Intro & Sampling
This is or this is not a valid statistical question: What percent of U.S. residents think the president is doing a good job?
What is "this is"?
A college administrator wants to esimate the mean distance that students at a large community college live from campus. To find out, she obtains a list of all students from the registrar's database. Describe in detail how you could select an SRS of 100 students.
What is, assign each student a number, then use a random number generator to pick 100 numbers from that list?
A sample of 880 drivers was asked the following question: "Recalling the last ten traffic lights you drove through, how many of them were red when you entered the intersection?" Of the 880 respondents, 171 adminitted that at least one of them had been red. The drivers were selected by random sampling all listed residential telphone numbers. Explain how undercoverage may have led to bias in this survey.
What is "most people with residential phones might be older and less likely to blow red lights"?
Can watching fast-paced cartoons reduce the mental functioning of children? Sixty 4-year-old children were randomly divided into three groups. One group was shown a fast-paced cartoon, one was shown an educational cartoon, and one was given art supplies and instructed to draw pictures. All of the children spent 9 minutes watching the cartoons or drawing. Afterward, the 4-year-olds who watched the fast-paced cartoon scored significantly worse than the other two groups on four different tests that measured brain function. Explain the purpose of the random assignment in the context of this experiment.
What is to eliminate confounding variables and create roughly equivalent groups?
This person is the only junior in the class.
Who is Hayden?
A department store mails a customer-satisfaction survey to people who make credit card purchases at the store. This month, 45,000 people made credit card purchases. Surveys are mailed to 1000 of these people, chosen at random, and 137 people return the survey form. Identify the sample in this setting.
Who are the 137 people who returned the survey?
A college administrator wants to esimate the mean distance that students at a large community college live from campus. To find out, she obtains a list of all students from the registrar's database.This would more likely yield a sample result closer to the true population mean: an SRS of 50 students or an SRS of 100 students.
What is an SRS of 100 students?
A sample of 880 drivers was asked the following question: "Recalling the last ten traffic lights you drove through, how many of them were red when you entered the intersection?" Of the 880 respondents, 171 adminitted that at least one of them had been red. The drivers were selected by random sampling all listed residential telphone numbers. Explain how response bias might affect the results of this survey.
What is "people might lie about what they actually did so there might be more people who did this than actually admit it"?
An experiment was done to determine if Botox can reduce back pain. This experiment randomly assigned patients with back pain to receive 200 units of Botox or the placebo treatment, saline solution. The decrease in back pain for each patient was measured after 8 weeks. This is the reason it was important to measure each patient after the same amount of time (8 weeks).
What is to know if the type of injection was the reason for the changes in back pain versus just the length of time?
These students all had surgery on their legs in just the first two months of the school year.
Who are Elijah, Hannah, and Rodney?
A department store mails a customer-satisfaction survey to people who make credit card purchases at the store. This month, 45,000 people made credit card purchases. Surveys are mailed to 1000 of these people, chosen at random, and 137 people return the survey form. Identify the population in this setting.
Who are the 45,000 people who made credit card purchases this month?
A recent Gallup poll conducted telephone interviews with a random sample of 1000 adults aged 18 and older. Of these, 37% said that football is their favorite sport to watch on television. The margin of error for this estimate is 3.1 percentage points. Interpret the margin of error.
What is "we expect the true population of all adults 18 and over who say football is their favorite sport to be between 33.9% and 40.1%"?
In a study of a random sample of 1739 adults from Nova Scotia, Canada, researchers interviewed each participant and, among other variables, assessed their attitude using a formal psychological survey. It was found that adults who had a more positive attitude were less likely than their peers to have coronary heart disease over a 10-year period. Based on this study is it reasonable to conclude that a positive attitude causes a decrease in the risk of coronary heart disease in adults in Nova Scotia? Explain.
What is no? Confounding variables possible
In the 100-point question in this column we learned about the experiment to determine if watching a fast-paced cartoon, watching an educational cartoon, or drawing had an effect on the brain function of 4-year-old children. Sixty children were randomly assigned to one of these treatments. One of the decision-making tasks at the end of the study was a delay of gratification. If children could wait long enough, they could have 10 pieces of snack food, but if they couldn't wait long enough, they would get only 2 pieces of snack food. The response variable was how long, in seconds, the children were able to wait. The average waiting time for children in the educational cartoon group was 257.20 seconds, compared with an average of 146.15 seconds for the fast-past cartoon group. the 111.05-second different was found to be statistically significant. This is what a statistically significant difference means.
What is that the average wait time was too large to be due only to change variation in the random assignment of groups?
These students frequently speak in annoying accents.
Who are Colton and Kendra?
To fund a program to buy electronic tablets for every second-grade student in Springdal public schools, the board of education proposes a 5% increase in property taxes. Once local "golden oldies" radio station asks listeners to call in to voice their support for, or opposition to, the proposal. The station finds that 78% of the callers are opposed. This is the type of sample the radio station obtained.
What is voluntary response?
Melissa and Madeline love pepperoni pizza, but sometimes they are disappointed with the small number of pepperonis on their pizza. To investigate, they went to their favorite pizza restaurant at 10 random times during the week and ordered a large pepperoni pizza. The sample mean for these data is 37.4 pepperonis. The SD of the simulated sample mean for 500 random samples of size 10 is 2.127. Approximate the margin of error for the esimate of the mean number of pepperonis on a large pizza from this restaurant.
What is 4.254?
Can reducing calorie intake increase the length of one's life? Researchers randomly assigned 46 rhesus monkeys to a calorie-restricted (CR) diet group or to a control group that received a standard diet. The CR group was monitored to prevent malnutrition. It was found that the CR group lived longer on average. Explain why it was necessary to include the control group.
What is to provide a baseline for comparing the effects of the calorie-restricted group?
Recall the study on the effect of fast-paced cartoons on decision making in children. The children were randomly divided into 3 groups. The children spent 9 minutes watching cartoons or drawing. Then tests of decision making were given 30 minutes after the children finished the drawing. The results of this study can or cannot be generalized to all 4-year-olds. Explain.
What is cannot because it was not a random sample?
These students play on the soccer team.
Who are Avan and Emmanuel?
To fund a program to buy electronic tablets for every second-grade student in Springdal public schools, the board of education proposes a 5% increase in property taxes. Once local "golden oldies" radio station asks listeners to call in to voice their support for, or opposition to, the proposal. The station finds that 78% of the callers are opposed. This is likely greater than or less than the percent of all Springdale residents who oppose the proposal. Explain.
What is greater than because it is likely older residents?
Melissa and Madeline love pepperoni pizza, but sometimes they are disappointed with the small number of pepperonis on their pizza. To investigate, they went to their favorite pizza restaurant at 10 random times during the week and ordered a large pepperoni pizza. The sample mean for these data is 37.4 pepperonis. The SD of the simulated sample mean for 500 random samples of size 10 is 2.127. Interpret the margin of error.
What is "we expect the true average amount of pepperoni on all large pizzas to between 33.229 and 41.733"?
You may have heard that Botox is used for cosmetic surgery, but could it have other beneficial uses? A total of 31 patients who suffered chronic low-back pain were randomly assigned to receive 200 units of either Botox or saline solution through 5 injections at 5 different locations in their backs. The saline injection was not expected to reduce pain but was given as a placebo treatment. After 8 weeks, 10 of the 15 Botox patients (66.7%) experienced pain relief, comparted with 3 of the 16 (18.8%) saline patients. In this experiment, the patients didn't know which injections they received. This term defines this concept, and why is this important in an experiment?
What is blinding and to eliminate the placebo effect?
Recall the study on the effect of fast-paced cartoons on decision making in children. The children were randomly divided into 3 groups. The children spent 9 minutes watching cartoons or drawing. Then tests of decision making were given 30 minutes after the children finished the drawing. Based on the study, it is or it is not reasonable to say that fast-paced cartoons cause a decrease in brain function.
What is it is reasonable because the groups were randomly assigned?
This was the only student in the class to get an A in quarter 1.
Who is Ethan?