13.3 Facts About the F Distribution

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 percent and determine if there is a difference in GPA among the teams.

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…

Another fourth grader also grew bean plants, but in a jelly-like mass. The heights were (in inches) 24, 28, 25, 30, and 32. Do a one-way ANOVA test on the four groups. Are the heights of the bean plants different? Use the same method as shown in the example.

What happens to the curves as the degrees of freedom for the numerator and the denominator get larger?

What is the df(denom)?

What are the sum of squares and mean squares errors?

What is the p-value?

What is the df(num)?

What are the SS_between and MS_between?

What is the F Statistic?

At the 10 percent significance level, are the scores among the different groups different?

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 percent, test t…

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?

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…

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.