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elementary statistics
Questions and Answers of
Elementary Statistics
Following are the current prices and last year’s prices of a gallon of regular gas at a sample of 14 gas stations. Can you conclude that the median price is different now from what it was a year
Corn was grown on 12 plots of land. Half of each plot was treated with fertilizer A, and the other half was treated with fertilizer B. Yields in bushels per acre were as follows. Can you conclude
For the signed-rank test, we reject H0 when the value of the test statistic is _________________ than the critical value.In Exercises 3 and 4, fill in each blank with the appropriate word or phrase.
The signed-rank test does not require that the population be normal, but is does require that it be ________________ .In Exercises 3 and 4, fill in each blank with the appropriate word or phrase.
When performing the signed-rank test, we rank the absolute values of the differences.In Exercises 5 and 6, determine whether the statement is true or false. If the statement is false, rewrite it as a
When performing the signed-rank test, we reject H0 if the test statistic is greater than or equal to the critical value.In Exercises 5 and 6, determine whether the statement is true or false. If the
In Exercises 7–10, compute the test statistic and the critical value, and determine whether to reject H0 at the α = 0.05 level. Sample 1 73 48 38 45 42 32 75 66 56 58 46 54 Sample 2 59 32 22 15 30
In Exercises 7–10, compute the test statistic and the critical value, and determine whether to reject H0 at the α = 0.05 level. Sample 1 342 264 263 253 260 183 249 257 190 Sample 2 324 219 248
In Exercises 7–10, compute the test statistic and the critical value, and determine whether to reject H0 at the α = 0.05 level. Sample 1 67 51 54 52 53 51 47 56 52 64 58 Sample 2 75 60 56 44 62 53
In Exercises 7–10, compute the test statistic and the critical value, and determine whether to reject H0 at the α = 0.05 level. Sample 1 614 567 691 588 620 644 636 543 Sample 2 438 449 751 556
A sample of 12 students participated in an online tutoring program in mathematics. Each student took a pretest before the program started, and a posttest after completing the program. Following are
To determine whether rents are increasing in a certain town, an economist compared the current monthly rents for eight studio apartments with the rents for those same apartments one year ago. The
To determine whether traffic levels differ between the morning and evening rush hours, a traffic engineer counted the number of cars passing through a certain intersection during five-minute periods
A sample of nine men participated in a regular exercise program at a local gym. They were weighed both before and after the program. The results were as follows.Can you conclude that the median
A sample of 14 people attended a financial seminar. Each participant was given a 20-point financial literacy quiz both before and after the seminar with the following results.Can you conclude that
Hurricane Katrina made landfall in August 2005 causing the evacuation of numerous people from the area.The total number of births was observed each month for a year following the hurricane in the
Consider the following paired samples and their differences.a. Verify that the median of the sample differences is equal to 0.b. Compute the test statistic for the signed-rank test.c. Do you reject
Following is a sample from a population with median m. Use the sign test to test H0: m = 30 versus H1: m ≠ 30.a. What is the value of the test statistic?b. Is H0 rejected at the α = 0.05 level?c.
Following is a sample from a population with median m. Use the sign test to test H0: m = 20 versus H1: m > 20.a. What is the value of the test statistic?b. Is H0 rejected at the α = 0.05 level?c.
The sign test is performed to test H0: m = 42 versus H1: m ≠ 42.There are 19 plus signs, 5 minus signs, and 4 zeros.a. What is the value of the test statistic?b. Is H0 rejected at the α = 0.05
The sign test is performed to test H0: m = 250 versus H1: m < 250.There are 15 plus signs, 36 minus signs, and 6 zeros.a. What is the value of the test statistic?b. Is H0 rejected at the α = 0.05
n1 = 20, n2 = 30, S = 400, H1: m1 < m2.Exercises 5–7 present sample sizes and the sum of ranks for the rank-sum test. Compute μS, σS, and the value of the test statistic z. Then find the P-value.
n1 = 25, n2 = 32, S = 850, H1: m1 ≠ m2.Exercises 5–7 present sample sizes and the sum of ranks for the rank-sum test. Compute μS, σS, and the value of the test statistic z. Then find the
n1 = 15, n2 = 18, S = 280, H1: m1 > m2.Exercises 5–7 present sample sizes and the sum of ranks for the rank-sum test. Compute μS, σS, and the value of the test statistic z. Then find the P-value.
In Exercises 8–10, use the signed-rank test to test the null hypothesis that the population medians are equal. Compute the test statistic, the critical value, and determine whether to reject H0 at
In Exercises 8–10, use the signed-rank test to test the null hypothesis that the population medians are equal. Compute the test statistic, the critical value, and determine whether to reject H0 at
In Exercises 8–10, use the signed-rank test to test the null hypothesis that the population medians are equal. Compute the test statistic, the critical value, and determine whether to reject H0 at
Following are the number of runs scored by both teams in a sample of 20 Major League Baseball games played in a recent season.Can you conclude that the median is different from 8? Use the α = 0.05
Describe the assumptions necessary for the rank-sum test. How do they differ from the assumptions necessary for the two-sample t-test?
Describe a situation in which the signed-rank test would be preferable to the paired t-test. Describe a situation in which the paired t-test would be preferable to the signed-rank test.
Microorganisms play a crucial role in wastewater treatment by transforming solid organic matter into carbon dioxide and water. In a wastewater treatment system, the solids retention time is average
Prices for a gallon of regular gas were recorded for a sample of 12 gas stations, as shown below. Can you conclude that the median price is less than $4.00? Use theα = 0.05 level of
The registrar at a college sampled 30 students and recorded the GPA for each, as shown below. Can you conclude that the median GPA is less than 2.90? Use theα = 0.05 level of significance.a. State
A disadvantage of the sign test is that when the population is approximately normal the sign test is __________________ likely to reject a false null hypothesis than the t-test.In Exercises 3 and 4,
The sign test is valid for any continuous population.In Exercises 5 and 6, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
The test statistic for the sign test is the frequency of the most frequently appearing sign.In Exercises 5 and 6, determine whether the statement is true or false. If the statement is false, rewrite
Compute the value of the test statistic for the following sample, for testing H0: m = 10 versus H1: m ≠ 10. 14 11 9 3 42 14 11 95
Compute the value of the test statistic for the following sample, for testing H0: m = 50 versus H1: m < 50.
The sign test is performed to test H0: m = 35 versus H1: m ≠ 35.There are 16 plus signs, 4 minus signs, and 3 zeros.a. What is the value of the test statistic?b. Is H0 rejected at the α = 0.05
The sign test is performed to test H0: m = 500 versus H1: m < 500.There are 9 plus signs, 26 minus signs, and 2 zeros.a. What is the value of the test statistic?b. Is H0 rejected at the α = 0.05
A weight loss company claims that the median weight loss for people who follow their program is at least 15 pounds. Weight losses for a random sample of 20 people in the program were recorded, and
A sample of 12 movies released in a given year had the following running times, in minutes.Can you conclude that the median running time for movies released that year was greater than 120 minutes?
Heights, in feet, of a sample of 18 mature oak trees in a forest were measured. The results were as follows.Can you conclude that the median height of oak trees in this forest is greater than 60
The highest non-irrigated wheat yields in the United States are in the Palouse region of Eastern Washington and Northern Idaho. Following are hypothetical yields, in bushels, for 15 randomly selected
Monthly rents were recorded for a sample of 36 apartments in a certain city. The results were as follows.Can you conclude that the median rent is less than $1000 per month? Use the α = 0.05 level of
A random sample of 30 commuters were asked how long their typical morning commute is. The results, in minutes, were as follows.Can you conclude that the median commute time is less than 60 minutes?
The rates of fraud complaints (per 100,000 people)for the 20 largest metropolitan areas in the United States in a recent year are as follows.Can you conclude that the median fraud complaint rate is
The Gallup poll approval ratings for the United States Congress each month during a three-year period are as follows.Can you conclude that the median approval rating differs from 17? Use the α =
In a certain city, 45% of the households have no dog, 30% have one dog, 10% have two dogs, 10% have three dogs, and 5% have four dogs. The population median number of dogs is therefore 1.In a sample
Heart rates, in beats per minute, were measured for samples of 12 track athletes and 15 swimmers. The results are shown below. Can you conclude that the median heart rate is greater for swimmers than
Battery lifetimes, in hours, were measured for two types of batteries commonly used in laptop computers. Twelve batteries of one type and 13 of another type were tested.The results are shown below.
If two or more values are the same when assigning ranks, we assign them the _________________ of the preliminary ranks.In Exercises 3 and 4, fill in each blank with the appropriate word or phrase.
To use the normal approximation to find the P-value for a rank-sum test, both sample sizes must be at least _______________ .In Exercises 3 and 4, fill in each blank with the appropriate word or
To compute the test statistic for the rank-sum test, we sum the ranks of the larger sample.In Exercises 5 and 6, determine whether the statement is true or false. If the statement is false, rewrite
The null hypothesis for the rank-sum test is that the two population medians are equal.In Exercises 5 and 6, determine whether the statement is true or false. If the statement is false, rewrite it as
n1 = 15, n2 = 18, S = 244, H1: μ1 < μ2.In Exercises 7–10, compute μS, σS, and the value of the test statistic z. Then find the P-value for the specified alternate hypothesis and values of n1,
n1 = 20, n2 = 25, S = 607, H1: μ1 ≠ μ2.In Exercises 7–10, compute μS, σS, and the value of the test statistic z. Then find the P-value for the specified alternate hypothesis and values of n1,
n1 = 17, n2 = 23, S = 272, H1: μ1 ≠ μ2.In Exercises 7–10, compute μS, σS, and the value of the test statistic z. Then find the P-value for the specified alternate hypothesis and values of n1,
n1 = 14, n2 = 27, S = 308, H1: μ1 > μ2.In Exercises 7–10, compute μS, σS, and the value of the test statistic z. Then find the P-value for the specified alternate hypothesis and values of n1,
Gas mileages, in miles per gallon, were measured for samples of compact cars and midsize cars.The results were as follows.Can you conclude that the median mileage is less for compact cars than for
Prices of a 12-ounce latte (including tax) were determined at samples of coffee shops in two cities. The results were as follows.Can you conclude that the median price differs between the two cities?
In an experiment to determine the effect of curing time on the compressive strength of concrete blocks, two samples of 15 blocks each were prepared identically except for curing time. The blocks in
A new postsurgical treatment was compared to a standard treatment. Ten subjects received the new treatment, while 12 others (the controls) received the standard treatment. The recovery times, in
Times, in seconds, for a Blu-ray to load were measured for samples of standard Blu-ray players and 3-D Blu-ray players. The results were as follows.Can you conclude that the median load time for 3-D
The costs, in dollars, per load of laundry were measured for samples of high-efficiency detergents like those used in many front-loading washing machines and standard detergents. The results were as
Consider the following two samples.a. Compute the median of each sample to show that they are equal.b. Compute μS, σS, and the value of the test statistic z.c. Compute the P-value for testing H0:
Dental researchers conducted an investigation of the manufacture of dental resins in which the response variable was the hardness of the resin. The factors were the distance between the curing tip
Environmental scientists performed a two-factor experiment in which the response variable was the amount of an herbicide absorbed by a certain type of plant. The factors were the concentration of the
A psychiatrist studied the effects of three antidepressants on subjects in three different age groups. Each subject was rated on a scale of 0 to 100, with higher numbers indicating greater relief
Following are interaction plots for three data sets. Which data set has the largest interactions? Which has the smallest? A B C
When the effect of one factor depends on the level of another factor, an _________________ is present.In Exercises 5 and 6, fill in each blank with the appropriate word or phrase.
In two-way ANOVA, the factors can have two kinds of effects on the response: ________________ and _________________ .In Exercises 5 and 6, fill in each blank with the appropriate word or phrase.
In two-way ANOVA, we should not interpret the main effects when there are no interactions.In Exercises 7 and 8, determine whether the statement is true or false. If the statement is false, rewrite it
In two-way ANOVA, the results can be difficult to interpret if the design is unbalanced.In Exercises 7 and 8, determine whether the statement is true or false. If the statement is false, rewrite it
In a two-way ANOVA, the P-value for interactions is P = 0.45, and the P-values for the main effects are P = 0.023 for the row factor and P = 0.34 for the column factor.a. Can you reject the
In a two-way ANOVA, the P-value for interactions is P = 0.07, and the P-values for the main effects are P = 0.003 for the row factor and P = 0.014 for the column factor.a. Can you reject the
In Exercises 11–14, interpret the interaction plot by explaining whether there appear to be large interactions between the factors. Cell Mean A B Factor Level C
In Exercises 11–14, interpret the interaction plot by explaining whether there appear to be large interactions between the factors. Cell Mean A B Factor Level C
In Exercises 11–14, interpret the interaction plot by explaining whether there appear to be large interactions between the factors. Cell Mean A B Factor Level C
In Exercises 11–14, interpret the interaction plot by explaining whether there appear to be large interactions between the factors. Cell Mean A B Factor Level C
An education professor wants to find out which subject students find most difficult. She obtains final exam scores for three randomly selected freshmen and three randomly selected sophomores from
Vermont maple sugar producers sponsored a testing program to determine the benefit of a new fertilizer. A random sample of 27 maple trees in Vermont were chosen and treated with one of three levels
Construct and interpret an interaction plot for the data in Exercise 15.Exercise 15An education professor wants to find out which subject students find most difficult. She obtains final exam scores
Construct and interpret an interaction plot for the data in Exercise 16.Exercise 16Vermont maple sugar producers sponsored a testing program to determine the benefit of a new fertilizer. A random
A study was done to determine the effects of two factors on the latherability of soap. The two factors were type of water (tap or distilled) and glycerol (present or absent). The outcome measured was
An experiment was performed to measure the effects of two factors on the ability of cleaning solutions to remove oil from a piece of cloth. The factors were the concentration of soap (in percent by
Construct and interpret an interaction plot for the data in Exercise 19.Exercise 19A study was done to determine the effects of two factors on the latherability of soap. The two factors were type of
Construct and interpret an interaction plot for the data in Exercise 20.Exercise 20An experiment was performed to measure the effects of two factors on the ability of cleaning solutions to remove oil
Two parts will be fastened together with an adhesive. The adhesive will be applied to each part, and then the parts will be pressed together. Two types of adhesive are available. The amount of
The following table presents measurements of the tensile strength (in kilopascals) of asphalt-rubber concrete beams for three levels of binder content and three levels of rubber content.a. Can you
Construct and interpret an interaction plot for the data in Exercise 23.Exercise 23Two parts will be fastened together with an adhesive. The adhesive will be applied to each part, and then the parts
Construct and interpret an interaction plot for the data in Exercise 24.Exercise 24 The following table presents measurements of the tensile strength (in kilopascals) of asphalt-rubber concrete beams
An agricultural scientist performed a two-way ANOVA to determine the effects of three different pesticides on the yield of lemons, in pounds, from four different varieties of lemon tree. The
An online retailer sends many packages to customers. To investigate the quality of shipping, the retailer employed three firms to ship packages. Each firm was given four packages to ship at each of
A component can be manufactured according to either of two designs, and with either of two types of material.Two components are manufactured with each combination of design and material, and the
How many degrees of freedom are there for SSTr and for SSE?Exercises 1–4 refer to the following data:At a certain college, random samples of students with various majors were taken, and their grade
Compute the sums of squares SSTr and SSE and the mean squares MSTr and MSE.Exercises 1–4 refer to the following data:At a certain college, random samples of students with various majors were taken,
Compute the value of the test statistic F.Exercises 1–4 refer to the following data:At a certain college, random samples of students with various majors were taken, and their grade point averages
Can you conclude that there are differences in mean GPA among the majors? Use the α = 0.05 level of significance.Exercises 1–4 refer to the following data:At a certain college, random samples of
Can you reject the null hypothesis of no interactions? Explain.Exercises 5–7 refer to the following data:A machine shop has four machines used in precision grinding of bearings. Three machinists
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