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statistical sampling to auditing
Statistical Methods For The Social Sciences 5th Global Edition Alan Agresti - Solutions
Other things being equal, quadrupling the sample size causes the width of a confidence interval to (a) double,(b) halve, (c) be one quarter as wide, (d) stay the same.
Increasing the confidence level causes the width of a confidence interval to (a) increase, (b) decrease, (c) stay the same.
The reason we use a z-score from a normal distribution in constructing a confidence interval for a proportion is that(a) For large random samples, the sampling distribution of the sample proportion is approximately normal.(b) The population distribution is normal.(c) For large random samples, the
To use the large-sample confidence interval for a proportion, you need at least 15 outcomes of each type.Show that the smallest value of n for which the method can be used is (a) 30 when πˆ = 0.50, (b) 50 when πˆ = 0.30,(c) 150 when πˆ = 0.10.That is, the overall nmust increase as πˆ moves
The publication Attitudes towards European Union Enlargement from Eurobarometer states, “The readers are reminded that survey results are estimations, the accuracy of which rests upon the sample size and upon the observed percentage. With samples of about 1000 interviews, the real percentages
You would like to find the proportion of bills passed by a ruling party in a certain country that were vetoed by the president in the last five years. After checking the records, you see that for the population of all 44 bills passed, 2 were vetoed. Does it make sense to construct a confidence
Explain the reasoning behind the following statement:Studies about more diverse populations require larger sample sizes. Illustrate for the problem of estimating mean income for all medical doctors in a country compared to estimating mean income for all entry-level employees at a restaurant in the
How does population heterogeneity affect the sample size required to estimate a population mean? Illustrate with an example.
Give an example of a study in which it would be important to have(a) A high degree of confidence.(b) A high degree of precision.
Why would it be unusual to see a (a) 99.9999%,(b) 25% confidence interval?
Explain why confidence intervals are wider with(a) larger confidence levels, (b) smaller sample sizes.
An interval estimate for a mean is more informative than a point estimate, because with an interval estimate you can figure out the point estimate, but with the point estimate alone you have no idea about the width of the interval estimate.(a) Explain why this statement is correct, illustrating
What is the purpose of forming a confidence interval for a parameter? What can you learn from it that you could not learn from a point estimate?
(a) Explain what it means for an estimator to be unbiased.(b) Explain why the sample range is a biased estimator of the population range.
The observations on daily TV watching for the 15 subjects in a 2016 survey who were obese were 0, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 8. A 95% confidence interval for the mean of the corresponding population is (2.84, 4.76).Suppose the observation of 8 was incorrectly recorded as 80. What would
When parents in a recent survey were asked whether they agreed with the following statements, the (yes, no)counts under various conditions were as follows:• Homework should be banned: (250, 1545).• Single-sex schools are better for students: (640, 1189).• Teachers should not be allowed to
A recent survey asked married respondents, “Did you live with your husband/wife before you got married?”The responses were 60 yes and 118 no for those who called themselves politically liberal, and 50 yes and 245 no for those who called themselves politically conservative. Analyze these data,
In 2016, a survey asked about the number of hours a week spent on the social networking sites, excluding e-mail (variable denoted WWWHR). State a research question you could address about this response variable and a relevant explanatory variable. Go to sda.berkeley.edu/GSS and analyze the data.
Refer to the data file created in Exercise 1.12(page 22). For variables chosen by your instructor, pose a research question, and conduct inferential statistical analyses using basic estimation methods. Summarize and interpret your findings, and explain how you could use them to answer the research
Refer to the Students data file (Exercise 1.11 on page 21). Using software, construct and interpret a 95%confidence interval for (a) the mean weekly number of hours spent watching TV, (b) the proportion believing in life after death. Interpret.
Refer to the previous exercise. Using this applet, let’s check that the confidence interval for a proportion may work poorly with small samples. Set the population proportion π = 0.10, with n = 10. Draw 100 random samples, each of size 10, forming 95% confidence intervals forπ for each one.(a)
Use the Explore Coverage applet at www.pearsonglobaleditions.com/Agresti to repeatedly generate random samples and construct confidence intervals for a proportion, to illustrate their behavior when used for many samples. Set the population proportion value (labeled as p) to 0.50, the sample size to
Refer to Example 5.9 (page 141). Construct a 95%confidence interval for the median time since a book was last checked out. Interpret.
Refer to Exercise 5.33.Use the bootstrap to construct a 95% confidence interval for the median annual income of the public housing residents. Interpret.
You randomly sample five students at your school to estimate the proportion of students who like broccoli.None of the five students say they like it.(a) Find the sample proportion who like it and its standard error. Does the usual interpretation of se make sense?(b) Why is it not appropriate to use
An anthropologist wants to estimate the proportion of children in a tribe who die before reaching adulthood.For families she knew who had children born between 1990 and 1995, 4 of 32 children died before reaching adulthood.Can you use the ordinary large sample formula to construct a 95% confidence
How large a sample size is needed to estimate the mean annual income of natives of Country X correct to within $1,000 with probability 0.99? There is no prior information about the standard deviation of annual income of natives, but we guess that about 95% of their incomes are between $6,000 and
Asocial scientist plans a study of adult South Asians to investigate educational attainment in women. In some parts, the women are not required to attend school, so some of them had very little education. How large a sample size is needed so that a 95% confidence interval for the mean number of
An estimate is needed of the mean acreage of farms in Region X. The estimate should be correct to within 100 acres with probability 0.95.A preliminary study suggests that 400 acres is a reasonable guess for the standard deviation of farm size.(a) How large a sample of farms is required?(b) A random
In 2006, a survey reported that the percentage of people in a university who reported a lot of, or some confidence(instead of not too much, or no confidence) in the elected Student Body President was 15% in House Red, 29% in House Blue, 26% in House Green, and 5% in House Yellow. In 2014, the
A 2015 poll in Country X indicated that 48% of its residents favored that all citizens who do not vote should pay a fine.Areport by related polls did not report the sample size but stated, “Polls of this size are considered to be accurate within 2.5 percentage points 95% of the time.” If this
A public health unit wants to sample death records for the past year in South Asia to estimate the proportion of deaths that were due to accidents. They want the estimate to be accurate to within 0.03 with probability 0.95.(a) Find the necessary sample size if, based on the data published, they
A television network plans to predict the outcome of an election between Candidate A and Candidate B.They will do this with an exit poll on election day. They decide to use a random sample size for which the margin of error is 0.05 for 95% confidence intervals for population proportions.(a) What
To estimate the proportion of traffic deaths in a region last year that were due to overspeeding, determine the necessary sample size for the estimate to be accurate to within 0.05 with probability 0.90.Based on results of studies reported by the region’s Traffic Safety Administration, we expect
Ahospital administrator wants to estimate the mean number of admissions of patients in that hospital. Based on a systematic random sample of 100 records of patients for the previous year, she reports that “the sample mean was 7.4.In repeated random samples of this size, the sample mean could be
A study estimates the mean annual family income for families living in public housing in Chicago. For a random sample of 30 families, the annual incomes (in hundreds of dollars) are in the Chicago data file at the text website and here:133 140 127 150 133 114 128 142 123 172 146 110 135 136 158 120
At sda.berkeley.edu/GSS, consider responses to the question “On how many days in the past 7 days have you felt lonely” (coded LONELY) for the most recent survey in which this was asked.(a) Find a point estimate of the population mean.(b) Construct the 95% confidence interval, and interpret.
The General Social Survey asks respondents to rate their political views on a seven-point scale, where 1 = extremely liberal, 4 = moderate, and 7 = extremely conservative.A researcher analyzing data from the 2014 GSS gets software output:-----------------------------------------------------Mean
For the Students data file mentioned in Exercise 1.11, software reports the results for responses on the number of times a week the subject reads a newspaper:-------------------------------------------------------Variable N Mean Std Dev SE Mean 95.0% CI News 60 4.1 3.0 0.387 (3.32,
A survey asked respondents how many jobs they had changed in the last 5 years. Software reports:--------------------------------------------------------Variable N Mean StDev SE Mean 95.0% CI Jobs 3000 0.885 0.825 0.015 (0.856, 0.914)--------------------------------------------------------(a)
Arecent survey asked, “How many times in the past 8 months have you fallen sick?” The 900 women who responded had a median of 2, mean of 2.71, and standard deviation of 1.43.The 683 men who responded had a median of 1, mean of 1.24, and standard deviation of 1.34.(a) Find a 95% confidence
A survey asked subjects, “How long have you lived in the city, town, or community where you live now?” The responses of the 1600 subjects had a median of 14 years, a mean of 19.8, and a standard deviation of 17.2.(a) Do you think that the population distribution is normal?Why or why not?(b)
In response to a survey question in 2016 about the number of hours daily spent jogging, the responses by the seven subjects were 1, 1, 1, 2, 2, 3, 4.(a) Estimate the mean, standard deviation, and standard error.(b) Construct a 95% confidence interval for the population mean, specifying its
A 2014 survey asked, “On an average, about how many hours a day do you watch television?” Stata software reports:-----------------------------------------------------Mean estimation Number of obs = 1500 Mean Std. Err. [95.0% Conf. Interval]TVHOURS 3.56 0.085 (3.55,
Example 5.5 (page 129) analyzed data from a study that compared therapies for anorexia. For the 17 girls who received the family therapy, the changes in weight during the study (which are in the data file Anorexia at the text website) were 11, 11, 6, 9, 14,−3, 0, 7, 22,−5,−4, 13, 13, 9, 4, 6,
Refer to the previous exercise. For the 450 male students in the sample, the mean was 6.80 and the standard deviation was 1.24.(a) Show that the standard error of the sample mean is 0.058.(b) Show that the 95% confidence interval for the population mean is (6.69, 6.91), and explain what “95%
A survey asked, “What do you think is the ideal number of hours a child should study?” The 528 female students who responded had a median of 5, mean of 6.02, and standard deviation of 2.75.(a) Find and interpret the standard error of the sample mean.(b) The 95% confidence interval is (5.79,
A survey in 2015 asked respondents how many ice creams they have had since last week. For the 200 children in the sample between the ages of 13 and 16, the median= 4 and mode = 2 (16.8% of the sample). Software summarizes other results:------------------------------------------------------Variable
Find and interpret the 95% confidence interval forμ, if ¯y = 70 and s = 10, based on a sample size of (a) 5,(b) 20.
Report the t-score that multiplies by the standard error to form a(a) 95% confidence interval for μ with 15 observations.(b) 95% confidence interval for μ with 25 observations.(c) 95% confidence interval for μ with df = 25.(d) 99% confidence interval for μ with df = 25.
In 2016, a poll reported results of a survey about religious beliefs. Of 3250 adults surveyed, 24% believed in reincarnation. Treating this as a random sample, a 95%confidence interval for the population proportion believing in reincarnation is (0.225, 0.255). Without doing any new calculation,
For an exit poll of people who voted in a regional election, 45% voted for Candidate A and 55% for Candidate B. Assuming this is a random sample of all voters, construct a 99% confidence interval for the proportion of votes that CandidateAreceived, if the sample size was (a)500 and (b) 50. In each
Of the 1824 voters sampled in the exit poll discussed in the previous chapter (page 92), 60.5% said they voted for Jerry Brown. Is there enough evidence to predict the winner of the election? Base your decision on a 95%confidence interval, stating needed assumptions for that decision.
A 2016 report by the Center for Healthy Lifestyle provided a point estimate of 20.1% for the percentage of adults who regularly exercise. The sample size was 20,345.Assuming that this sample has the characteristics of a random sample, construct and interpret a 99% confidence interval for the
When a survey asked whether reading novels enhanced their child’s language, 65.4% of 1200 respondents answered that this was probably or definitely not true. Find a 99% confidence interval for the corresponding population proportion, and indicate whether you can conclude that a majority of
The General Social Survey has asked respondents,“Do you think the use of marijuana should be made legal or not?” View results for all years at sda.berkeley.edu/GSS by entering the variables GRASS and YEAR.(a) Of the respondents in 2014, what proportion said legal and what proportion said not
A 2015 survey asked respondents whether they favored or opposed the death penalty for people convicted of murder. Software shows results:x n Sample prop 95.0% CI 900 1600 0.5625 (0.554, 0.572)Here, x refers to the number of respondents who were in favor.(a) Show how to obtain the value reported
State the z-score used in constructing a confidence interval for a proportion with confidence level (a) 0.98,(b) 0.90, (c) 0.50, and (d) 0.9973.
When a survey asked whether the government should impose strict laws to discourage people from smoking, a 95% confidence interval for the population proportion responding yes was (0.85, 0.89). Would a 99%confidence interval be wider, or shorter?Why?
When a 2016 research study asked whether there is solid evidence of global warming, 87% of liberals said yes whereas 25% of conservatives said yes. For conservatives, if n = 400, find and interpret a (a) 95% and (b) 99% confidence interval for a relevant parameter.
A recent survey asked, “If the residents of an area don’t vote in favor of an eatery, is it right that it should not be opened in that area?” Of 458 respondents, 355 said yes and 103 said no. Show that a 99% confidence interval for the population proportion who would say yes is (0.725,
The General Survey asks whether you agree or disagree with the following statement: “It is much better for everyone involved if the girls in the family were not educated as much as the boys.” The sample proportion agreeing was 0.78 in 1977 and 0.17 in 2016 (n = 1845).(a) Show that the estimated
One question in a recent General Survey asked, “Do you think that it should be government’s responsibility to provide secondary level education to the poor?” Those answering yes included 85 of the 155 subjects who called themselves strong supporters of Party A in political party
TheWorld Health Survey in 2014–2016 asked if abortion was justifiable, on a scale from 1 (never) to 10(always). The response never was given by 25.6% of the 3465 respondents in Country A and by 5.9% of the 1504 respondents in Country B.Areport stated that the margin of error for Country A equals
A survey of adults in Country A conducted in May 2017 by Alpha Research Center asked whether they were in favor of allowing laptops to school. Of the 400 conservatives sampled, 25% were in favor, whereas of the 250 liberals, 82% were in favor. Find the estimated standard errors for the sample
In a survey byWanderlust, a travel agency, it was estimated that of a region-wide random sample of 800 college graduates between the ages of 17 and 28, a proportion of 0.78 women like to go to a beach on their spring break.Find the standard error of this estimate, and interpret.
In response to a recent survey question about the number of hours daily spent playing outdoors, the responses by the seven subjects who identified themselves as Buddhists were 2, 3, 1, 1, 2, 3, 2.(a) Find a point estimate of the population mean hours daily spent playing outdoors for Buddhists.(b)
Of 288,503 people involved in motor vehicle accidents in Florida recently, 206,439 were wearing seat belts(Florida Department of Highway Safety and Motor Vehicles).Find a point estimate of the population proportion of Florida motorists wearing seat belts.
Amedical university conducts an annual national survey of cancer patients who are in remission about their lifestyle habits. In 2016, 1764 patients were surveyed.Identify the (a) subject, (b) sample, and (c) population.
In 2015, a French national survey asked adults about marriage and divorce. Of the 1754 individuals surveyed, 43% reported that they were married. Of the entire adult French population, 41% were married.(a) What was the population and what was the sample?(b) Identify a statistic and a parameter.
A lecturer at an arts college wants to research social media usage among students. The lecturer sends out an online questionnaire to the entire student body of 2,234 students. Out of this, only 127 students respond. One question asked is, “How many hours per day do you spend on social
In January 2016, an educational polling organization in the United Kingdom surveyed a sample of 1156 high school students asking, “Do you plan to attend university?”The response percentages were 42% (“Yes”), 27%(“No”), and 29% (“Undecided”). Are these values descriptive statistics
A social survey agency in Norway conducted a study on a sample of 1520 subjects and asked whether eating a vegan diet reduces chances of suffering a stroke. Out of 1520 sampled subjects, 761 responded probably true, and 759 responded probably not true. The proportion responding probably not true
Go to the General Social Survey website, sda.berkeley.edu/GSS. By entering TVHOURS in the Row box, find a summary of responses to the question“On a typical day, about how many hours do you personally watch television?”(a) What was the most common response?(b) Is your answer in (a) a descriptive
At the General Social Survey website, sda.berkeley.edu/GSS, by entering HEAVEN in the Row box, you can find the percentages of people who said yes, definitely; yes, probably; no, probably not; and no, definitely not when asked whether they believed in heaven.(a) Report the percentage who gave one
A private polling organization conducts a national study on physical exercise. The reported responses for 1,507 individuals surveyed were as follows: 21.7% exercised daily, 39.1% exercised two to three times per week, 21.4% exercised four to six times per week, and 17.8% reported being
Amulticountry poll in 2009 asked if people were willing to bear higher prices for energy and other goods to take steps to fight climate change. The percentages of people who responded by saying yes in various countries were 68% (China), 59% (Vietnam), 53% (Japan), 51% (Iran), and 51% (Mexico). The
Using R (statistical software), create a data file to display the characteristics of five pet dogs. The characteristics measured were breed (Pomeranian, Apso, Dachshund, Labrador, Pug), color (White, Gray, Black, Brown, Gray), age (2, 2, 2, 3, 5), energy level (High, Moderate, Moderate, High,
The Students data file at the text websites www.pearsonglobaleditions.com/Agresti shows responses of a class of social science graduate students at the University of Florida to a questionnaire that asked about GENDER (1 = female, 0 = male), AGE, HSGPA = high school GPA (on a four-point scale),
Using statistical software or a spreadsheet program(such as Microsoft Excel), your instructor will help the class create a data file consisting of the values for class members of characteristics such as those in the previous exercise. One exercise in each chapter will use this data file.(a) Copy
For the statistical software your instructor uses for your course, find out how to access the software, enter data, and print any data files that you create. Create a data file using the data in Figure 1.1 on page 19, and print it.
Illustrating with an example, explain(a) the difference between a sample and a population.(b) design of a research study.
A researcher in his study finds that a particular drug is very effective in alleviating symptoms of anxiety. The researcher would like to infer the results to the conceptual population. What is the conceptual population in this case?
A sociologist wants to estimate the average age at marriage for women in New England in the early eighteenth century. She finds within her state archives marriage records for a large Puritan village for the years 1700–1730. She then takes a sample of those records, noting the age of the bride for
In a recent public opinion poll conducted by a survey agency on the impact of globalization on the development of nations, a stark difference was found in opinion of various nations. The majority of nations that agreed on a positive impact of globalization included Bangladesh (59%), Vietnam (76%),
At the homepage www.gallup.com for the Gallup Poll, from the information listed or linked, give an example of (a) sample in a study, and (b) population of interest.
Browse through electronic journals of your choice, such as, Journal of Experimental Psychology, Journal of Educational and Behavioral Statistics, Journal of Social Psychology, etc. Pick an article that interests you.Make a presentation to explain the gist of the article in terms of the design of
Explain the difference between(a) quantitative and qualitative variables.(b) interval scale and ordinal scale.(c) experiment and survey.
Identify each variable as categorical or quantitative:(a) Level of education (high school, bachelor’s, master’s).(b) Number of times married.(c) Hair color.(d) Preferred type of exercise.(e) Type of residence (rented apartment, owned apartment, rented house, owned house).(f) Number of household
Which scale of measurement (nominal, ordinal, or interval) is most appropriate for(a) City of residence?(b) Number of people you have known who have had lung cancer (0, 1, 2, 3, or more)?(c) Temperature (Celsius)?(d) Eye color (brown, black, blue, hazel, etc.)?(e) Attitude toward paid paternity
Which scale of measurement is most appropriate for(a) Subjects in a course (French, Spanish, German, . . .)?(b) Relationship status (single, married, divorced, widowed,. . .)?(c) Time taken per trial (between 0 and 10 seconds)?(d) Statewide female birth rate (per 1000 population)?(e) Headcount of
Which scale of measurement is most appropriate for“personal characteristics of children” measured as(a) Height and weight of child?(b) Developmental milestone (rolling over, sitting with support, crawling, . . .)?(c) Color of eyes (brown, green, blue, . . .)?
Identify the following variables as categorical or quantitative, and as continuous or discrete.(a) Gender (male, female)(b) Number of siblings(c) Age(d) IQ(e) Favorite film genre(f) Employment status (yes, no)(g) Annual income
A study conducted by YouGov (yougov.com) asked people from different countries from around the world,“Which of the following best describes the way you feel about your country?” The response choices were best in the world, better than most other countries, as good as most other countries, not
Aresearcher decides to use the experimental method to see the effectiveness of a new teaching method on the achievement scores of subjects. Two groups are formed, that is, the experimental group (those who receive training using the new teaching method) and the control group(those who receive
Identify which of the following variables are discrete and which would be measured on a continuous scale.(a) Level of education(b) Favorite type of music(c) Annual income(d) Religious affiliation(e) Number of family members(f) Finish time for a marathon(g) Distance traveled to work
Which of the following variables are both discrete and quantitative?(a) Number of records sold(b) Time to swim 200 meters(c) Occupation(d) Number of years employed(e) Age when first married(f) Student population(g) Cups of coffee consumed per day
Select the telephone numbers of at least 30 people you know. Number these telephone numbers from 1 to 30.Using a statistical software, create a table of random numbers and drawa random sample of five telephone numbers from the total list. What were the numbers selected?
Make a list of the total number of states/districts in your country. Suppose you have to draw a sample of three states randomly.What are the steps involved in drawing a random sample without a statistical software?
Explain whether you would conduct an experiment or an observational study for the following scenarios. Justify your reasoning.(a) Whether or not enrollment in a preparatory program improves student retention rates.(b) Whether public transport or carpooling provides a shorter commute time.(c)
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