Exam 16: Asking and Answering Questions About More Than Two Means

A market researcher wants to compare market prices for the same product made by several popular manufacturers. A random sample has been generated for the product of each manufactory. The information is presented in the table below. ​ Carry out multiple comparison procedure and interpret the results using 95% Tukey-Kramer confidence interval.

Professor wants to know whether her students have equally absorbed the themes of the learning term. During the term she conducted three in-class tests. The average scores of students were 71.8, 81.5 and 75.8 (with maximum of 100 points). Using the information above answer the question how should the professor define the difference between the three average in-class test scores.

A course work of a student is dedicated to the investigation of sleep. To begin with, it is important to establish whether there is a difference in the average duration of sleep for people of different age groups. For this purpose the student considers several random samples to study four age groups. ​ Carry out an ANOVA test and find the F and P values.

When you research question about the difference between three or more population means, the null hypothesis states that all the means are equal. Should the alternative hypothesis always state that at least two population means are not equal or it can vary? Explain why, or why not.

A company manufacturing details for the large machinery updates its milling machines. When at the first factory all the milling machines were replaced with the new ones, it was decided to conduct a study in order to define whether the average production time of one detail had decreased. For this purpose, at each of the company's factories (note that Factory A has only new milling machines and three other factories have both old and new milling machines), a sample determining the average production time of one detail had been generated. The result of this study is shown on the following underscoring pattern. Interpret this underscoring pattern.

When issuing a textbook, there is always a number of defective copies. The publishing house conducts a study to determine whether the number of defective copies depends on the format of the textbook. For the study, three random samples of textbook editions for the different book sizes were generated: a large portrait, a portrait, and a US letter, each of the editions has approximately equal number of copies. Twenty-one textbooks of each format were used for the study. Table containing summary data is presented below. Using a multiple comparison procedure identify differences between average number of defective copies. Use 95% Tukey-Kramer confidence interval. ​

Researcher investigates the average life expectancy of Americans by their ethnicity. He generates four random samples for each of the major ethnicity groups: White, African-American, Hispanic and Asian-American. The table below represents the summary data for the study. ​ Using a multiple comparison procedure identify differences between average precipitation for considered age cities. Use 95% Tukey-Kramer confidence interval.

The two main human blood group systems are the ABO and Rhesus (Rh) systems. According to the information of the American Red Cross ( "https://www.redcrossblood.org"), Rhesus Negative blood type is more rare than Rhesus Positive. A Researcher wants to know if the proportion of people with Rh (-) is equal for each ABO human blood type. To exclude the spread of people through the different ABO types, the researcher generates 10 random samples of equal size (100 people) for each of the ABO types, and draws attention to the number of people with RhD(-).The summary results of the blood test are represented in the table below. ​ Chose the correct null and alternative hypotheses statements for the F-test.

A recruitment agency provides a study of the average amount of time people work in IT companies. Four companies were considered for the study: big old company A, big new company B, small old company C and small new company D. In this study, a company is considered as new if it has been founded less than 20 years ago and considered as old if has been founded more than 50 years; small company has about 200 employees and big company has more than 1,000 employees. Is it correct to conduct an F-test for these four companies? Choose the correct statement.

Meteorologists study the climate of Texas. Using the data from the website ("http://www.usclimatedata.com" ), they estimate the average precipitation in inches for three cities: Austin, Dallas and San Antonio. The table below represents the summary data for the study. Using a multiple comparison procedure identify differences between average precipitation for considered age cities. Use 95% Tukey-Kramer confidence interval.

A researcher wants to know if people of different age groups spend the same time on purchasing goods and services. The researcher considers four age groups and conducts a survey using a random sample for each of these groups. Each person in the samples answers the question about how many hours does he or she spend per week on average on purchasing goods and services. The results are represented in the table below. Carry out an ANOVA F-test and interpret the results using the 95% confidence level.

A company has three branches, A, B, and C, located in different cities. Management of the company needs to estimate the efficiency of the work of each branch. The study considers the profit of each branch per a month (in million dollars) during the last year. Suppose that the samples are independent and have normal distributions. Results of the study are represented below. ​ Carry out an ANOVA test and find the F and P values.

The two main human blood group systems are the ABO and Rhesus (Rh) systems. According to the information of the American Red Cross ("https://www.redcrossblood.org" ), Rhesus Negative blood type is more rare than Rhesus Positive. A researcher wants to find out if the proportion of people with Rh(-) is equal for each ABO human blood type. The researcher consequently generates 10 random samples of equal size (100 people) four times, and pays attention to the number of people with RhD(-)The results of the blood test are represented in the table below. ​ The researcher notices that the sample means (people per hundred) are very different and he cannot use the null hypothesis . What did the researcher do wrong that he got the data unsuitable for the F-test? Choose the correct statement. What should the researcher do to make it possible to apply the F-test for the study?

Below are the input data for four F-tests. Choose a situation where the application of the F-test is most justified.

Professor is interested if the average scores of her students in the math class are equal during the learning term or not. She considers the scores of her students for three in-class tests, end-of-course exam and the final score. The final score is calculated by the following formula: . ​ Is it possible for the professor to carry out an ANOVA F-test using all five sample treatments? Choose the correct statement.

Meteorologists study the climate of Texas. Using the data from the website ("http://www.usclimatedata.com") they estimate the average precipitation in inches for three cities: Austin, Houston and San Antonio. Using a multiple comparison procedure the meteorologists identify the differences between the average precipitation level, in inches per month, for the considered three cities, and construct the Tukey-Kramer confidence interval for 95% Studentized range critical value. ​ Help the meteorologists to draw a correct conclusion about the differences between the average precipitation levels in these cities.

A researcher wants to find out if the best sprinters of the planet improve the racing time at world championships in the 100 meters running discipline among men. He considers the results of the final racings of the last three world championships and compares the average time in each final racing. These data are represented in the table below ("https://www.iaaf.org/results/iaaf-world-championships-in-athletics"). ​ ​ Carry out an ANOVA test and find the F and P values.

A technical support call center works every day, including weekends and public holidays. In order to test the expediency of working in weekends and public holidays, it is necessary to compare the intensity of calls coming to the call center within one working hour on a working day, on a weekend and on a public holiday. Three random samples of the numbers of calls received during an hour for working days, weekends and holidays were randomly generated. These samples can be considered representative for the population. The summary data are presented below. ​ Carry out an ANOVA F test and interpret the results using the 95% confidence level. ​

A researcher wants to know if people of different age groups spend the same time on purchasing goods and services. The researcher considers four age groups and conducts a survey using random sample for each of these groups. Each person answered the question, how many hours, on average, he or she usually spends on purchasing goods and services during a week. The results are represented in the table below. ​ Chose the correct null and alternative hypotheses statements. ​

At a large construction website, a construction service company has four teams that carry out facing works. The management of the company has decided to find out whether they work at the same speed or not. For each team, a sample of several typical pieces of work was generated and the number of days spent on its implementation was analyzed. Data for this analysis are presented below. ​ Carry out an ANOVA F-test and interpret the results using the 95% confidence level. ​