Exam 12: One-Way Analysis of Variance

A study compares four groups with six observations in each group.How large does the F statistic need to be for rejecting the null hypothesis at the 5% significance level?

A service center for electronic equipment is conducting a study on three of their technicians: Joe,John,and James.All three specialize in repairing computer drives.The study was performed to study the service time of fixing the computer drives.The manager of the service center wishes to assess if the average service times for the three technicians are equal: H₀: ₁ = ₂ = ₃.Each technician was given a random sample of computer drives,and the service time for each was recorded.The ANOVA table and descriptive statistics are given below. What is the value of the coefficient of determination R²?

A contrast expresses an effect in the population as a combination of population means,of the form .The contrast can be estimated or tested using the sample data.Which of the following statements about or properties of contrasts is/are FALSE?

A study on color brightness for different types of projectors involved three different brands: A,B,and C.The projectors were rated for color brightness (a higher score means brighter colors).Random samples of 15 of the ratings from each brand were taken.The SPSS output from the analysis is (partially)given below. The SPSS output for the contrast ,which compares the color brightness of B to the average of the other two brands,is given below. What is the P-value for testing if the color brightness of B is significantly higher than the average of the other two brands?

A service center for electronic equipment is conducting a study on three of their technicians: Joe,John,and James.All three specialize in repairing computer drives.The study was performed to study the service time of fixing the computer drives.The manager of the service center wishes to assess if the average service times for the three technicians are equal: H₀: ₁ = ₂ = ₃.Each technician was given a random sample of computer drives,and the service time for each was recorded.The ANOVA table and descriptive statistics are given below. Under the null hypothesis of equality of population means,what is the appropriate model for the test statistic?

At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991.Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute.The resulting data were grouped by month of birth: January,May,and September: Crawling age is given in weeks.Assume the data represent three independent simple random samples,one from each of the three populations consisting of babies born in that particular month,and that the populations of crawling ages have Normal distributions. A partial ANOVA table is given below. What are the degrees of freedom for the groups term?

At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991.Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute.The resulting data were grouped by month of birth: January,May,and September: Crawling age is given in weeks.Assume the data represent three independent simple random samples,one from each of the three populations consisting of babies born in that particular month,and that the populations of crawling ages have Normal distributions. A partial ANOVA table is given below. What are the degrees of freedom for the error term?

In a study on scholastic test scores of entering college freshmen,a random sample of colleges across the nation is selected and the average SAT Math score for the freshman class is recorded.The colleges are categorized according to their affiliation: public,private,or church.Does it appear that freshmen entering the three different types of schools do equally well on the SAT Math? Computer output is included below. The value of the F statistic in the ANOVA table is reported as 5.696.The value of the corresponding P-value is 0.005.If we were to draw the F distribution and mark the value of 5.696 on the x axis,how would we indicate the P-value in the graph?

Battery life of tablet computers is of great concern to customers.A consumer group has tested four brands of such tablets to determine the battery life.Samples of tablets of each brand were fully charged and left to run until the battery died.The number of hours that each tablet lasted was recorded.The following graphs and tables from the analysis of the data are provided.(Note: Some entries have been omitted and replaced with _**.) How many degrees of freedom are there for error (DFE),and what is the value of the MSE?

In a study on scholastic test scores of entering college freshmen,a random sample of colleges across the nation is selected and the average SAT Math score for the freshman class is recorded.The colleges are categorized according to their affiliation: public,private,or church.Does it appear that freshmen entering the three different types of schools do equally well on the SAT Math? Computer output is included below. Under the null hypothesis of equality of population means,what is the distribution of the test statistic?

Which of the following statements about the one-way ANOVA model for i = 1,…,I and j = 1,…, Is/are FALSE?

It is widely believed that a person's level of fitness prior to undergoing corrective knee surgery is an important factor in the speed of rehabilitation following surgery.A study was undertaken with 24 randomly selected male subjects who were to undergo such surgery.The physical fitness status of each subject before the surgery was categorized as being below average (n = 8),average (n = 10),or above average (n = 6).Following surgery,the number of days spent in physical therapy by each patient until fully rehabilitated was determined.Examination of side-by-side boxplots indicated that it was reasonable to assume that the samples came from populations with equal standard deviations. The following ANOVA table was obtained.(Some entries have been replaced with _**.) What is the value of the estimate for the common population variance, ?

It is widely believed that a person's level of fitness prior to undergoing corrective knee surgery is an important factor in the speed of rehabilitation following surgery.A study was undertaken with 24 randomly selected male subjects who were to undergo such surgery.The physical fitness status of each subject before the surgery was categorized as being below average (n = 8),average (n = 10),or above average (n = 6).Following surgery,the number of days spent in physical therapy by each patient until fully rehabilitated was determined.Examination of side-by-side boxplots indicated that it was reasonable to assume that the samples came from populations with equal standard deviations. The following ANOVA table was obtained.(Some entries have been replaced with _**.) What are the values of the mean square for error (MSE)and the F statistic for testing the null hypothesis H₀: ?

Which of the following concerning the ANOVA model,procedures,and table is/are FALSE?