominator degrees of freedom for the block F-statistic?  [1 pt(s)]

Which interval of the table contains your computed block (Highway) p-value? (Use the table on the course site.)
p-value ≤ 0.001
0.001 < p-value ≤ 0.01
0.01 < p-value ≤ 0.05
0.05 < p-value ≤ 0.1
0.1 < p-value ≤ 0.25
p-value > 0.25
[3 pt(s)]

Source	DF	SS	MS	F
Paint Type
Error
Total

Suppose now that Highway is not used as a block and that Paint Type is the only factor, with 3 replicates. Compute the values needed to fill in the blanks.

Compute the value of the Error degrees of freedom.  [1 pt(s)]

Compute the Error sum of squares.  [1 pt(s)]

Compute the value of MSE.  [1 pt(s)]

Compute the factor (Paint type) F-statistic.  [3 pt(s)]

Which interval of the table contains your computed factor (Paint type) p-value? (Use the table on the course site.)
p-value ≤ 0.001
0.001 < p-value ≤ 0.01
0.01 < p-value ≤ 0.05
0.05 < p-value ≤ 0.1
0.1 < p-value ≤ 0.25
p-value > 0.25
[3 pt(s)]

I really need help with these please! I have only one try on these answers and it is due soon. I would appreiate any help recieved.

Thank you!

Answer 1

The answers are given in the images ...