Exam 12: One-Way Analysis of Variance

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. The null hypothesis for the ANOVA F test is that the population mean crawling ages are equal for all three birth months.What is the alternative hypothesis?

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 _**.) What conclusion might one draw by looking at the side-by-side boxplots?

A study compares five groups with 10 observations in each group.An F statistic of 3.75 is reported.What are the degrees of freedom for this F statistic?

Quality ratings of a new line of take-home refrigerated entrées were obtained from three randomly formed groups of customers who were exposed to different types of advertisements about the product.One group,with 55 customers,saw ads that were designed to undermine their expected positive association of quality with advertisements;a second group of 36 customers saw ads that were designed to affirm their positive association of quality with advertisements;the third group with 36 subjects served as the control group.The following is the ANOVA table obtained from the data in the study.(Some entries have been replaced by _**.) What is the estimate of the common population standard deviation ?

At a large automobile factory,four different machines are used to produce disc brakes.To make sure that the disc brakes are all being produced with comparable diameters,daily samples of 16 disc brakes are taken from the production lines of each of the four machines and their diameters measured.The deviation from the goal diameter of 322 micrometers is measured to the nearest micrometer.Assume that the distribution of these deviations is approximately Normal with a common standard deviation.Does it appear that disc brakes made on the four machines are made with equal mean diameters? SPSS output is included below. What is the value of the estimate of the common population standard deviation?

A realtor wishes to assess whether a difference exists between home prices in three subdivisions.Independent samples of homes from each of the three subdivisions are obtained and their prices are recorded.The analysis of variance results for comparing these prices are provided below. What is the value of the estimate of the common population standard deviation of the populations of home prices in the three subdivisions?

At a large automobile factory,four different machines are used to produce disc brakes.To make sure that the disc brakes are all being produced with comparable diameters,daily samples of 16 disc brakes are taken from the production lines of each of the four machines and their diameters measured.The deviation from the goal diameter of 322 micrometers is measured to the nearest micrometer.Assume that the distribution of these deviations is approximately Normal with a common standard deviation.Does it appear that disc brakes made on the four machines are made with equal mean diameters? SPSS output is included below. Some summary measures for the four machines are given below. Suppose we are interested in the contrast that compares the average of machines 1,3,and 4 (the most recently purchased machines)to machine 2 (a slightly older model). Do the data show evidence of a violation of the assumption that the four populations have the same standard deviation?

Which of the following statements about the one-way ANOVA table is/are TRUE?

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. What is the value of the estimate of the common population variance?

Which of the following statements about one-way analysis of variance is/are TRUE?

A realtor wishes to assess whether a difference exists between home prices in three subdivisions.Independent samples of homes from each of the three subdivisions are obtained and their prices are recorded.The analysis of variance results for comparing these prices are provided below. Under the null hypothesis of equality of population means,what is the appropriate assumption for the distribution for home prices in the three populations?

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 is the value of the ANOVA F statistic for testing the equality of the population means?

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. How many computer drives were included in the study?

A realtor wishes to assess whether a difference exists between home prices in three subdivisions.Independent samples of homes from each of the three subdivisions are obtained and their prices are recorded.The analysis of variance results for comparing these prices are provided below. How many homes were sampled in total?

A study was conducted to compare five different training programs for improving endurance.Forty subjects were randomly divided into five groups of eight subjects in each group.A different training program was assigned to each group.After 2 months,the improvement in endurance was recorded for each subject.A one-way ANOVA is used to compare the five training programs,and the resulting F statistic is 3.69. What can we say about the P-value for this F test?

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 _**.) What conclusion might you reach based on these analyses?

Wild horse populations on federal lands have been protected since 1971.Since that time,the populations have grown large and need to be managed and kept to a supportable size.Management of the mustang population has been a controversial issue;one common method is periodic removal of the horses.Researchers were curious if a new method would work better.In 1985,12 horses were rounded up and male horses in the group of 12 were treated.The number of foals in each group of 12 horses for 3 years was recorded.Year 1 was prior to treatment,year 2 was the year the treatment was applied,and year 3 was 1 year after treatment.The average number of foals per group along with the standard deviation is given in the table below. The researchers did an ANOVA F test of the data and obtained the following results. What are the degrees of freedom for the F statistic?

A study was conducted to compare five different training programs for improving endurance.Forty subjects were randomly divided into five groups of eight subjects in each group.A different training program was assigned to each group.After 2 months,the improvement in endurance was recorded for each subject.A one-way ANOVA is used to compare the five training programs,and the resulting F statistic is 3.69. At a significance level of 0.05,what is the appropriate conclusion about mean improvement in endurance?

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 an estimate of the common standard deviation?

A storeowner wishes to compare the average amount of money high school and college students spend on music downloads.He randomly selects 10 students from three different student populations: high school,undergraduate,and graduate.The statistical assumptions required to perform a one-way ANOVA to compare the means of these three groups are reasonable based on the data.A partially completed ANOVA table is provided below. What is the value of the pooled standard deviation?