stats 8

An investigator conducts an experiment with four treatment groups. The response variable is growth of a plant during the experiment. She performs an​ F-test. What is the null hypothesis the researcher is testing with the​ F-test?

All four treatment groups have the same average growth of the plants during the experiment.

An investigator conducts an experiment with four treatment groups. The response variable is growth of a plant during the experiment. She performs an​ F-test. What is the alternative hypothesis the researcher is testing with the​ F-test?

At least one treatment group has a different average growth of plants during the​ experiment, but not all four necessarily have different mean growths.

If we use the amounts​ (in millions of​ dollars) grossed by movies in categories with​ PG, PG-13, and R​ ratings, we obtain the SPSS analysis of variance results shown below. Use a 0.01 significance level to test the claim that PG​ movies, PG-13​ movies, and R movies have the same mean gross amount.

Reject H0. There is sufficient evidence to warrant rejection of the claim that PG​movies, PG-13​movies, and R movies have the same mean gross amount.

SSE

SSE is the error sum of squares. It represents the variation within the samples. SSwithin

SST

SST is the total sum of squares. It represents the total variation among all the sample data.

SSTR

SSTR is the treatment sum of squares. It represents the variation among the sample means. SSbetween

Which of the following is NOT true when using​ one-way analysis of variance for testing equality of three or more population​ means?

Small F test statistics indicate that the decision is to reject the null hypothesis of equal means.

Which of the following is NOT a property of the F​ distribution?

The F distribution is bell shaped.

An experiment is conducted in which 68 participants each fill out a personality​ test, but not according to the way the participants see themselves.​ Instead, 17 are randomly assigned to fill it out according to the way they think their mothers see​ them; 17 as their fathers would fill it out for​ them; 17 as their best friends would fill it out for​ them; and 17 as the professors they know best would fill it out for them. The main results appear in the accompanying table. Explain these results to a person who has never had a course in statistics.

The null hypothesis is that the groups Mother, Father, Friend, and Professor are from populations of main personality scales with equal means. There are four such​ hypotheses, one each for Conformity, Extroversion, Maturity, and Self-Confidence. If the null hypothesis is true, the variance of these populations can be estimated in two ways.​ (i) Estimate from the variation within each of the four groups and then average them.​ (ii) Estimate from the variation between the four​ means, multiplying by the size of each sample group. Since the estimates should be approximately​ equal, the ratio of the two estimates should be approximately 1. If the null hypothesis is false, the estimate​ (ii) is greater than the estimate​ (i) and the​ ratio, F, of​ (i) to​ (ii) is greater than 1. The fact that F=4.27 is much larger than 1 and p<0.01 indicates that the null hypothesis for Conformity can be rejected. The fact that F=2.05 is not much larger than 1 indicates that the null hypothesis for Extroversion cannot be rejected. The fact that F=3.19 is much larger than 1 and p<0.05 indicates that the null hypothesis for Maturity can be rejected. The fact that F=3.62 is much larger than 1 and p<0.05 indicates that the null hypothesis for Self-Confidence can be rejected.

An​ F-curve has df=(15,7).

The number of degrees of freedom for the numerator is 15 The number of degrees of freedom for the denominator is 77.

The​ "treatment groups" or​ "model" source of variation in the Analysis of Variance table can also be thought of as​ ________ variation while the​ "error" of​ "residual" source of variation in the Analysis of Variance table can also be thought of as​ ________ variation.

The​ "treatment groups" or​ "model" source of variation in the Analysis of Variance table can also be thought of as between group mean variation while the​ "error" of​ "residual" source of variation in the Analysis of Variance table can also be thought of as within group variation.

When doing a multiple comparison method by performing​ two-sample t-tests comparing two group means at a​ time, the significance level on​ ________ two-sample​ t-test is​ ________ to keep the probability of making​ ________ ________ at some predetermined significance level.

When doing a multiple comparison method by performing​ two-sample t-tests comparing two group means at a​ time, the significance level on each two-sample t-test is reduced to keep the probability of making at least one Type I error at some predetermined significance level.

Suppose that a​ one-way ANOVA is being performed to compare the means of four populations and that the sample sizes are 17, 16, 16, and 11. Determine the degrees of freedom for the​ F-statistic.

df=(3, 56)

The​ F-statistic in a​ one-way Analysis of Variance problem has how many numerator degrees of​ freedom?

the number of groups being compared minus 1

The​ F-statistic in a​ one-way Analysis of Variance problem has how many denominator degrees of​ freedom?

the total sample size of all groups combined minus the number of groups being compared

The following question pertains to the anxiety scores for each of the three groups shown​ below: Treatment​ A: 1,​ 5, 3 Treatment​ B: 5,​ 3, 7 Treatment​ C: 10,​ 8, 12

​F(2,6) =​ 9.75, MSE​ = 4.00, p​ < .05

To study the effect of one factor on the mean of a response variable

​one-way ANOVA

To study the effect of two factors on the mean of a response variable

​two-way ANOVA