13.3 Facts About the F Distribution
Right-skewed, non-negative shape of the ratio distribution, and working a full analysis of variance through to a decision about the group means.
Introductory Statistics 2e, 13.3 Facts About the F Distribution
14 exercises
13.3 Exercise 2
There are multiple variants of the virus that causes COVID-19. The length of hospital stays for patients afflicted with various strains of COVID-19 is shown in the table.
Test whether the mean length of hospital stay is the same or different for the various strains of COVID-19. Construct the ANOVA table, find the p-value, and state your conclusion. Use a 5% significance level.
13.3 Exercise 5
A fourth grade class is studying the environment. One of the assignments is to grow bean plants in different soils. Tommy chose to grow his bean plants in soil found outside his classroom mixed with dryer lint. Tara chose to grow her bean plants in potting soil bought at the local nursery. Nick chose to grow his bean plants in soil from his mother's garden. No chemicals were used on the plants, on…
13.3 Exercise 8
What happens to the curves as the degrees of freedom for the numerator and the denominator get larger?
13.3 Exercise 10
What is the df(denom)?
13.3 Exercise 12
What are the Sum of Squares and Mean Squares Errors?
13.3 Exercise 14
What is the p-value?
13.3 Exercise 16
What is the df(num)?
13.3 Exercise 18
What are the SSbetween and MSbetween?
13.3 Exercise 20
What is the F Statistic?
13.3 Exercise 22
At the 10% significance level, are the scores among the different groups different?
Weights of Student Lab Rats
Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a significance level of 10%, test the hypo…
13.3 Exercise 29
Eliminate one magazine type that you now feel has a mean length different from the others. Redo the hypothesis test, testing that the remaining three means are statistically the same. Use a new solution sheet. Based on this test, are the mean lengths for the remaining three magazines statistically the same?
13.3 Exercise 31
Are the means for the final exams the same for all statistics class delivery types? the table shows the scores on final exams from several randomly selected classes that used the different delivery types.
Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance…
13.3 Exercise 33
Are the mean numbers of daily visitors to a ski resort the same for the three types of snow conditions? Suppose that the table shows the results of a study.
Assume that all distributions are normal, the four population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.
Adapted from Introductory Statistics 2e © 2023 Rice University. Licensed under CC BY 4.0. Source: Introductory Statistics 2e. Imported at revision 50ec917.