Questions and Answers of OpenIntro Statistics

17.28 Of the 300 pages in a particular book, 180 pages are primarily nontechnical, while the remainder of the pages are technical. Independent random samples of technical and nontechnical pages were
17.27 The University of Jordan, the Middle East, is counting the mean research papers published per year by its faculty members—professors, senior lecturers, and lecturers. The university has 55
17.26 A researcher at Procter & Gamble (P&G) wants to determine the consumers’ satisfaction proportion on 3 different fabric softener brands—Downy (United States), Cuddly (Australia), and Makom
17.25 Carefully explain the distinction between stratified random sampling and cluster sampling. Provide illustrations of sampling problems where each of these techniques might be useful.
17.24 Alex Perry is an Australian fashion designer and television presenter, known for his womenswear. To estimate the mean time (in hours) taken by a tailor to create a woman’s gown, which will be
17.23 A cellphone technician wishes to estimate the average lifetime (in years) of a cellphone battery in the current market. In total there are 1183 different brands of cellphone battery selling in
17.22 A bank holds 720 delinquent mortgages in residential properties. It required an estimate of the mean current appraised value of these properties. Initially, a random sample of 20 was appraised,
17.21 A city is divided into 50 geographic subdivisions. An estimate was required of the proportion of households in the city interested in a new lawn-care service. A random sample of three
17.20 In the survey of Exercise 17.18, the clerical employees in the eight sampled subdivisions were asked if they were satisfied with the operation of the bonus plan.The results obtained are listed
17.19 In the survey of Exercise 17.17, the households were asked if they had cable television. The numbers having cable are given in the accompanying table.Precinct 1 2 3 4 5 6 7 8 9 10 Number 12 11
17.18 A property agent is investigating the average renting price per month for the factories in an area. In his study area, totally there are 8 types of factories. He randomly selected 4 different
17.17 An economist is studying the average profit earned by companies in Stuttgart, Germany. Assume that Stuttgart consists of 576 companies. A simple random sample of 10 companies was selected, and
17.16 Mean household income must be estimated for a town that can be divided into three districts. The relevant information is shown in the table.District Population Size Estimated Standard Deviation
17.15 The program director for Aarhus School of Business, Denmark, is analyzing the marks obtained by students from three different modules—Business Economics, and Political Science. For Business,
17.14 Refer to the data in Exercise 17.2. Determine the sample size for Copenhagen under each of the following schemes.a. Proportional allocationb. Optimum allocation for the overall population mean
17.13 A company has three divisions. To estimate the total amounts of the company’s accounts receivable, random samples of these accounts were taken for each of the three divisions, yielding the
17.12 Refer to the data in Exercise 17.4. Determine the sample size for female individuals in Porvoo, Finland, by under each of the following schemes.a. Proportional allocationb. Optimum allocation
17.11 Refer to the data in Exercise 17.3. Determine the sample size for Group 1 under each of the following schemes.a. Proportional allocationb. Optimum allocation for the overall population mean
17.10 Refer to Exercise 17.2. If a total sample of 130 faculty members is to be taken, determine how many of these should be full professors under each of the following schemes.a. Proportional
17.9 66°North, an outdoor apparel store in Iceland, is analyzing the defective items three items—parkas, trousers, and sweaters. From a total of 500 parkas, 780 trousers, and 720 sweaters, it
17.8 Bónus, an Icelandic supermarket chain, wants to know the level of consumer satisfaction derived from its four products—A, B, C, and D. The company’s sales records showed that 10,000
17.7 Of the 1,395 colleges in the United States, 364 have 2-year schools. In a random sample of 40 two-year schools, it was found that the text Statistics Can Be Fun was used in 10 of the schools. In
17.6 JM Property, a Nordic property developer, is considering the price for three housing subdivisions (apartment, single storey, and double storey) in Malmö, Sweden. Random samples of prices were
17.5 A college has 152 assistant professors, 127 associate professors, and 208 full professors. The college administration is investigating the amount of time these faculty members spend in meetings
17.4 In a stratified random sample of individuals—male and female—in Porvoo, Finland, sample members were asked to share the amount of time they spent on reading (in hours) per week. The results
17.3 A teacher would like to know the average height (in inches) of the students in her school. She divided the students into 4 groups based on their ages from the youngest to the oldest. The total
17.2 A researcher in Denmark is studying the reading habits of the people in the country. His sample that comprises three different cities—Aarhus, Esbjerg, and Copenhagen. Assume there are 150
17.1 A small town contains a total of 1,800 households. The town is divided into three districts, containing 820, 540, and 440 households, respectively. A stratified random sample of 300 households
17.2 Other Sampling Methods Cluster Sampling Two-Phase Sampling Nonprobabilistic Sampling Methods
17.1 Stratified Sampling Analysis of Results from Stratified Random Sampling Allocation of Sample Effort Among Strata Determining Sample Sizes for Stratified Random Sampling with Specified Degree of
16.43 Another equality topic addressed in the OECD’s gender studies is the pay gap. Using pay gap data in the data file OECD Pay Gap Data, develop a first-order and second-order autoregressive
16.42 Another equality topic addressed in the OECD’s gender studies is the pay gap. Using pay gap data in the data file OECD Pay Gap Data, develop a first-order and second-order autoregressive
16.41 Using the employment data in the data file OECD Employment Gap Data, based on the OECD employment gap studies, develop a first-order autoregressive model, including one lagged values as
16.40 Using the employment data in the data file OECD Employment Gap Data, based on the OECD employment gap studies, develop a second-order autoregressive model, including two lagged values as
16.39 Using the data file Product Sales, estimate autoregressive models of orders 1–4 for product sales. Using the procedure of Section 16.4 for testing the hypothesis that the autoregressive order
16.37 The data file Product Sales shows 24 annual observations on sales of a product. Use simple exponential smoothing with smoothing constant a = 0.5 to obtain forecasts of sales for the next 3
16.36 The data file Bank Assets shows the quarterly total assets (in trillions of kronor) of a large European bank over 17 years.a. Draw a time plot of these data. Does this graph suggest the
16.35 What is meant by the seasonal adjustment of a time series? Explain why government agencies expend a large amount of effort on the seasonal adjustment of economic time series.
16.34 A manager in charge of inventory control requires sales forecasts for several products, on a monthly basis, over the next 6 months. This manager has available monthly sales records over the
16.33 In many business applications, forecasts for future values of time series, such as sales and earnings, are made exclusively on the basis of past information on the time series in question. What
16.32 Explain the statement that a time series can be viewed as being made up of a number of components. Provide examples of business and economic time series for which you would expect particular
16.31 Refer to the data file Hourly Earnings, showing earnings over 24 months. Denote the observations xt 1t = 1, 2,c, 242. Now, form the series of first differences:zt = xt - xt-1 1t = 2, 3,c, 242
16.30 For many time series, particularly prices in speculative markets, the random walk model has been found to give a good representation of actual data. This model is written as follows:xt = xt-1 +
16.29 For a certain product it was found that annual sales volume could be well described by a third-order autoregressive model. The estimated model obtained was as follows:xt = 188 + 1.90xt-1 -
16.28 In Figure 16.10, fitted autoregressive models of orders 1 through 4 are given for annual sales data. We then selected a model by testing the null hypothesis of autoregression of order p - 1
16.27 From the data file Earnings per Share on corporate earnings per share, fit autoregressive models of orders 1 through 4. Use the procedure of this section to test the hypothesis that the order
16.26 Using the data file Housing Starts, estimate autoregressive models of orders 1 through 4. Use the method of this section to test the hypothesis that the order of the autoregression is p - 1
16.25 The data file Trading Volume shows the volume of transactions (in hundreds of thousands)in shares of a corporation over a period of 12 weeks.Using these data, estimate a first-order
16.24 Using the data in the data file Earnings per Share, estimate a first-order autoregressive model for the earnings per share. Use the fitted model to obtain forecasts for the next 4 days.
16.23 The data file Government Net Lending Euro Area contains the time series of general government net lending as a percent of the GDP for the Euro area countries. The dataset covers the period
16.22 The data file Government Spending France contains the time series of general government expenditures as a percent of the GDP for France. The dataset covers the period 2002:Q1 to 2019:Q4, for a
16.21 The data file Profit Margins shows percentages of profit margins of a corporation over a period of 11 years. Obtain forecasts for the next 2 years, using the Holt-Winters method with smoothing
16.20 As part of their studies into gender equality, the OECD publishes the employment gap data for several countries. Analyze the time series of women’s employment in Korea using the data file
16.19 The data file Hourly Earnings shows manufacturing hourly earnings in the United States over 24 months. Use the Holt-Winters procedure with smoothing constants a = 0.7 and b = 0.6 to obtain
16.18 As part of their studies into gender equality, the OECD publishes the employment gap data for several countries. Analyze the time series of men’s employment in Korea using the data file OECD
16.17 Comment on the following statement: We know that all business and economic time series exhibit variability through time. Yet if simple exponential smoothing is used, the same forecast results
16.16 Suppose that in the simple exponential smoothing method, the smoothing constant a is set equal to 1.What forecasts will result?
16.15a. If forecasts are based on simple exponential smoothing, with xn t denoting the smoothed value of the series at time t, show that the error made in forecasting xt, standing at time 1t - 12,
16.14 The data file High Yield Index contains the time series of the percent yield on bonds issued by European corporations. This yield is a measure of the return to investors of investing in these
16.13 The data file Housing Starts shows private housing units started per thousand of population in the United States over a period of 24 years. Using the data, employ the method of simple
16.12 The data file Gold Price shows the year-end price of gold (in dollars) over 14 consecutive years. Use the method of simple exponential smoothing, with a smoothing constant of a = 0.7, to obtain
16.11 The data file GDP Growth contains observations on the economic growth in Germany over the period 1992 to 2019. Use the method of exponential smoothing to obtain forecasts of the GDP growth rate
16.10a. Show that the centered s-point moving average series of Section 16.2 can be written as follows:x*t =xt-1s > 22 + 21xt-(s > 22+1 + g + xt+1s > 22-1) + xt+1s > 22 2sb. Show that x*t +1 = x*t
16.9 The data file Government Revenue Poland contains the time series of general government revenue as a percent of the GDP of Poland. The dataset covers the period 2002:Q1 up to 2019:Q4, for a total
16.8 Let x*t =1 2m + 1 am j= -m xt+j be a simple, centered 12m + 12-point moving average.Show that x*t +1 = x*t xt+m+1 - xt-m 2m + 1 How might this result be used in the efficient computation of
16.7 The data file High Yield Index contains the time series of the percent yield on bonds issued by European corporations. This yield is a measure of the return to investors of investing in these
16.6 The data file Housing Starts shows private housing units started per thousand of population in the United States over a period of 24 years.Compute a simple, centered 5-point moving average
16.5 The data file Gold Price shows the year-end price of gold (in dollars) over 14 consecutive years. Compute a simple, centered 3-point moving average series for the gold price data. Plot the
16.4 The data file Government Net Lending Euro Area contains the time series of general government net lending as a percent of GDP for the Euro area countries.The dataset covers the period 2002:Q1 up
16.3 The data file Government Spending France contains the time series of general government spending as a percent of the GDP for France. The dataset covers the period 2002:Q1 up to 2019:Q4, for a
16.2 The data file High Yield Index contains the time series of the percent yield on bonds issued by some European corporations from 1998 to 2021. This yield is a measure of the return to investors
16.1 The data file Housing Starts shows private housing units started per thousand of population in the United States over a period of 24 years. Use a computer to prepare a time plot of this series
16.5 Autoregressive Integrated Moving Average Models
16.4 Autoregressive Models
16.3 Exponential Smoothing The Holt-Winters Exponential Smoothing Forecasting Model Forecasting Seasonal Time Series
16.2 Moving Averages Extraction of the Seasonal Component Through Moving Averages
16.1 Components of a Time Series
15.73 Catherine Tate owns a restaurant in Maltby Street Market, London, and serves four different main dishes.She randomly recorded the time (in hours) spent at her restaurant by customers, grouped
15.72 Having carried out the study of Exercise 15.66, the investigator decided to take a second independent random sample of one student from each of the nine income–SAT score categories. The grade
15.71 In the study of Exercise 15.70, information on the cellular phone system was also shown to MBA students.Part of the analysis of variance table for their quality assessments is shown here.
15.70 Purchasing agents were given information about a cellular phone system and asked to assess its quality.The information given was identical except for two factors—price and country of origin.
15.69 Consider the two-way analysis of variance setup, with m observations per cell.a. Show that the between-groups sum of squares can be written as follows:SSG = Hm a Ki=1 x2i~~ - HKmx2b. Show that
15.68 Refer to Exercise 15.66 and consider the observation on moderate-income group and high SAT score 1x22 = 3.52.a. Estimate m.b. Estimate and interpret G2.c. Estimate and interpret B2.d. Estimate
15.67 For the two-way analysis of variance model with one observation per cell, write the observation from the ith group and jth block as Xij = m + Gi + Bj + eij Refer to Exercise 15.65 and consider
15.66 Students were classified according to three parental income groups and also according to three possible score ranges on the SAT examination. One student was chosen randomly from each of the
15.65 Three real estate agents were each asked to assess the values of five houses in a neighborhood. The results, in thousands of dollars, are given in the table. Prepare the analysis of variance
15.64 A delivery company manager needs information on the mean delivery time (in minutes) for five different locations in Sichuan, China—Chengdu, Leshan City, Garze, Jiuzhaigou County, and Daocheng
15.63 Consider the two-way analysis of variance setup, with one observation per cell.a. Show that the between-groups sum of squares can be written as follows:SSG = H a Ki=1 x2i~ - nx2b. Show that the
15.62 Consider the one-way analysis of variance setup.a. Show that the within-groups sum of squares can be written as follows:SSW = a Ki=1 ani j=1 x2 ij - a Ki=1 nix2 ib. Show that the between-groups
15.61 Dorris owns a homemade soymilk business and is looking for a machine that can produce the most soymilk within an hour. She collected 25 observations and measured the quantity of soymilk
15.60 For the data of Exercise 15.59, use the Kruskal-Wallis test to test the null hypothesis that the population mean spatula prices of same sizes are the same for four different materials. Use a
15.59 Independent random samples of the selling prices of same size spatula for four different materials were taken. The selling prices are shown in the following table. Test the null hypothesis that
15.58 The manager of an automobile repair shop is looking for a car battery that may troubleshoot the factors that shorten a car’s battery lifetime and ensure a longer battery life. Three car
15.57 A tourism study was conducted to analyze whether there is a significant difference in the average number of tourists (in millions) visiting a country per year against the yearly crime rate
15.56 A developer is hiring a construction company for their new project. The developer’s main concern is the project’s completion time. To determine the completion time for a construction
15.55 Different formulation of laundry detergents show different cleaning effects, and most laundry detergent brands are reformulated at least once a year. A manufacturer has reformulated its laundry
15.54 A farmer bought three different types of fertilizers from a seller and wants to know which fertilizer will yield the most tomatoes on his farm. According to the seller, the granular fertilizer
15.53 State the differences between the one-way analysis of variance and the two-way analysis of variance.
15.52 What is the objective of conducting the analysis of variance (ANOVA)? How does ANOVA work with random factors?
15.51 Having carried out the study of Exercise 15.34, the instructor decided to replicate the study the following year. The results obtained are shown in the table.Combining these results with those

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