Question

Four pharmaceutical drugs, suspected of decreasing the rate of growth of a brain tumour, were compared in an experiment involving 20 mice. The mice were randomly divided into four groups, with each group receiving one of the drugs in its diet. At the end of the experiment, the following data on tumour size were recorded. drugt <-c(3.64, 4.65, 5.33, 4.42, 5.64) drug2 <-c(5.64, 5.54, 4.98, 4.87, 3.96) drug3 <-c(8.74, 9.62, 8.72, 10.36, 9.66) drug4 <-c(9.34, 8.97, 8.91, 8.68, 9.35) Put the data in an R data frame with 20 rows and 2 columns. Column 1 should contain treatment labels generated as follows. drug <- rep(c(1:4), each = 5) Be sure to make this column a factor. The second column should have the above tumour sizes, stacked with the data for drugi followed by the data for drug2, etc. Compute an appropriate analysis of variance table using R. [A] How many degrees of freedom for treatments are there? [B] How many degrees of freedom for replication are there? [C] What is the value of the F statistic that tests all treatment means are equal? Report your answer to one decimal place. [D] What is the p-value for the above test? Report your answer to three decimal places. [E] Plot the data. What is the best interpretation of the plot? A. The differences in treatment means between the four drugs appear to be statistically insignificant compared to the variation within drugs. B. The differences in treatment means between the four drugs appear to be statistically significant compared to the variation within drugs. C. The differences in treatment means between any pair of drugs appears to be statistically significant compared to the variation within the two drugs. D. Some of the drugs appear to have treatment means that differ significantly from those of the other drugs, compared to the variation within drugs. E. The differences in treatment means between any pair of drugs appear to be statistically insignificant compared to the variation within the two drugs.

Answer 1

Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	95.9110	3	31.9703	78.1050	0.0000	3.2389
Within Groups	6.5492	16	0.4093
Total	102.4602	19

A) degree of freedom for treatment =3

B) degree of freedom for replication =16

C)Value of the test statistic F =78.1

D)p value =0..000

E)

D. Some of the drugs appear to have treatment means that differ significantly from those of the other drugs, compared to the variation within drugs.