The calculated value of F in a one-way analysis is 8.23. The numerator degrees of freedom and denominator degrees of freedom are 4 and 8, respectively. The most accurate statement to be made about the p-value is:
A) p-value > 0.05
B) 0.05 > p-value > 0.025
C) p-value > 0.01
D) 0.01 > p-value
One-way ANOVA is performed on three independent samples with: n1 = 6, n2 = 7 , and n3 = 8. The critical value obtained from the F-table for this test at the 2.5% level of significance equals:
A large annuity company holds many industry group stocks. Among the industries are banks, business services and construction. Seven companies from each industry group are randomly sampled to test the hypothesis that the mean price per share is the same among industries. The data are: Compute the F test statistic.
A randomized block experiment having five treatments and six blocks produced the following values: SSTR = 287, SST = 1,446, SSE = 180. The value of SSB must be:
In a two-way ANOVA, there are 3 levels for factor A and 4 levels for factor B, and three observations within each cell. The number of treatments in this experiment will be:
The solution provides answers of multiple choice questions from ANOVA.
1. Increasing the number of scores in a sample from n = 10 to n = 20 will increase the width of a confidence interval to estimate the population mean. (Assume all other factors are held constant.)
2. An educational psychologist gives a group of third-grade students a reading test at the beginning of the school year and again at the end of the year. The psychologist wants to use the data to estimate how much reading scores change during the year. The psychologist should use the independent-measures t statistic for the estimation.
3. A researcher uses a sample of n = 25 scores to construct a 90% confidence interval to estimate an unknown population mean. The correct interpretation of the confidence interval is:
None of these.
If another sample of n = 25 scores was selected, there is a 90% probability that the sample mean will be in the interval.
All of these.
There is a 90% probability that the unknown population mean is in the interval.
4. If the null hypothesis is true, the F-ratio for ANOVA is expected (on average) to have a value of 1.00.
5. In an analysis of variance, if all other factors are held constant, the larger the differences between the sample means, the bigger the value for the F-ratio.
6. The F-ratio for an analysis of variance comparing two treatments with n = 10 in each treatment would have df = 2, 18.
7. In an analysis of variance, which of the following is directly influenced by the size of the sample mean differences?
SS within treatments
All three SS values are influenced.
SS between treatments
8. Which of the following is not normally calculated as part of an analysis of variance?
9. A researcher uses an analysis of variance to test for mean differences among three treatment conditions using a sample of n = 10 participants in each treatment. The F-ratio from this analysis would have
df = 2, 29
df = 2, 27
df = 3, 27
df = 29
10. A researcher reports an F-ratio with df = 3, 36 from an independent-measures research study. Based on the df values, how many treatments were compared in the study and what was the total number of participants participating in the study?
2 treatments and 35 participants
3 treatments and 37 participants
4 treatments and 40 participants
4 treatments and 36 participants