Chapter 13 Quiz
The marketing department of a company has assigned three different boxes for its product. It wants to determine which box will produce the largest amount of sales. Each box will be test marketed in five different stores for a period of a month. The information on sales is given below. Box 1: Store 1 = 210, Store 2 = 230, Store 3 = 190, Store 4 = 180, Store 5 = 190 Box 2: Store 1 = 195, Store 2 = 170, Store 3 = 200, Store 4 = 190, Store 5 = 193 Box 3: Store 1 = 295, Store 2 = 275, Store 3 = 290, Store 4 = 275, Store 5 = 265 What type of design does this experiment have? A) Randomized block design B) Completely randomized design C) Fisher's LSD design D) Cluster sampling design
A) Randomized block design
An experimental design that permits statistical conclusions about two or more factors is a: A) factorial design. B) randomized block design. C) randomized design. D) completely randomized design.
A) factorial design.
The F ratio in a completely randomized ANOVA is the ratio of _____. A) MSE/MSTR B) MSTR/MSE C) MST/MSE D) MSE/MST
B) MSTR/MSE
Which of the following is not a required assumption for the analysis of variance? A) The variance associated with the random variable must be the same for each population. B) The populations have equal means. C) The random variable of interest for each population has a normal probability distribution. D) At least two populations are under consideration.
B) The populations have equal means.
Which of the following options is not a required assumption for the use of ANOVA procedures? A) The variance of the response variable is the same for all of the populations. B) The sample size of each group must be 30 or more. C) For each population, the response variable is normally distributed. D) The observations must be independent.
B) The sample size of each group must be 30 or more.
An experimental design in which the treatments are randomly assigned to the experimental units is called a: A) randomized block design. B) completely randomized design. C) simple random sample design. D) matched samples design.
B) completely randomized design.
An experimental design that allows simultaneous conclusions about two or more factors is called a: A) randomized block experiment. B) factorial experiment. C) matched samples experiment. D) completely randomized experiment.
B) factorial experiment.
The test statistic for the Fisher's LSD test follows the: A) z distribution. B) t distribution. C) x^2 distribution. D) F distribution.
B) t distribution.
ANOVA procedures can be used to determine: A) whether the population standard deviations are equal. B) whether the population means are equal. C) whether the population variances are equal. D) whether the population sizes are equal.
B) whether the population means are equal.
An ANOVA procedure is used for data obtained from five populations. Five samples, each comprised of 10 observations, were taken from five populations. The null hypothesis for this ANOVA problem is: A) H0: μ1 = μ2 = μ3 = μ4. B) H0: μ1 = μ2 = μ3 = μ4 = μ5 = μ6 = μ7 = μ8 = μ9. C) H0: μ1 = μ2 = μ3 = μ4 = μ5. D) H0: μ1 = μ2 = μ3 = μ4 = μ5 = μ6 = μ7 = μ8 = μ9 = μ10.
C) H0: μ1 = μ2 = μ3 = μ4 = μ5.
To test whether there is a difference between treatments A, B, and C, a sample of 12 observations have been randomly assigned to the 3 treatments. The results are given below. Treatment A - Observations : 20, 30, 25, 33 Treatment B- Observations: 22, 26, 20, 28 Treatment C- Observations: 40, 30, 28, 22 Determine the p-value. A) 0.04 B) 0.19 C) 0.08 D) 0.39
D) 0.39
In an analysis of variance problem, if SST = 120 and SSTR = 80, then SSE is _____. A) 120 B) 200 C) 80 D) 40
D) 40 120 = 80 + ____
The marketing department of a company has assigned three different boxes for its product. It wants to determine which box will produce the largest amount of sales. Each box will be test marketed in five different stores for a period of a month. The information on sales is given below. Box 1: Store 1 = 210, Store 2 = 230, Store 3 = 190, Store 4 = 180, Store 5 = 190 Box 2: Store 1 = 195, Store 2 = 170, Store 3 = 200, Store 4 = 190, Store 5 = 193 Box 3: Store 1 = 295, Store 2 = 275, Store 3 = 290, Store 4 = 275, Store 5 = 265 Identify the factors and the blocks. A) The factors are the box designs, and the blocks are the sales. B) The factors are the stores, and the blocks are the box designs. C) The factors are the sales, and the blocks are the box designs. D) The factors are the box designs, and the blocks are the stores.
D) The factors are the box designs, and the blocks are the stores.
The process of using the same or similar experimental units for all treatments is called: A) confounding. B) randomization. C) stratification. D) blocking.
D) blocking.
The independent variable of interest in an ANOVA procedure is called _____. A) a factor B) a partition C) either a partition or a treatment D) a treatment
A) a factor
The Nestle Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to increase the productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs, and their output for a day's work has been recorded. The results are given below. Program A: 150, 130, 120, 180, 145 Program B: 150, 120, 135, 160, 110 Program C: 185, 220, 190, 180, 175 Program D: 175, 150, 120, 130, 175 State the null and alternative hypotheses. A) H0: x̄ 1 = x̄ 2 = x̄ 3 = x̄ 4 ; Ha: Not all of x̄ 1, x̄ 2, x̄ 3, and x̄ 4 are equal. B) H0: x̄ 1 = x̄ 2 = x̄ 3 = x̄ 4 = x̄ 5 ; Ha: Not all of x̄ 1, x̄ 2, x̄ 3, x̄ 4, and x̄ 5 are equal. C) H0: μ1 = μ2 = μ3 = μ4 ; Ha: Not all of μ1, μ2, μ3, and μ4 are equal. D) H0: μ1 = μ2 = μ3 = μ4 = μ5 ; Ha: Not all of μ1, μ2, μ3, μ4, and μ5 are equal.
C) H0: μ1 = μ2 = μ3 = μ4 ; Ha: Not all of μ1, μ2, μ3, and μ4 are equal.
The purpose of the randomized block design is to: A) distribute the differences between the groups equally. B) add an additional source of variation, improving upon the completely randomized design. C) control some of the extraneous sources of variation. D) isolate the treatment with the greatest effect.
C) control some of the extraneous sources of variation.
To determine whether the means of two populations are equal, _____. A) a chi-square test must be performed B) a t test must be performed C) either a t test or an analysis of variance can be performed D) an analysis of variance must be performed
C) either a t test or an analysis of variance can be performed
In an experimental design, another word used for the independent variable is the: A) level. B) design. C) factor. D) treatment.
C) factor.
The mean square is the sum of squares divided by _____. A) the sample size B) the total number of observations C) its corresponding degrees of freedom D) its corresponding degrees of freedom minus 1
C) its corresponding degrees of freedom
The process of allocating the total sum of squares and degrees of freedom is called _____. A) replicating B) blocking C) partitioning D) factoring
C) partitioning
The Nestle Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to increase the productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs, and their output for a day's work has been recorded. The results are given below. Program A: 150, 130, 120, 180, 145 Program B: 150, 120, 135, 160, 110 Program C: 185, 220, 190, 180, 175 Program D: 175, 150, 120, 130, 175 The ANOVA procedures provide enough evidence to conclude that the population means are not all equal. When carrying out the Fisher's LSD procedure to determine which mean is different from the others, using α = 0.05, what is the comparisonwise Type I error rate? A) 0.05 B) 0.20 C) 0.03 D) 0.01
A) 0.05
An experiment was designed in order to determine how to make the ideal steak. One factor that studied was how long the steaks marinated before being cooked: 30 minutes, 1 hour, 2 hours, and 4 hours. Another factor was the method used for cooking the steak: charcoal grill, gas grill, oven, or pan seared. Assume that 5 steaks will be cooked using each of the treatment combinations. Replication is a term used within experimental design. How many replications are used in this experimental design? A) 5 B) 20 C) 16 D) 80
A) 5
The process of allocating the total sum of squares and degrees of freedom into their corresponding sources is called: A) partitioning. B) factoring. C) replicating. D) blocking.
A) partitioning.
An experiment was designed in order to determine how to make the ideal steak. One factor that was studied was how long the steaks marinated before being cooked: 30 minutes, 1 hour, 2 hours, and 4 hours. Another factor was the method used for cooking the steak: charcoal grill, gas grill, oven, or pan seared. How many total treatment combinations were studied? A) 8 B) 16 C) 4 D) 12
B) 16
In a completely randomized design involving three treatments, the following information is provided: Sample Size: Treatment 1 = 5, Treatment 2 = 10, Treatment 3 = 5 Sample Mean: Treatment 1 = 4, Treatment 2 = 8, Treatment 3 = 9 The overall mean for all the treatments is: A) 7.00 B) 7.25 C) 6.67 D) 4.89
B) 7.25 (4)(5) + (8)(10) + (9)(5) / 5+10+5 = 145 / 20 = 7.25
The effect produced when the levels of one factor interact with the levels of another factor in influencing the response variable is called: A) Factorial Design B) Replication C) Confounding D) Interaction
D) Interaction
An experimental design where the experimental units are randomly assigned to the treatments is known as _____. A) factor block design B) random factor design C) systematic sampling D) completely randomized design
D) completely randomized design
The objects of interest in the experiment are called the: A) response variables. B) treatments. C) experimental factors. D) experimental units.
D) experimental units.
A term that means the same as the term "variable" in an ANOVA procedure is _____. A) variance within B) treatment C) replication D) factor
D) factor
The number of times each experimental condition is observed in a factorial design is known as a(n) _____. A) experimental condition B) partition C) factor D) replication
D) replication
The Nestle Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to increase the productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs, and their output for a day's work has been recorded. The results are given below. Program A: 150, 130, 120, 180, 145 Program B: 150, 120, 135, 160, 110 Program C: 185, 220, 190, 180, 175 Program D: 175, 150, 120, 130, 175 The ANOVA procedures provide enough evidence to conclude that the population means are not all equal. When carrying out the Fisher's LSD procedure to determine which mean is different from the others, using α = 0.05, what is the experimentwise Type I error rate? A) 0.26 B) 0.05 C) 0.01 D) 0.20
A) 0.26 1 - 0.95^6 = 0.2649 ≈ 0.26 *there are 6 different piecewise comparisons to make when carrying out the Fisher's LSD procedure, hence raising 0.95 to the 6th power.
In an analysis of variance problem involving three treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is _____. A) 14.8 B) 30.0 C) 13.32 D) 133.2
A) 14.8
An ANOVA procedure is used for data obtained from five populations. Five samples, each comprised of 10 observations, were taken from the five populations. The numerator and denominator (respectively) degrees of freedom for the critical value of F are _____. A) 4 and 45. B) 5 and 10. C) 4 and 49. D) 4 and 9.
A) 4 and 45. k - 1 => 5 - 1 = 4 n - k => 50 - 5 = 45
Six observations were selected from each of three populations. The data obtained is shown below. Sample 1: 31, 28, 34, 32, 26, 29 Sample 2: 37, 32, 34, 24, 32, 33 Sample 3: 37, 31, 32, 39, 30, 35 What type of experimental design was used? A) Completely randomized design B) Randomized design C) Factorial Design D) Randomized block design
A) Completely randomized design
What is the difference between a Complete block design and an incomplete block design? A) Complete block design indicates that every subject who has selected for the experiment agreed to participate. B) Complete block design indicates that all available subjects were utilized in the blocks. C) Complete block design indicates that the experiment was carried out to completion on every experimental unit. D) Complete block design indicates that each experimental unit of each block is subjected to all k treatments.
D) Complete block design indicates that each experimental unit of each block is subjected to all k treatments.
When carrying out an ANOVA from a randomized block design, which of the following options gives the degrees of freedom, respectively for the numerator and denominator of the test statistic? A) n - 1 and nT - k B) k - 1 and nT - k C) n - 1 and (k-1)(b-1) D) k - 1 and (k-1)(b-1)
D) k - 1 and (k-1)(b-1)
Statistical procedures that can be used to conduct statistical comparisons between pairs of population means are called: A) normal probability comparisons. B) ANOVA procedures. C) correlation analyses. D) multiple comparison procedures.
D) multiple comparison procedures.
The required condition for using an ANOVA procedure on data from several populations is that the _____. A) selected samples are dependent on each other B) sampled populations have equal means C) sampled populations are all uniform D) sampled populations have equal variances
D) sampled populations have equal variances
In the analysis of variance procedure (ANOVA), factor refers to _____. A) different levels of a treatment B) the dependent variable C) the critical value of F D) the independent variable
D) the independent variable
In ANOVA procedures, the between-treatments approach provides a good estimate of σ^2 only when: A) there are 3 or more treatments. B) the sample size of each treatment group is 30 or more. C) the alternative hypothesis is true. D) the null hypothesis is true.
D) the null hypothesis is true.
The ANOVA procedure is a statistical approach for determining whether the means of _____. A) two samples are equal B) more than two samples are equal C) two or more samples are equal D) two or more populations are equal
D) two or more populations are equal