Chapter 4 STAT 1312

According to an April 2018 survey, a majority of employed American adults (59%) are confident about their job security, stating it is not at all likely for them to lose their job or be laid off in the next 12 months. The survey methods section of the poll states that for results based on the total sample of employed adults, the margin of sampling error is ±5 percentage points at the 95% confidence level. All reported margins of sampling error include computed design effects for weighting. Identify the sources of error in the poll result that are not included in the margin of error.

Nonresponse Inclusion errors Response errors Undercoverage Processing errors Extended Answer: The margin of error occurs due to variability from sample to sample. It can be controlled by choosing the size of the random sample. Nonsampling errors are errors not related to the act of selecting a sample from the population. Nonsampling errors can be present even in a census and are not easy to handle. Incorrect gathering of the sampling frame can lead to undercoverage when some groups of the population are not represented in the sample. Frame errors can also arise from erroneous inclusions, which can occur if units that are not in the population appear in the frame. Response errors occur when a subject gives an incorrect response. Nonsampling errors also include processing errors. Mistakes in mechanical tasks, such as entering responses into a computer, are the reason for processing errors. Nonresponse is the most serious problem facing sample surveys. Nonresponse is the failure to obtain data from an individual selected for a sample. All these errors are not related to the act of selecting a sample from the population. Thus, the listed nonsampling errors are not included in the margin of error. Random sampling error is the deviation between the sample statistic and the population parameter caused by chance in selecting a random sample. Since the margin of error can be controlled by choosing the size of the random sample, random sampling errors are included in the margin of error.

A club has 30 student members and 10 faculty members. The students are Student Members Aguirre Cooper Kemp Peralta Stankiewicz Butterfield Dobbs Kessler Risser Steele Caporuscio Freeman Koepnick Rodriguez Tong Carlson Girard Macha Ryndak White Chilson Gonzales Makis Soria Williams Clement Grebe Palacios Spiel Zhang The faculty members are Faculty Members Atchade Everson Hansen Nair Romero Craigmile Fink Murphy Nguyen Turkmen The club can send 3 students and 2 faculty members to a convention. It decides to choose those who will go by random selection. Use Table A to choose a stratified random sample of 3 students and 2 faculty members. To select the students, number the students from 01 to 30 alphabetically, and use Line 102. To select the faculty, number the students from 0 to 9 alphabetically, and use Line 127. The tokens are ordered alphabetically with students first, and then the faculty are listed alphabetically afterwards.

Satisfied Sample -Peralta -Steele -Tong -Fink -Hansen Extended Answer: To select the students, number the students in the table alphabetically using numbers 01 to 30. Student Members 01 - Aguirre 07 - Cooper 13 - Kemp 19 - Peralta 25 - Stankiewicz 02 - Butterfield 08 -Dobbs 14 - Kessler 20 - Risser 26 - Steele 03 - Caporuscio 09 - Freeman 15 - Koepnick 21 - Rodriguez 27 - Tong 04 - Carlson 10 - Girard 16 - Macha 22 - Ryndak 28 - White 05 - Chilson 11 - Gonzales 17 - Makis 23 - Soria 29 - Williams 06 - Clement 12 - Grebe 18 - Palacios 24 - Spiel 30 - Zhang Using the random numbers in Table A, go to line 102 and select pairs of numbers until you find three numbers within the range 01 to 30. Keep in mind that the spaces in the table do not mean anything. They are just there to make the table easier to read. Without the spaces, row 102 is 7367647150994000192727754426488242536290 You may find it helpful to group the digits in pairs. 73 67 64 71 50 99 40 00 19 27 27 75 44 26 48 82 42 53 62 90 Skip over any number that is not in the range 01 to 30. Stop when you get three distinct numbers. If you do not find three distinct numbers on row 102, continue to row 103. 73 67 64 71 50 99 40 00 19⎯⎯⎯⎯ 27⎯⎯⎯⎯ 27 75 44 26⎯⎯⎯⎯ 48 82 42 53 62 90 Skip 27 the second time it occurs because you cannot select the same person twice. The pairs of digits are 19, 27, and 26, so the sample is Peralta, Tong, and Steele. To select the faculty, number them alphabetically from 0 to 9. Faculty Members 0 - Atchade 2 - Everson 4 - Hansen 6 - Nair 8 - Romero 1 - Craigmile 3 - Fink 5 - Murphy 7 - Nguyen 9 - Turkmen Using line 127, first two digits are 4 and 3, so the selected faculty are Fink and Hansen. The five people selected to go in the stratified sample are Peralta, Tong, Steele, Fink, and Hansen.

An online survey of college parents was conducted during February and March 2007. Emails were sent to 41,000 parents who were listed in either the College Parents of America database or the Student Advantage database. Parents were invited to participate in the online survey. Out of those invited, 1727 completed the online survey. The survey protected the anonymity of those participating in the survey but did not allow more than one response from an individual IP address. One of the survey results was that 33% of mothers communicate at least once a day with their child while at school. Do you think that the margin of error is a good measure of the accuracy of the survey's results? Explain your answer.

The margin of error is not a good measure of the accuracy of the survey's results because of undercoverage in the sampling frame. Extended Answer: The sampling frame consists of parents who registered online with either the College Parents of America or the Student Advantage websites. These databases do not include all parents of college students (undercoverage) and therefore cannot account for undercoverage errors. This results in bias that is in favor of only those parents who registered with at least one of the websites. The provided survey result is phrased: "33% of mothers communicate at least once a day with their child while at school." This implies that the results are being used to represent all mothers of college students instead of only those who registered with at least one of the websites. Although 95% accuracy is quite good, the magin of error only covers random sample errors, which is the variation that occurs between different rangom samples. The margin of error does not cover sampling errors such as undercoverage and nonresponse. A sample size of 1727 is large enough to produce accurate results if it is chosen at random from the entire population of interest. Huge samples are not needed to produce accurate results. Think of the soup analogy. A small margin of error is not always an accurate one. As an anlogy, a scale might give your weight to the nearest milligram but could still be wrong if the scale was not properly calibrated.

Determine if each of the potential sample survey questions is clear or is slanted towards a desired response. (a) Which of the following best represents your opinion on gun control? The government should take away our guns. We have the right to keep and bear arms. (b) In light of skyrocketing gasoline prices, we should consider opening up a very small amount of Alaskan wilderness for oil exploration as a way of reducing our dependence on foreign oil. Do you agree or disagree? (c) Do you think that excessive restrictions placed on U.S. law enforcement agencies hampered their ability to detect the 9/11 terrorist plot before it occurred? (d) Do you use drugs?

The question is clear: a d The question is slanted toward a desired response: b c Extended Answer: Questions (a) and (d) are both clear and not slanted towards a desired response. Question (a) asks participants which statement represents their opinion in a clear and non-slanted way by providing two statements that contain no words with negative connotations that may lead the participant to choose one over the other. Similarly, question (d) asks a straightforward and simple question with a yes/no response. Both questions (b) and (c) are slanted. The introduction to question (b) provides language that suggests there is a problem that needs to be corrected, leading the participant to pick yes rather than no. Similarly, the use of the word excessive in question (c) slants the respondent towards a particular response.

Is the following question slanted toward a desired response? If so, how? In view of escalating environmental degradation and incipient resource depletion, would you favor economic incentives for recycling of resource‑intensive consumer goods? Please select the correct answer.

The question is slanted. The part of the question "In view of escalating environmental degradation and incipient resource depletion" leads the respondent to answer yes. Extended Answer: A slanted question leads the respondents to a specific or desired answer. Slanted questions reflect author bias. The results of a survey with slanted questions will provide unreliable data. The phrase "In view of escalating environmental degradation and incipient resource depletion" may cause a respondent to feel anxious about the environment. This emotional response could lead respondents who might say no to say yes instead. Clear, concise, and uncomplicated language is best for survey questions. If the question was "Would you favor economic incentives for recycling of resource‑intensive consumer goods?" the question is no longer leading. The results would give an accurate account of whether the respondents felt economic incentives for recycling of resource‑intensive consumer goods is a good idea.

You are writing an opinion poll question about a proposed amendment to the Constitution. You can ask if people are in favor of "changing the Constitution" or "adding to the Constitution" by approving the amendment. Why may the responses to these two questions produce different percentages in favor?

The words "changing" and "adding" have different connotations. Extended Answer: The questions will produce different percentages in favor because the words "changing" and "adding" invoke different feelings about the Constitution. Americans are likely to be hesitant about changing the Constitution. Thus, it is likely that a higher percentage will favor the option to add to the Constitution. The two questions are not said to occur at different times. Therefore, the possibility of a person's opinion changing over time is not a factor. Being unaware of how the Constitution gets amended or being unaware of current amendments will not cause a different response between the two question types. The words "changing" and "adding to" are not impacted by these factors. It is not true that more people will prefer "changing the Constitution." Many Americans prefer that the Constitution is protected. This is also evident by the infrequent changes that have been made to the Constitution in history. Although it is true that people would prefer the phrase "adding to the Constitution" over the phrase "changing the Constitution," it is not true that the Constitution has had frequent additions.

Two basic types of questions are closed questions and open questions. A closed question asks the subject for one or more of a fixed set of responses. An open question allows the subject to answer in his or her own words; the interviewer writes down the responses and classifies them later. An example of an open question is What do you believe about the afterlife? An example of a closed question is What do you believe about the afterlife? Do you believe a. there is an afterlife and entrance depends only on your actions? b. there is an afterlife and entrance depends only on your beliefs? c. there is an afterlife and everyone lives there forever? d. there is no afterlife? e. I don't know. What are the advantages and disadvantages of open and closed questions?

-An advantage of closed questions is that they are easier to answer. A disadvantage of closed questions is that an individual may simplify their answer to fit a choice. -An advantage of open questions is that it allows for many different answers. A disadvantage of open questions is answers can be difficult to analyze due to unclear or vague responses. Extended Answer: An advantage of closed questions is that they are easier to answer. A disadvantage of closed questions is that an individual may simplify their answer to fit a choice. An advantage of open questions is that it allows for many different answers. A disadvantage of open questions is that answers can be difficult to analyze. Closed questions are easier to answer because respondents do not have to think of an answer independently. However, this does lead to respondents simplifying their true response to fit one of the answer choices. This is a disadvantage because it could lead to less true responses. Open questions allow for many different answers, so responses are very true and not simplified. This can lead to difficulties in analysis. It is difficult to summarize dozens of different responses. A possible response to the open question, "What do you believe about the afterlife?" could be a paragraph that includes the person's beliefs when they are feeling optimistic and when they are feeling pessimistic, which may differ significantly. It may be very difficult to pinpoint what their exact opinions are for unclear responses like this. Open questions answers can vary a significant amount between respondents. Some individuals may answer the question in a few words, and others will write an entire paragraph. This means that the level of detail will not be equal in each response. An open question allows a person to answer the question exactly, so individuals are less likely to give an incorrect or dishonest response. Closed questions limit the responses available, so subjects cannot choose any answer they can think of like with an open question. Closed questions typically have shorter responses, since each answer is predetermined.

An online survey of college parents was conducted during February and March 2007. Emails were sent to 41,000 parents who were listed in either the College Parents of America database or the Student Advantage database. Parents were invited to participate in the online survey. Out of those invited, 1727 completed the online survey. The survey protected the anonymity of those participating in the survey but did not allow more than one response from an individual IP address. One of the survey results was that 33% of mothers communicate at least once a day with their child while at school. Use the quick method to estimate the margin of error for a random sample of size 1727. Give your answer to three decimal places. margin of error:

0.024 Extended Answer: To calculate the margin of error using the quick method for a 95% confidence approximation, divide 1 by the square root of the sample size. 1sample size⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√=1parents who completed survey⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√=11727⎯⎯⎯⎯⎯⎯⎯⎯√=0.024

What is the chance, 𝑃(Romero),P(Romero), that the faculty member Romero is chosen? Give your answer as a percentage rounded to the nearest whole number. 𝑃(Romero)=

10% Extended Answer: There is 1 faculty named Romero in the list and there are 10 faculty in the list, so the chance that Romero is chosen is 𝑃(Romero)=1/10=0.10=10%

A club has 30 student members and 10 faculty members. The students are Student Members Aguirre Cooper Kemp Peralta Stankiewicz Butterfield Dobbs Kessler Risser Steele Caporuscio Freeman Koepnick Rodriguez Tong Carlson Girard Macha Ryndak White Chilson Gonzales Makis Soria Williams Clement Grebe Palacios Spiel Zhang The faculty members are Faculty Members Atchade Everson Hansen Nair Romero Craigmile Fink Murphy Nguyen Turkmen The club can send 3 students and 2 faculty members to a convention. It decides to choose those who will go by random selection. What is the chance, 𝑃(White), that the student named White is chosen? Give your answer as a percentage rounded to the nearest whole number. 𝑃(White)=

3% Extended Answer: There is 1 student named White in the list and there are 30 students in the list, so the chance that White is chosen is 𝑃(White)=1/30=0.033=3%

An online survey of college parents was conducted during February and March 2007. Emails were sent to 41,000 parents who were listed in either the College Parents of America database or the Student Advantage database. Parents were invited to participate in the online survey. Out of those invited, 1727 completed the online survey. The survey protected the anonymity of those participating in the survey but did not allow more than one response from an individual IP address. One of the survey results was that 33% of mothers communicate at least once a day with their child while at school. What was the response rate for this survey? Round to one decimal place. response rate:

4.2% Extended Answer: To calculate the response rate, divide the total number of parents who completed the online survey by the total number of parents who were contacted by email. parents who completed surveytotal parents contacted=1727/41000=0.042=4.2% To convert a decimal into a percentage, multiply the decimal by 100.

One of these choices of wording will produce a much higher percentage in favor. Which one? Why?

A higher percentage of people will prefer adding to the Constitution because many Americans are hesitant about changing the original constitution. Extended Answer: The questions will produce different percentages in favor because the words "changing" and "adding" invoke different feelings about the Constitution. Americans are likely to be hesitant about changing the Constitution. Thus, it is likely that a higher percentage will favor the option to add to the Constitution. The two questions are not said to occur at different times. Therefore, the possibility of a person's opinion changing over time is not a factor. Being unaware of how the Constitution gets amended or being unaware of current amendments will not cause a different response between the two question types. The words "changing" and "adding to" are not impacted by these factors. It is not true that more people will prefer "changing the Constitution." Many Americans prefer that the Constitution is protected. This is also evident by the infrequent changes that have been made to the Constitution in history. Although it is true that people would prefer the phrase "adding to the Constitution" over the phrase "changing the Constitution," it is not true that the Constitution has had frequent additions.

Archaeologists plan to examine a sample of two‑meter square plots near an ancient Greek city for artifacts visible in the ground. They choose separate samples of plots from floodplain, coast, foothills, and high hills. What kind of sample is this?

A stratified sample Extended Answer: For a stratified random sample, the sampling frame is divided into groups, followed by independent sampling in each group. In this study, the archaeologists divided the plot into four strata and took separate samples from each stratum. Therefore, this is an example of stratified sampling. Since the plots were divided into groups, this is not a simple random sample or a voluntary response sample. After dividing the plots into groups, the archaeologists chose separate samples from each grouped plot. This is not part of a cluster sample. In a cluster sample, the groups are randomly selected. Then, all objects in the chosen groups, or clusters, are included in the sample.

When the Current Population Survey asked the adults in its sample of 60,000 households if they voted in the 2016 presidential election, 56% said they had. The margin of error was less than 0.3%. In fact, only 55% of the adult population voted in that election. Give a reasonable explanation for how the CPS could choose a sample properly and still miss by 3 times the margin of error.

People who did not actually vote probably claimed that they had voted. The margin of error covers sampling errors only, not other forms of error. Extended Answer: The margin of error only accounts for random sampling error, not all forms of error in a survey. A random sampling error is when the sample statistic differs from the population parameter, which is caused by chance error in the random sample selected. The margin of error cannot account for any other type of error. It is likely that there may have been other sources of error in the study that caused this discrepancy. With a confidence interval of 95%, it does not mean that there is 5% chance that the confidence will not contain the true proportion. A 95% confidence level means that if we took many samples and calculated many intervals, 95% of the calculated intervals would contain the population value. The sample size was large enough to not be the cause of the discrepancy between the study and the population. Many surveys collect data on far fewer people and give reliable results. Although biased samples produce inaccurate results, and sample surveys tend to be plagued by undercoverage and nonresponse, an inaccurate result is not proof that the sample was biased. If the respondents lie, even a well‑chosen sample can give inaccurate results.

Which of the following are sources of sampling error and which are sources of nonsampling error?

Sampling error: -Data are gathered by asking people to go to a website and answer questions online -Interviewers choose people on the street to interview Nonsampling error: -The subject lies about past illegal drug use -A typing error is made in recording the data -The telephone directory is used as a sampling frame. -The subject cannot be contacted in five calls Extended Answer: Sampling errors are errors caused by the act of taking a sample. They cause sample results to be different from the results of a census. If researchers invite people to participate in a website poll or choose passers‑by on the street, they rely on voluntary response, which means that the individuals decide whether to respond or not. This kind of survey attracts people who feel strongly about the issue in question, so the obtained data can be misleading. Since voluntary response is a biased sampling method, it causes sampling errors. Nonsampling errors are errors not related to the act of selecting a sample from the population. They can be present even in a census. Examples of nonsampling errors are undercoverage, nonresponse, response errors, and processing errors. When some groups in the population are not presented in the sampling frame, it leads to undercoverage. These are called frame errors, and are a type on nonsampling error. Using telephone directories as the frame for a telephone survey would miss everyone with an unlisted telephone number. Also, it would miss everyone who cannot afford a phone. Nonresponse is the failure to obtain data from an individual selected for a sample. Most nonresponse happens because some subjects cannot be contacted. This type of error can occur for any type of sample. Another type of nonsampling error is a processing error, which occurs when data handling was done improperly. An example of this error is a typing error in recording data. The response error caused by incorrect answers of the respondents is not dependent on the sampling method. Therefore, the lying of subjects about illegal drug use is an example of a nonsampling error.

The statistics department at Cal Poly, San Luis Obispo, has 18 faculty members and 80 undergraduate majors. Use Table A, starting at line 111 , to choose a stratified sample of 1 faculty member and 1 student to attend a reception being held by the university president. Begin numbering students and faculty with 01 . Enter the number corresponding to the faculty member and student chosen. faculty member:

faculty member: 12 student: 48 Extended Answer: To select the faculty member to attend the reception, label the 18 faculty members 01 to 18. It does not matter how you assign these labels to the faculty members. If you have a list of their names and the list is sorted alphabetically, that will work just fine. The labels will be selected randomly, so the faculty members will be selected randomly no matter how the labels are assigned to the individuals. The entries in row 111 of Table A are 81486 69487 60513 09297 00412 71238 27649 39950 The spaces do not mean anything. They are there to make the table easier to read. It may help to break the numbers down into pairs of digits. 81 48 66 94 87 60 51 30 92 97 00 41 27 12 38 27 64 93 99 50 Skip any number that is not one of the pairs of digits 01,02,...,18. 81 48 66 94 87 60 51 30 92 97 00 41 27 12 38 27 64 93 99 50 The first pair of digits in the range from 01 to 18 is 12. To select the undergraduate, label the 80 undergraduates 01 through 80 and do the same as you did for the faculty member. 81 48 66 94 87 60 51 30 92 97 00 41 27 12 38 27 64 93 99 50 The undergraduate is the one labeled 48.

When a margin of error is reported for a survey, it includes

random sampling error, but not other practical difficulties like undercoverage and nonresponse. Extended Answer: Random sampling error is the deviation between the sample statistic and the population parameter caused by chance in selecting a random sample. The margin of error in a confidence statement includes only random sampling error, and this error can be decreased by choosing a larger sample. Nonsampling errors, like undercoverage, nonresponse, response errors, and wording errors, are errors not related to the act of selecting a sample from the population. They do not affect the value of the margin of error.