STAT 110 Exam 1

Increasing the size of an SRS has these beneficial effects:

The margin of error is smaller than it is for smaller SRSs.

In the "Help on Exam" experiment, the response variable is

midterm exam score

For what confidence level are margins of error usually reported?

95%

Large samples give ________ variable results as compared to smaller samples.

Less

A Harris Poll conducted in October 2006 reports that 42% of a sample of 2010 adults said they are not "absolutely certain" there is a God. Only 29% said they believe that God controls what happens on earth. Using the quick method, the estimated margin of error for 95% confidence is ___. (Give your answer to one decimal place.)

2.2% (For 95% confidence, the margin of error is estimated as 1/√2010 = 0.0223 = ±2.2% approximately.)

A November 2007 Gallup Poll of 1004 adults found that 572 are satisfied with the total cost they pay for their health care. The announced margin of error is ±3 percentage points. The announced confidence level is 95%. The value of the sample proportion phat.JPG who say they are satisfied with the total cost they pay for their health care is ___%.

57% (The value of sample proportion phat.JPG who say they are satisfied with the total cost they pay for their health care is calculated as: 572/1004 = 0.5697 = 57%.)

A psychologist wants to know if adults with normal vision can be fooled by a certain optical illusion. She recruits 50 students from her PSY 120 class and finds that 42 of them are fooled by the illusion. The population in this study is:

Adults w/ normal vision

A college wants to gather student opinion about parking for students on campus. It isn't practical to contact all students. Which of the following is a way to choose a sample of students that is poor practice because it depends on voluntary response?

Asking students to respond to a survey posted on the campus website

True or False One can always use an observational study to determine cause and effect between two variables.

False: (In general, experiments are used to show cause and effect. Observational studies can typically show an association only.)

A national polling organization uses a random digit dialing device to dial residential phone numbers in the United States. Of 100 numbers dialed, 43 are unlisted numbers. This is not surprising because 40% of all residential phones in the United States are unlisted. Choose the best answer in terms of the problem.

Sample Size = 100 parameter = 40% statistic = 43% (The sample size is 100 since the random digit dialing method gets ahold of unlisted and listed phone numbers. A parameter is a number that describes the population. So, 40% is a parameter, related to the population, which is the whole lot. A statistic is a number that describes a sample. So, 43% is a statistic, related to the sample of 100 numbers dialed)

"Congress passed a ban on the sale of assault weapons. Now there is a move to repeal that ban. Do you agree that the ban on sale of assault weapons should be repealed?" You ask that question to an SRS of 1,000 adults in Texas (population 18 million people) and to a separate SRS of 1,000 adults in Indiana (population 5.7 million people). You make 95% confidence statements about the percents of all adults in both states who agree. It would be cheaper to just announce the question on TV and ask people to call in with their opinions. Is this the best approach?

This is a bad idea, because allowing people to volunteer may result in large bias.

A university has 30,000 undergraduate and 10,000 graduate students. A survey of student opinion concerning health care benefits for domestic partners of students selects 300 of the 30,000 undergraduate students at random and then separately selects 100 of the 10,000 graduate students at random. The 400 students chosen make up the sample. Which of the following statements is correct about the sample chosen?

This is a not a Simple Random sample (SRS) because not every set of students has equal chance of being selected. (Each sample contains exactly 300 undergraduates and 100 graduate students. This is not an SRS because not all samples of size 400 have equal chance and some of the samples are not possible at all. For example, there cannot be a sample containing 301 undergraduate students and 99 graduate students.)

The essential difference between an experiment and an observational study is

an experiment imposes treatments to the subjects , but an observational study does not

A parameter:

is usually unknown and estimated by a statistic (Instructor feedback: A parameter is a fixed, usually unknown value which we estimate with a statistic. A statistic is calculated from a random sample.)

An experiment is conducted to compare the effect of a new anti-aging cream to a placebo cream. Subjects are recruited into the study and have the creams placed on their face nightly for 6 weeks. Randomization is used to determine which side of the face gets the new anti aging cream and which side gets the placebo during the 6 week trial. Reduction of fine lines is measured at the end of the trial. What is the best description for the design of the experiment?

simple random sample

A New York Times Poll on women's issues interviewed 1025 randomly selected women and 472 randomly selected men from the United States, excluding Alaska and Hawaii. The poll found that 47% of the women said they do not get enough time for themselves and announced a margin of error of ±3 percentage points for 95% confidence in its conclusions. The confidence statement, in relation to the given scenario, is: "We are 95% confident that between 44% and 50% of all women would say that they do not get enough time for themselves." Which of the following statements is correct about the relation of margin of error for women and margin for error for men?

The margin of error for men will be greater than margin of error for women.

A November 2007 Gallup Poll of 1004 adults found that 572 are satisfied with the total cost they pay for their health care. The announced margin of error is ±3 percentage points. The announced confidence level is 95%. The population proportion, p, is:

The proportion of the all adults who are satisfied with the total cost they pay for their health care. (The population parameter p is the proportion of the population that is satisfied with the total cost they pay for their health care.)

In an experiment to see if St. John's Wort reduces symptoms of attention-deficit/hyperactivity disorder (ADHD), a placebo is

a pill that looks, tastes, and feels like the St. John's Wort pill, but contains no St. John's Wort

In an experiment, a non-adherer is

a subject who does not follow experimental protocal

In a randomized block design, blocks often represent different levels of

a variable suspected to be a lurking variable

A study at Yale Medical School investigated treatments for chronic cocaine abusers. Of the 72 subjects, all cocaine users who wanted to quit, 24 were assigned at random to each of three drugs: (a) desipramine (b) lithium (c) a placebo After 6 weeks the subjects reported whether they had stayed off cocaine. This study is an example of:

an experiment

Do doctors in managed care plans give less charity care? Researchers chose 60 communities at random, then chose doctors at random in each community. In all, they interviewed 10,881 doctors. Overall, 77.3% of the doctors said they had given some care free or at reduced rates because of the patient's financial need in the month before the interview. Doctors who received at least 85% of their practice income from managed care plans were significantly less likely than other doctors to provide charity care. Some doctors who did not give any charity care may say that they did. If so, the study suffers from:

bias: the sample result will systematically overestimate the true percent of doctors who give charity care.

An experiment is being conducted to determine the effect of an exercise regimen on percent body fat. Body fat is known to be generally higher in women, so the experimenters divide the subjects into groups by gender (male and female). Within each gender group, the subjects are divided evenly into treatment groups. Which term best describes the experimental design?

block design (This is a block design, where the blocking variable is gender. Subjects cannot randomly be assigned into gender groups, so it is not a completely randomized design. And in order for the design to be matched pairs, we would have had to have matched subjects between groups on some trait (like height and gender).)

A researcher might use ______________ sampling if the focus was on efficiency in sampling.

clusters in random (Choose a stratified random sample if the interest is in specific groups. Clusters are used when the focus is on efficiency. Any good sampling scheme should have random sampling involved at some level.)

Three essential components of statistically designed experiments are

compare treatments, randomly allocate subjects to treatments, use large enough sample sizes

When we take a census, we attempt to obtain data from

every individual in the population

An experiment was conducted to determine whether music playing in the background could help students on an exam. Students in a large statistics class were randomly divided into two groups. The first group took the midterm exam with soft music playing in the background while the second group later took the exam with no music playing. The scores of the two groups on the exam were compared.

music (whether music is playing or not)

Which is always the largest in size?

population (Instructor feedback: Size order from smallest to largest: sample, sampling frame, population.)

To reduce the variability of estimates from a simple random sample, you should:

use a larger sample.

If a sampling method is biased then:

we need to improve the sampling method to remove the bias.

You take an SRS of size 500 from the 39,000 students at Purdue University. You then take an SRS of size 500 from the 4,735,000 adults in the state of Indiana. The margin of error in a 95% confidence statement for the Indiana sample is:

about the same as for the Purdue sample because both are samples of size 500.

A university has 30,000 undergraduate and 10,000 graduate students. A survey of student opinion concerning health care benefits for domestic partners of students selects 300 of the 30,000 undergraduate students at random and then separately selects 100 of the 10,000 graduate students at random. The 400 students chosen make up the sample. Which of the following statements correctly explains why this sampling method gives each student an equal chance to be chosen?

Any student, undergraduate or graduate, has a 1/100 of being selected. (For undergraduates students, 300/30,000 or 1% are chosen. For graduate students, 100/10,000 or 1% is chosen. So any student, undergraduate or graduate, has a 1 in 100 chance of being selected.)

Pregnant and breast-feeding women should eat at least 12 ounces of fish and seafood per week to ensure their babies' optimal brain development, according to a coalition of top scientists from private groups and federal agencies. A nutritionist wants to know whether pregnant women are eating at least 12 ounces of fish per week. To do so, she obtains a list of the 340 members of a local chain of prenatal fitness clubs and mails a questionnaire to 60 of these women selected at random. Only 21 questionnaires are returned. Which of the following is the sample for this study?

Women who returned the surveys

You want to ask a sample of undergraduates at State Tech how they feel about a proposal to delay future Spring Breaks by a week. Opinions may differ depending on the class of the student, especially because seniors will have left before the policy is changed. So you take separate SRS's of 200 seniors and 200 non-seniors and combine them to form your sample.The results of your Spring Break survey are as follows: 72% of the non-seniors favor delaying Spring Break by a week, but only 28% of the seniors do. If you wanted an estimate of the percentage of all State Tech undergraduates who favor delaying the break, which of the following would be the most reasonable?

61% = (3/4)(72%) + (1/4)(28%), taking into account that there are about three times as many non-seniors as seniors. (Instructor feedback: We have a stratified sample, seniors and non-seniors. So to combine, we will weight the results.)

The following is a true story... During a childhood visit to HersheyPark, I was selected to participate in a taste test. I was presented two chocolate bars and asked to say which one tasted better. My interviewer had the Hershey logo flipped to be the bottom side of the bars. When she wasn't looking, I peeked at the "Hershey" logo on the dark chocolate bar. ...Thinking that I was supposed to choose the Hershey brand as the one I liked (since I was at HersheyPark), I lied to the interviewer and told her I liked the dark chocolate bar better. Which type of error happened here?

Non Sampling Error: Response Error

Pregnant and breast-feeding women should eat at least 12 ounces of fish and seafood per week to ensure their babies' optimal brain development, according to a coalition of top scientists from private groups and federal agencies. A nutritionist wants to know whether pregnant women are eating at least 12 ounces of fish per week. To do so, she obtains a list of the 340 members of a local chain of prenatal fitness clubs and mails a questionnaire to 60 of these women selected at random. Only 21 questionnaires are returned. Which of the following is the population for the study?

Pregnant women

Highway planners decided to make a main street in West Lafayette, Indiana, a one-way street. The Lafayette Journal and Courier took a one-day poll where residents were asked to call a telephone number to record their comments. The next day, the paper reported: "Journal and Courier readers overwhelmingly prefer two-way traffic flow in West Lafayette's Village area to one-way streets. By nearly a 7-1 margin, callers to the newspaper's Express Yourself opinion line on Wednesday complained about the one-way streets that have been in place since May. Of the 98 comments received, all but 14 said no to one-way." What population do you think the newspaper wants information about?

Residents of West Lafayette (and lafayette)

There may be a "gender gap" in political party preference in the United States, with women more likely than men to prefer Democratic candidates. A political scientist interviews a large sample of registered voters, both men and women. She asks each voter whether he or she voted for the Democratic or the Republican candidate in the last presidential election. Identify the type of study.

Special Type of Observational Study: Sample Survey (The poll was a sample survey because a sample was selected to get information about the entire population and the individuals provided their own responses.)

A New York Times Poll on women's issues interviewed 1025 randomly selected women and 472 randomly selected men from the United States, excluding Alaska and Hawaii. The poll found that 47% of the women said they do not get enough time for themselves and announced a margin of error of ±3 percentage points for 95% confidence in its conclusions. The confidence statement, in relation to the given scenario, is: "We are 95% confident that between 44% and 50% of all women would say that they do not get enough time for themselves." Which of the following statements correctly explains the meaning of the term '95% confidence', in the confidence statement?

The interval 44% to 50% is based on a procedure that includes the true population value 95% of the time. (The correct explanation of the term 95% confidence is "The interval 44% to 50% is based on a procedure that gives correct results, that is, includes the true population value, 95% of the time.)

In February 2004, USA Today conducted an online poll. Visitors to their Web site were asked the following question: "Should the U.S. pass a constitutional amendment banning gay marriage?" Visitors could vote by clicking a button. The result as of 3:30 pm on February 25 was that 68.61% voted "No" and 31.39% voted "Yes." A total of 63,046 votes had been recorded. It was found that the margin of error for 95% confidence for a sample of this size is roughly equal to four-tenths of one percentage point.

The result of the poll is based on a voluntary response sample. Therefore, it cannot be said that 68.61%, plus or minus 0.4%, of American adults are opposed to having the United States pass a constitutional amendment banning gay marriage, since voluntary response samples often bias results.

In the "Help on Exam" experiment, identify the design of experiment

completely randomized design

The Physicians' Health Study I reported in its findings that there was not significant evidence that beta-carotene alone reduces the chance for cancer. We can conclude that,

differences noticed in cancer rates between those who take beta-carotene and those who do not could easily be attributed to chance, even if beta-carotene has no effect

A college wants to gather student opinion about parking for students on campus. It isn't practical to contact all students. Which of the following is an example of a bad way to choose a sample that uses convenience sampling?

interviewing students as they leave the campus parking lot

Medical experiments, such as the one to compare aspirin to a placebo are often double blind. This means that

neither the subject nor the doctors know which treatment the subject is receiving

A researcher studying the effect of pre-school on test scores later in life studied the academic records (grades and teacher comments) of 573 students who attended pre-school and 175 students who did not. What type of study is this?

observational study, but not a sample survey (This is not an experiment because the researcher did not assign treatments (he did not dictate whether students went to pre-school or not). This is not a sample survey since the students did not provide their own data)

The Physicians' Health Study I reported in its findings that there was significant evidence aspirin reduces the chance for myocardial infarction (heart attack). What does this mean? This means that even if there really was no effect of aspirin on the chance for myocardial infarction,

observing differences this large in the rates of heart attacks between groups would rarely occur by chance.

A national survey of TV network news viewers found that 48% said they would believe a phone-in poll of 300,000 persons rather than a random sample of 1000 persons. Of the viewers, 42% said they would believe the random sample poll. Which of the following statements correctly explains why the opinions of only 1000 randomly chosen respondents are a better guide to what all people think than the opinions of 300,000 callers?

The 1000 randomly chosen respondents represent the population as a whole, whereas the 300,000 callers did not do so (Call-in polls, especially those that cost to call in, and voluntary response polls in general, tend to attract responses from those who have strong opinions on the subject. These polls are often not the representative of the population as a whole. A random sample of size 1,000 will ideally be representative of the population as a whole. Although 300,000 callers represent an impressive number, but voluntary response of these callers must be biased.)

Suppose the results of an election poll estimate that 49% will vote for candidate A and 51% will vote for candidate B with a 3% margin of error. What conclusion would you draw?

The election is too close to call.

Suppose that we take many simple random samples of size 20 from a large class and for each sample we compute the average height of the students in the sample. Which of the following statements is true?

The variation in the means of the samples is described by a distribution. (Remember looking at the distribution of p-hat for many samples srawn from the same population? We showed its distribution on a histogram in class. The sample mean is also a statistic (just like p-hat) and it varies from sample to sample - some will be way higher than the population mean, some will be way lower, but most of the sample means will cluster closely around the population mean. We could plot this distribution on a histogram, just like we did for p-hat in class.)

A November 2007 Gallup Poll of 1004 adults found that 572 are satisfied with the total cost they pay for their health care. The announced margin of error is ±3 percentage points. The announced confidence level is 95%. Which of the statements is a correct and complete confidence statement in this scenario?

We are 95% confident that the percent of all adults who are satisfied with the total cost they pay for healthcare is between 54% and 60%. (A confidence statement states the level of confidence, the confidence interval lower and upper bound and talks about the population (not the sample!). So, the correct and complete confidence statement is: We are 95% confident that percent of all adults who are satisfied with the total cost they pay for healthcare is between 54% and 60%.)

Confounding often defeats attempts to show that one variable causes another. Counfouding means that

the effects of two variables are mixed up, so we cannot say which one is having an effect on the response

If we take many simple random samples from the same population, we expect:

the values of the statistic will vary from sample to sample.

In the "Help on Exam" experiment, a possible lurking variable is

time of day (span style=";"Time of day could affect the midterm exam score, but was not accounted for as one of the variables studied./span)

An important reason for using randomization when designing an experiment is

to reduce the effect of confounding