12.3 The F Distribution and the F-Ratio
Mean square between groups over mean square within, its two separate degrees-of-freedom counts, and the sums-of-squares table that assembles the whole calculation.
Introductory Business Statistics 2e, 12.3 The F Distribution and the F-Ratio
13 exercises
12.3 Exercise 1
As part of an experiment to see how different types of soil cover would affect slicing tomato production, Marist College students grew tomato plants under different soil cover conditions. Groups of three plants each had one of the following treatments
- bare soil
- a commercial ground cover
- black plastic
- straw
- compost
All plants grew under the same conditions and were the same variety. Students rec…
12.3 Exercise 3
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.
GPAs for four sports teams
Four sports teams took a random sample of players regarding their GPAs for the last year. The results are shown in the table.
Use a significance level of 5%, and determine if there is a difference in GPA among the teams.
12.3 Exercise 6
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…
12.3 Exercise 8
What is the Sum of Squares Factor?
12.3 Exercise 10
What is the df for the numerator?
12.3 Exercise 12
What is the Mean Square Factor?
12.3 Exercise 14
What is the F statistic?
12.3 Exercise 16
What is the df for the numerator?
12.3 Exercise 18
What is SSwithin?
12.3 Exercise 20
What is MSwithin?
12.3 Exercise 22
Judging by the F statistic, do you think it is likely or unlikely that you will reject the null hypothesis?
12.3 Exercise 24
Hα: At least any two of the group means µ1, µ2, …, µ5 are not equal.
degrees of freedom – denominator: df(denom) = ________
Adapted from Introductory Business Statistics 2e © 2023 Rice University. Licensed under CC BY 4.0. Source: Introductory Business Statistics 2e. Imported at revision 50ec917.