Analysis of Variance (57 problems)

Lengths (in feet) of a random sample of suspension bridges in the US, Europe, and Asia are shown. At a=.05, is there sufficient evidence to conclude that there is a difference in mean lengths?

If the null hypothesis is rejected use the Scheffe' test when the sample sizes are unequal to test the differences between the means, and use the Tukey test when the sample sizes are equal. Test at the .05 significance level.

State the hypotheses and identify the claim, find the critical value(s), compute the test value, make the decision, summarize the results, and explain where the differences in means are.

The head of the English dept. wants to determine if the average number of students taking an English course differs depending upon the time of day that the court is being offered.

If the null hypothesis is rejected use the Scheffe' test when the sample sizes are unequal to test the differences between the means, and use the Tukey test when the sample sizes are equal. Test at the .05 significance level.

State the hypotheses and identify the claim, find the critical value(s), compute the test value, make the decision, summarize the results, and explain where the differences in means are.

The head of the English dept. wants to determine if the average number of students taking an English course differs depending upon the time of day that the court is being offered.

Number of grams of fiber per serving for a random sample of 3 different kinds of foods is listed. It there sufficient evidence at the 0.05 level of significance to conclude that there is a difference in mean fiber content among breakfast cereals, fruits, and vegetable?

Numbers (in thousands) of farms per state found in 3 sections of the country are listed below. Test the claim at a=.05 that the mean number of farms is the same across these 3 geographic divisions.

Psychologists have found that people are generally reluctant to transmit bad news to their peers. This phenomenon has been termed the "MUM effect." To investigate the cause of the MUM effect, undergraduates at a certain university participated in an experiment. Each subject was asked to administer an IQ test to another student and then provide the test taker with his/her percentile score. (Unknown to the subject, the test taker was a bogus student who was working with the researchers.) The experimenters manipulated two factors, subject visibility and success of test taker, each at two levels Subject visibility was either visible or not visible to the test taker. Success of test taker was either top 20% or bottom 20%. Five subjects were randomly assigned to each of the 2 x 2 = 4 experimental conditions. Then the time (in seconds) between the end of the test and the delivery of the percentile score from the subject to the test taker was measured. (This variable is called the latency to feedback.) Describe the experiment, including the response variable, factors, factor levels, replications, and treatments.

a. Calculate the means

b. The MINITAB ANOVA printout is shown here. Test for interaction at the α = 0.05 level of significance.

Analysis of variance for response.

he chest deceleration data (g) are given below. Use a 0.05 significance level to test the null hypothesis that the different weight categories have the same mean. Do the data suggest that larger cars are safer?

Deliverable Length: 3-4 paragraphs

Details: A member of the management team at Widgecorp asks if an ANOVA test would be useful for any of the statistics you've produced to date.

Explain when an ANOVA test is useful. (You can find a description in the Presentation Resource for this Phase). Support your contention with three examples from your experience at other organizations or departments. Where applicable, for each example, indicate what are the treatments and blocking variables.

Objective: Explain analysis of variance, multivariate statistics, and non-parametric methods

Systolic Blood Pressure in Different Age Groups. A random sample of 40 women is partitioned into three categories with ages of below 20, 20 through 40, and over 40. The symbiotic blood pressure levels are obtained from Data Set 1 in Appendix B. The analysis of variance results obtained from Minitab are shown below.

a. What is the null hypothesis?

b. What is the alternative hypothesis?

c. Identify the value of the test statistic.

d. Identify the P-value.

e. Is there sufficient evidence to support the claim that the means for the different laboratories are not all the same?

A partially completed ANOVA table for a completely randomized design is shown below. How many treatments are involved in the experiment?

ANOVA: The following is a sample information. Test the hypothesis that the treatment means are equal. Use the 0.05 level of significance.

Treatment 1 Treatment 2 Treatment 3

State the null and alternative hypothesis.

State the decision rule.

What is the SST? SSE? SS Total? What is your decision regarding the hypothesis?

Chest Deceleration in a Car Crash. The chest deceleration data (g) are given below. Use a 0.05 significance level to test the null hypothesis that the different weight categories have the same mean. Do the data suggest that larger cars are safer?

For a randomized block experiment in which there are three treatments and two blocks, the calculated value of F = MSTR/MSE is 16.1. Using the 0.05 level of significance, what conclusion would be reached? Based on the F distribution tables, what is the most accurate statement that could be made about the p-value for the test?

In an analysis of variance comparing the output of five plants, data sets of 21 observations per plant are analyzed. The computed F statistic value is 3.6. Do you believe that there are differences in average output among the five plants? What is the approximate p-value? Explain.

An airline wishes to assess the amount of money spent on duty free purchases on an international flight by different types of passengers. The airline hires a consultant to conduct an analysis, and the consultant decides to categorize the passengers according to the fare type paid. 6 passengers in each fare category who made duty free purchases were selected at random. The total amounts of their purchases were as follows:

T1 = 457.61 T2 = 363.03 T3 = 357.16

a) Construct the analysis of variance table for this data.

b) Is there enough evidence to suggest a difference in the mean expenditures on duty-free purchases

based on the fare category of the passengers? Test your hypotheses with α = 0.05.

c) Use Tukey’s method of paired comparisons (α = 0.05) to identify the significant pairwise differences

between categories.

A randomized block design has five different age groups as blocks, and members of each block have been randomly assigned to the treatment groups shown here. For these data, use the 0.05 level in determining whether the treatment effects could all be zero. Using the 0.01 level, evaluate the effectiveness of the blocking variable.

A researcher at an accounting firm wants to out whether the current ratio for three industries is about the same. Random samples of eight firms in industry A, six firms in industry B, and six firms in industry C are available. The ratios are as follows:

Industry A: 1.38, 1.55, 1.90, 2.00, 1.22, 2.11, 1.98, 1.61

Industry B: 2.33, 2.50, 2.79, 3.01, 1.99, 2.45

Industry C: 1.06, 1.37, 1.09, 1.65, 1.44, 1.11

Conduct the test at = 0.05, and state your conclusion.

The data below represent the weight losses for people on three different exercise programs. At Alpha = 0.01, does it appear that a difference exists in the true mean weight loss produced by the three exercise programs?

Students in a large section of a biology class have been randomly assigned to one of two graduate students for the laboratory portion of the class. A random sample of final examination scores has been selected from students supervised by each graduate student, with the following results.

a. What are the null and alternative hypotheses for this test?

b. Use ANOVA and the 0.01 level of significance in testing the null hypothesis identified in part a.