Exam 12: Analysis of Variance

In conducting a one-way analysis of variance where the test statistic is less than the critical value, which of the following is correct?

A car company is interested in testing to see whether the mean miles that a car engine will last without changing oil is the same or different depending on which brand of oil is used. The engineers also wish to control for the type of transmission (manual or automatic) that is used. To conduct this test, the car company obtains enough engines so that all four oil brands can be tested in a design that involves no replication. Based on this information, how many engines will be needed to conduct the test?

Under the basic logic of one-way analysis of variance, if the within variation is large relative to the between variation, it is an indication that the population means are likely to be different.

A company's customer service department wants to compare the average service times at four different service locations. They want to conduct a hypothesis test to determine if all four means are the same or not. If n = 20 observations are taken at each of the four locations, then the degrees of freedom are D1 = 3 and D2 = 19.

Respond to the following questions using this partially completed one-way ANOVA table: How many different populations are being considered in this analysis?

The within sample variation is the dispersion that exists because the sample means for the various factor levels are not all equal.

The State Transportation Department is thinking of changing its speed limit signs. It is considering two new options in addition to the existing sign design. At question is whether the three sign designs will produce the same mean speed. To test this, the department has conducted a limited test in which a stretch of roadway was selected. With the original signs up, a random sample of 30 cars was selected and the speeds were measured. Then, on different days, the two new designs were installed, 30 cars each day were sampled, and their speeds were recorded. Suppose that the following summary statistics were computed based on the data: Based on these sample results and significance level equal to 0.05, what is the critical value for this hypothesis test?

A company has established an experiment with its production process in which three temperature settings are used and five elapsed times are used for each setting. The company then produces one product under each and measures the resulting strength of the product. The managers are mainly interested in determining whether the mean strength is the same at all temperature settings, but they know that controlling for process time is important. The following data were observed from the experiment: Based on these data and experimental design, the primary null hypothesis to be tested is H0 : μ1 = μ2 = μ3.

In conducing one-way analysis of variance, the population distributions are assumed normally distributed.

As a step in establishing its rates, an automobile insurance company is interested in determining whether there is a difference in the mean highway speeds that drivers of different age groups drive. To help answer this question, it has selected a random sample of drivers in three age categories: under 21, 21-50, and over 50. The engineers then recorded the drivers' speeds at a designated point on a highway in the state. The subjects were unaware that their speed was being recorded. The following one-way ANOVA output was generated from the sample data. Based upon this output, if the significance level is 0.05, the engineers should conclude that the mean speeds may all be equal since the p-value is less than alpha. ANOVA: Single Factor

A manager is interested in testing whether three populations of interest have equal population means. Simple random samples of size 10 were selected from each population. The following ANOVA table and related statistics were computed: Conduct the appropriate test of the null hypothesis assuming that the populations have equal variances and the populations are normally distributed. Use a 0.05 level of significance.

A two-factor analysis of variance is conducted to test the effect the price and advertising have on sales of a particular brand of bottled water. Each week a combination of particular levels of price and advertising are used and the sales level is recorded. The computer results are shown below. How many replications were used in this study?

A test is conducted to compare three different income tax software packages to determine whether there is any difference in the average time it takes to prepare income tax returns using the three different software packages. Ten different person's income tax returns are done by each of the three software packages and the time is recorded for each. Assuming that results show that blocking was effective, this means that:

Assume you are conducting a one-way analysis of variance using a 0.05 level of significance and have found that the p-value = 0.06. Which of the follow is correct regarding what you can conclude?

Damage to homes caused by burst piping can be expensive to repair. By the time the leak is discovered, hundreds of gallons of water may have already flooded the home. Automatic shutoff valves can prevent extensive water damage from plumbing failures. The valves contain sensors that cut off water flow in the event of a leak, thereby preventing flooding. One important characteristic is the time (in milliseconds) required for the sensor to detect the water leak. Sample data obtained for four different shutoff valves are contained in the file entitled Waterflow. Use the Tukey-Kramer multiple comparison technique to discover any differences in the average detection time. Use a significance level of 0.05.

A national car rental agency is interested in determining whether the mean days that customers rent cars is the same between three of its major cities. The following data reflect the number of days people rented a car for a sample of people in each of three cities. Assuming that a one-way analysis of variance is to be performed, the total sum of squares is computed to be approximately 120.9.

A study was conducted to determine if differences in new textbook prices exist between on-campus bookstores, off-campus bookstores, and Internet bookstores. To control for differences in textbook prices that might exist across disciplines, the study randomly selected 12 textbooks and recorded the price of each of the 12 books at each of the three retailers. You may assume normality and equal-variance assumptions have been met. The partially completed ANOVA table based on the study's findings is shown here: Based on the study's findings, was it correct to block for differences in textbooks? Conduct the appropriate test at the alpha = 0.10 level of significance.

The number of cells in a two-factor analysis of variance design is equal to the number of levels of factor A plus the number of levels of factor B.

Consider the following: How many populations are involved in this test?

In conducting one-way analysis of variance, the sample size for each group must be equal.