STAT 110: Quiz #11 Name: ______
Spring 2013
Point: 20

Circle the letter of the best response to each question.

  1. A college official conducted a survey to estimate proportions of students currently living in dormitories on campus who prefer each of the following room types: single, double, or multiple (more than two people). Five thousand students live in dormitories on campus. A random sample of 500 students was selected to receive the survey.

Indicate for the following statement whether you agree or disagree with the argument presented.

The survey results cannot be generalized to the population of students currently living in dormitories because it was sent to only 500 students.

  1. Agree
  2. Disagree
  1. A local television station for a city with a population of 500,000 recently conducted a poll where they invited viewers to call in and voice their support or opposition to a controversial referendum that was to be voted on in an upcoming election. Over 5,000 people responded, with 67% opposed to the referendum. The TV station announced that the referendum would most likely be defeated in the election.

Select the best answer below for why you think the TV station's announcement is valid or invalid.

  1. Valid, because the sample size is large enough to represent the population.
  2. Valid, because 67% is likely to be far enough above 50% to predict a majority vote
  3. Invalid, because the sample is too small given the size of the city
  4. Invalid, because the sample is not likely to be representative of the population
  1. Researchers surveyed 1,000 randomly selected adults in the United States. A strong, positive, statistically significant correlation was found between income and the number of containers the adults reported typically recycling in a week.

Can the researchers conclude that earning more money causes more recycling among U.S. adults?

  1. No, the study design does not allow causation to be inferred
  2. No, the sample size is too small to allow causation to be inferred
  3. Yes, the statistically significant result allowscausation to be inferred
  4. Yes, there is strong evidence that income causes people to care more about the environment
  1. A recent research study randomly assigned participants into groups that were given different levels of Vitamin E to take daily. One group received only a placebo pill. The research study followed the participants for eight years to see which ones developed a particular type of cancer during that time period.

What is the primary purpose of the use of random assignmentfor making inferences based on this study?

  1. To ensure that a person doesn’t know whether or not they are getting the placebo.
  2. To ensure that the groupsare similar in all respects except for the level of Vitamin E.
  3. To ensure that the study participants are representative of the larger population.

Use the following for Questions 5 and 6:

A researcher investigated the impact of a particular herbicide on fish. He randomly assigned 60 healthy fish to either be exposed or not be exposedto the herbicide, with 30 fish in each group. The fish exposed to the herbicide showed higher levels, on average, of an enzyme associated with cancer.

Suppose the difference in average enzyme level between the two groups of fish was determined NOTto be statistically significant (i.e., evidence of a difference between the groups was not found).

For questions 5 and 6, indicate whether the explanation provided is valid or invalid.

  1. The sample size may have been too small to detect a statistically significant difference even if the herbicide did have an impact.
  2. Valid
  3. Invalid
  1. The research results demonstratedstrong evidence that the herbicide does not cause higher levels of the enzyme.
  2. Valid
  3. Invalid

  1. Studies show that as women grow older they tend to have lower bone density.

Which of the following graphs illustrates this point?

  1. Graph A
  2. Graph B
  3. Graph C
  1. A certain manufacturer claims that 50% of the candies they produce are brown and that candy pieces are randomly placed into bags. Sam plans to buy a large family size bag of these candies and Kerry plans to buy a small fun size bag.

Which bag is more likely to have more than 70% brown candies?

  1. Sam’s, because a larger bag is more likely to have a larger proportion of brown candies.
  2. Kerry’s, because there is more variability in proportions of colors among smaller samples.
  3. Both have the same chance because the bags they buy are both random samples of candy pieces.
  1. Imagine you have a barrel that contains thousands of candies that are several different colors. We know that the manufacturer produces 35% yellow candies. Ten students each take a random sample of 20 candies and record the percentage of yellow candies in their sample.

Which of the following provides an accurate range for the percentage of yellow candies that you can reasonably expect to be obtained across theseten samples?

  1. About 0% to 100%
  2. About 15% to 55%
  3. About 30% to 40%
  4. About 35% to 65%

Use the following for Questions 10 and 11:

Jean lives about 10 miles from the college where she plans to attend a 10-week summer class. There are two main routes she can take to the school, one through the city and one through the countryside. The city route is shorter in miles, but has more stoplights. The country route is longer in miles, but has only a few stop signs and stoplights. Jean sets up a randomized experiment where each day she tosses a coin to decide which route to take that day. She records the minutes of travel time for 5 days of travel on each route.

Country Route: 17, 15, 17, 16, 18

City Route: 18, 13, 20, 10, 16

  1. It is important to Jean to arrive on time for her classes, but she does not want to arrive too early because that would increase her parking fees.

Based on the data gathered, which route would you advise her to choose?

  1. The Country Route
  2. The City Route
  3. No difference in routes
  1. Which of the following best matches the reason for your answer to question 10?
  1. Because the Country Route times are consistently between 15 and 18 minutes.
  2. Because she can get there in 10 minutes on a good day with the City Route.
  3. Because the average time for the City Route is less than for the Country Route.
  4. Because the times on the two routes are about the same.
  5. None of the above. Please give your own reason: ______

Use the following for Question 12

A sample of 250 people who frequently suffer from headaches were randomly selected from a large medical facility. 100 of these people were randomly assigned to receive a new headache medication when they had a headache, and the other 150 people received the old headache medication. The time until the patient reported that they no longer had a headache was recorded. The results are shown below.

  1. Three different students made the following statements. Choose the statement that makes the most valid inference based on the results above.
  1. The old formula may be preferable. Two people who took the old formula felt relief in less than 20 minutes, compared to none who took the new formula. Also, the worst result - near 120 minutes - was with the new formula.
  2. The new formula may be preferable. People taking the new formula will tend to feel relief about 20 minutes sooner, on average, than those taking the old formula.
  3. Neither formula is preferable. The number of patients in the two groups is not the same so there is no fair way to compare the two medications.

Use the following for Questions 13–16

A high school statistics class wants to estimate the average weight of the chocolate chips per cookie in a generic brand of chocolate chip cookies. They collect a random sample of cookies, rinse away the baked dough,and obtain the weightin grams of the chocolate chips for each cookie. Based on their data, the 95% confidence interval for the average weight of chocolate per cookie goes from 5.65 to 6.35 grams.

For questions 15 to 18, indicate whether the interpretation of the interval provided is valid or invalid.

  1. With 95% confidence, we can infer that each cookie for this generic brand has approximately 5.65 to 6.35 grams of chocolate.
  1. Valid
  2. Invalid
  1. With 95% confidence, we can infer that the average weight of chocolate per cookie in this generic brand is 6 grams plus or minus 0.35 grams.
  2. Valid
  3. Invalid
  4. We can infer that 95% of all cookies from this generic brand willhave between 5.65 to 6.35 grams of chocolate.
  1. Valid
  2. Invalid
  1. With 95% confidence, we can infer that the interval of 5.65 to 6.35 grams includes the true average weight of chocolate per cookie.
  1. Valid
  2. Invalid

Use the following for Questions 17– 23

A research question of interest is whether financial incentives can improve performance. Alicia designed a study to test whether video game players are more likely to win on a certain video game when offered a $5 incentive compared to when simply told to “do your best.” Forty subjects are randomly assigned to one of two groups, with one group being offered $5 for a win and the other group simply being told to “do your best.” She collected the following data from her study:

$5 incentive / “Do your best” / Total
Win / 16 / 8 / 24
Lose / 4 / 12 / 16
Total / 20 / 20 / 40

Based on these data, it looks like the $5 incentive is more successful than the encouragement, because the observed difference in “win” proportions is

In order to test whether this apparent difference might be due simply to chance, Alicia does the following:

  • She gets 40 index cards. On 24 she writes, "win" and on 16 she writes, "lose".
  • She then shuffles the cards and randomly places the cards into two stacks of 20 cards each. One stack represents "$5 incentive" and the other "verbal encouragement".
  • For this simulation, she computes the difference in the success rates by subtracting the success rate for the simulation's "verbal encouragement" group from the success rate of the simulation's "$5 incentive" group.
  • She repeats the previous two steps 100 times.
  • She plots the 100 statistics she observes from these trials.

This is the simulated data that Alicia generated from her 100 trials and used to test her research question:

  1. What is the explanation for the process Alicia followed?
  1. This process allows her to compare her actual result to what could have happened by chance if the incentive had no effect.
  2. This process allows her to determine the percentage of time the $5 incentive strategy would outperform the “do your best" strategy if the experiment were repeated many times.
  3. This process allows her to determine how many times she needs to replicate the experiment for valid results.
  1. Alicia simulated data using which of the following assumptions?
  1. The $5 incentive is more effective than verbal encouragement for improving performance.
  2. The $5 incentive and verbal encouragement are equally effective at improving performance.
  3. Verbal encouragement is more effective than a $5 incentive for improving performance.
  1. Which of the following is closest to the p-value for the observed difference in proportions of 0.40 based onthe simulated data from Alicia’s 100 trials?
  1. p-value= 0.00
  2. p-value= 0.01
  3. p-value= 0.02
  4. p-value= 0.03
  5. p-value= 0.04
  6. p-value = 0.10
  1. Which of the following conclusions is supported by the simulation results?
  1. The $5 incentive is not effective because the distribution is centered at 0.
  2. The $5 incentive is effective because the distribution is centered at 0.
  3. The $5 incentive is not effective because the p-value is greater than .05.
  4. The $5 incentive is effective because the p-value is less than .05.

For questions 21-23, indicate whether the interpretation of the p-value provided is valid or invalid.

  1. The p-value is the probability that the $5 incentive group would have the same or lower success rate than the “do your best” rate.
  2. Valid
  3. Invalid
  1. The p-value is the probability that the $5 incentive group would have a higher success rate than the “do your best” group.
  1. Valid
  2. Invalid
  1. The p-value is the probability of obtaining a result as extreme as was actually found, if the $5 incentive is really not helpful.
  1. Valid
  2. Invalid

Use the following for questions 24 – 25

A newspaper article claims that the average age for people who receive food stamps in a community is 40 years. A local researcher believes that the average age is less than that. The researcher takes a random sample of 100 people in the community who receive food stamps, and finds their average age to be 39.2 years, which is statistically significantly lower than the age of 40 stated in the article (p-value < .05). Indicate for each of the following interpretations whether they are valid or invalid.

  1. The statistically significant result indicates that the majority of people who receive food stamps is younger than 40.
  2. Valid
  3. Invalid
  4. An error must have been made. This difference in means (39.2 vs. 40 years) is too small to be statistically significant.
  5. Valid
  6. Invalid

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CATALST Project
Goals and Outcomes Associated with Learning Statistics (GOALS)