Probability + Statistics Exam 1

1 point) A simple random sample of 30 residents from Seattle is taken to estimate the median income of all Seattle residents. Is this study A. REPRESENTATIVE? B. NON-REPRESENTATIVE? A sample of professional football players is taken to estimate the mean weight of all adult males. Is this study A telephone survey is conducted during the day in order to determine the chances of a certain candidate winning an election. Is this study Using a sample of 40 patients from a local hospital, researchers measured cholesterol level in an attempt to estimate the mean cholesterol level of U.S. citizens. Is this study

A, B, B, B

In a box plot, what percent of the scores are between the lower and upper hinges?

50%

When plotted on the same graph, a distribution with a mean of 50 and a standard deviation of 10 will look more spread out than will a distribution with a mean of 60 and a standard deviation of 5.

True

Is this study appropriate for the statistical questions it's supposed to answer? Mark the most suitable choice. A. No, because they actively interfered with the test of the first group, and therefore affected their test results. B. Yes, because they randomized the subjects between the groups and used an appropriate measure for the effect (the test scores). C. No, because the type of study they used was inappropriate. D. No, because maybe one of the groups has significantly better reading comprehension skills than the other group, regardless of the highlighted text.

B

An ad for a new medical ointment claims '92% of people surveyed claim relief 2 hours after using this ointment for muscle pain.' No information is given about how the company obtained its data. Based on this data, which of the following conclusions are valid? Select all that apply. A. If you do not use this ointment, you will not feel better. B. This ointment works for most people. C. If you use this ointment, you will feel better in 2 hours. D. None of the above is valid.

D

An experiment investigated the effect of length and repetition of TV ads on students choosing to eat at Del Taco. All 60 students watched a 40-minute television program that included ads for Del Taco. Some students saw a 30-second commerical; others a 90-second commerical. The same commerical was shown either 1, 3, or 5 times during the program. After the viewing, each student was asked to rate their craving for Del Taco on a scale of 0 to 10. What are the levels of the length factor? A. 60 students B. 1, 3, or 5 commercials during the 40-minute television program C. craving for Del Taco on a scale of 0 to 10 D. 30-second and 90-second commericals E. 40-minute television program

D

City Councilwoman Kelly wants to know whether the residents of her district support a proposed school redistricting plan. Which of the following survey methods will allow Councilwoman Kelly to make a valid conclusion about whether residents of her district support the proposed plan? Select all that apply. A. Ask a group of parents at the local playground. B. Ask the residents of Shady Acres Retirement Community. C. Ask her neighbors. D. Ask 200 residents of her district whose names are chosen at random. E. None of the above

D

In a survey based on a random sample of high school seniors at a local high school, 70% of those surveyed said they do more than 3 hours of homework per day. Based on this data, which of the following conclusions are valid? Select all that apply. A. About 70% of all high school seniors do more than 3 hours of homework per day. B. Exactly 30% of all seniors at this high school do less than 3 hours of homework per day. C. Exactly 70% of all seniors at this high school do more than 3 hours of homework per day. D. About 70% of seniors at this high school do more than 3 hours of homework per day. E. None of the above

D

A pharmaceutical company wanted to check whether their new cough medicine really relieves coughs. To do that, they went over medical records of all clinics in the country and looked for an association between the type of medicine prescribed for patients who suffer from coughs and the level of their recovery. What is the objective of the company's study? A. They want to determine whether there is a correlation between taking the cough medicine and cough relief. B. They want to demonstrate that their cough medicine helps relieve coughs. C. They want to estimate the proportion of patients taking the cough medicine.

A

Ross wants to conduct a survey of his 100 classmates to determine which candidate for class treasurer, Warren or Willa, is in the lead in the upcoming election. Ross will ask the question, 'If the election were today, which candidate would get your vote?' Which of the following methods of surveying his classmates will allow Ross to make valid conclusions about which candidate is in the lead? Select all that apply. A. Ask all of Warren's friends. B. Ask all of the students in the student section at a basketball game. C. Ask every student in the class. D. Put the names of all the students in a hat and draw 100 names. Ask those students whose names are drawn. E. None of the above.

C, D

Chia Pets - those terra-cotta figurines that sprout fuzzy green hair - made the chia plant a household name. But chia has gained an entirely new reputation as a diet supplement. In one 2009 study, a team of researchers recruited 38 men and divided them evenly into two groups: treatment or control. They also recruited 38 women, and they randomly placed half of these participants into the treatment group and the other half into the control group. One group was given 25 grams of chia seeds twice a day, and the other was given a placebo. The subjects volunteered to be a part of the study. After 12 weeks, the scientists found no significant difference between the groups in appetite or weight loss. (a) What type of study is this? (b) Can we make a causal statement based on this study?

Controlled, Yes

An ad states that 'in a survey at Helping Hands Hospital, 97% of doctors stated they would not want to work anywhere else.' No information is given about how the hospital obtained its data. Based on this data, which of the following conclusions are valid? Select all that apply. A. Exactly 3% of all doctors at Helping Hands may prefer working somewhere else. B. Exactly 97% of all doctors at Helping Hands would not want to work anywhere else. C. About 97% of all doctors at Helping Hands would not want to work anywhere else. D. About 3% of all doctors working at Helping Hands may prefer working somewhere else. E. None of the above is valid.

E

In a survey based on a random sample of seniors at Pine Valley High School, 81% of students said they will need loans for college. Based on this data, which of the following conclusions are valid? Select all that apply. A. Exactly 19% of all seniors at Pine Valley will not need loans for college. B. About 81% of all students at Pine Valley will need loans for college. C. About 81% of seniors at Pine Valley will need loans for college. D. Exactly 81% of all seniors at Pine Valley will need loans for college. E. None of the above.

C

The city council of Helena wants to determine whether the residents favor a building plan for the town center. They will ask residents over 21 years of age, 'Do you favor the proposed building plan?' Which of the following methods of surveying the residents over 21 will allow the city council to make valid conclusions about the preferences of Helena's residents? A. Ask every resident over 21 years of age. B. Ask all of the residents over 21 who live west of the train tracks C. Ask 200 residents over 21 who are shopping at the mall on a particular Saturday. D. Put all of the names of residents over 21 into a computer program and allow the program to generate 200 random names. Ask those residents. E. None of the above

D

The median and mean of any list are always close together. Half of a list is always below average. If you add 7 to each entry on a list, that adds 7 to the mean. If you add 7 to each entry on a list, that adds 7 to the standard deviation. If you double each entry on a list, that doubles the mean. If you double each entry on a list, that doubles the standard deviation. If you change the sign of each entry on a list (multiply by negative 1), that changes the sign of the mean. If you change the sign of each entry on a list (multiply by negative 1), that changes the sign of the standard deviation.

F, T, F, T, T, T, F

A researcher is interested in the effects of exercise on mental health and he proposes the following study: Identify representative proportions of 18-30, 31-40 and 41-55 year olds from past medical records. Next, follow the medical records from the subjects' yearly exams and identify subgroups in each category that exercise at least twice per week and subgroups that report not to exercise. Finally, compare the scores on their latest mental health exams to their scores from their first exams (a) What type of study is this? (b) Can we make a causal statement based on this study?

observational, no

The engineers found that the average taste score of the new formula is 4 points lower than the average taste score of the old formula. What valid conclusions can be made from this result? A. The result suggests that the old formula tastes better among teenagers than the new one. B. There's a positive correlation between drinking the old formula and the perceived tastefullness among teenagers. C. The result suggests that the old formula tastes better among teenage boys than the new one. D. The old formula tastes better than the new one.

A

The school board administered a math test to all students in grades 6-8 at Johnsonville Middle School and determined that 15% of them were below grade level in math. Based on this data, which of the following conclusions are valid? A. 15% of all students in grades 6-8 at JMS are below grade level in math. B. 15% of eighth-grade students in the district are below grade level in math. C. 15% of all eighth-grade students at JMS are below grade level in math. D. 15% of all students at JMS are below grade level in math. E. None of the above

A

The taste engineers at 'Drinksoft' have developed a new formula for their major brand 'Cola-Loca.' They wanted to know how tasty it is to teenagers compared to the old formula, so they decided to set up a blind taste test. They randomly assigned 300 bilndfolded, teenaged participants to two groups. One group was given the old formula of 'Cola-Loca' and the other was given the new formula. Each participant was asked to fill a formal taste 10-point questionnaire, where 1 is considered 'awful' and 10 is considered 'delicious.' What is the objective of the engineers study? A. The engineers want to determine whether teenagers think the new formula of 'Cola-Loca' is tastier than the old formula. B. The engineers want to determine how good the new formula tastes. C. The engineers want to determine which formula of 'Cola-Loca' teenagers would select.

A

In a survey based on a random sample of 1000 customers, CableCom found that 42% of its customers are satisfied with CableCom's service. Based on this data, which of the following conclusions are valid? A. About 42% of all of CableCom's customers are satisfied with their service. B. Exactly 42% of those surveyed are satisfied with their service. C. Exactly 42% of all of CableCom's customers are satisfied with their service. D. Exactly 58% of all of CableCom's customers are not satisfied with their service. E. None of the above

A,B

An experiment investigated the effect of length and repetition of TV ads on students choosing to eat at Del Taco. All 60 students watched a 40-minute television program that included ads for Del Taco. Some students saw a 30-second commerical; others a 90-second commerical. The same commerical was shown either 1, 3, or 5 times during the program. After the viewing, each student was asked to rate their craving for Del Taco on a scale of 0 to 10. What is the response variable? A. 30-second and 90-second commericials B. craving for Del Taco on a scale of 0 to 10 C. 60 students D. 40-minute television program E. 1, 3, or 5 commercials during the 40-minute television program

B

Is the study appropriate for the statistical questions it's supposed to answer? Mark the most suitable choice. A. Yes, because the study assesses the connection between taking the cough medicine and cough relief. B. No, because the type of study isn't appropriate for the question. C. No, because the company didn't choose the clinics at random. D. No, because the study collects data of patients who took other medications.

B

Researchers were interested in the effect of pre-existing inappropriate highlighting of text on reading comprehension. They randomly assigned a group of 600 students to two groups. Both groups were asked to answer a reading comprehension test. The text given to the first group had inappropriate passages highlighted, while the text of the second group wasn't highlighted at all. Then, the researchers compared the average score of each group in the reading comprehension test. What is the objective of this study? A. The researchers want to see if there is a correlation between inappropriate highlighting and student reading comprehension. B. The researchers want to see if inappropriate highlighting causes student reading comprehension to decrease. C. The researchers want to estimate the level of reading comprehension in students.

B

The school lunch committee at Bayside High wants to determine what types of vegetables to serve in the cafeteria. As part of their survey, they ask all members of the Bayside boy's baseball team the question 'Do you like broccoli?' 15% of the team responds 'yes'. Based on this data, which of the following conclusions are valid? Select all that apply. A. 15% of the students on the baseball team at Bayside High like all vegetables. B. Exactly 15% of all students on the baseball team at Bayside High like broccoli. C. 15% of the students on the baseball team at Valley High (Bayside's main rival in baseball) like broccoli. D. About 15% of all students at Bayside High like broccoli. E. None of the above

B

Beth wants to go on a popular TV talent show. In order to be accepted, her audition must get at least 60% positive votes from people in the crowd. To make sure she's not going to embarrass herself, she performed her act in front of 100 random people from her school. About 90% of the people said they would give her a positive vote. She calculated the margin of error and found it's well within the range above 60%, so she decided to go to the audition. What is the objective of Beth's study? Is the study appropriate for the statistical questions it's supposed to answer?

B. She wants to sample the population to see if there is a correlation between her performance and the audience response. D. No, because the population she sampled isn't necessarily representative.

An experiment investigated the effect of length and repetition of TV ads on students choosing to eat at Del Taco. All 60 students watched a 40-minute television program that included ads for Del Taco. Some students saw a 30-second commerical; others a 90-second commerical. The same commerical was shown either 1, 3, or 5 times during the program. After the viewing, each student was asked to rate their craving for Del Taco on a scale of 0 to 10. What are the subjects of this experiment? A. 40-minute television program B. 1, 3, or 5 commercials during the 40-minute television program C. 60 students D. effect of length and repetion of TV ads E. craving for Del Taco on a scale of 0 to 10

C

An online ad for Dr. Mary Hart, a renowned cardiologist, states, 'in a survey of Dr. Hart's patients, 96% of a random sample of her patients say they would recommend Dr. Hart to other patients.' Based on this data, which of the following conclusions are valid? Select all that apply. A. 96% of all patients recommend Dr. Hart B. Exactly 96% of all Dr. Hart's patients would recommend her. C. About 96% of Dr. Hart's patients recommend her. D. 4% of Dr. Hart's patients do not recommend her. E. None of the above

C

After hundreds of consumer complaints, an inspection team wants to determine the percentage of defective phones produced by Sketchy Electronics. Which of the following methods will allow the team to make valid conclusions about the percentage of defective phones produced by Sketchy? Select all that apply. A. Each member of the team asks 20 of their friends who have phones from Sketchy's whether they are defective or not. B. Phone 200 of the people who have complained and ask them what was wrong with their phones. C. Phone all of their customers and ask whether their phones are defective. D. None of the above will allow them to make valid conclusions.

D