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Exam 3: Confidence Intervals

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Question 51

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Use the following to answer the questions below: There are 24 students enrolled in an introductory statistics class at a small university. As an in-class exercise the students were asked how many hours of television they watch each week. Their responses, broken down by gender, are summarized in the provided table. Assume that the students enrolled in the statistics class are representative of all students at the university. -You wish to provide a 95% confidence interval for the difference in the mean number of hours spent watching television for males and females at this university based on a bootstrap distribution. Which percentiles would you use?

A) The 2.5%- and 97.5%-iles
B) The 5%- and 95%-iles
C) The 10%- and 95%-iles
D) The 10%- and 90%-iles

E) B) and D)
F) B) and C)

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Question 52

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Use the following to answer the questions below: November 6, 2012 was election day. Many of the major television networks aired coverage of the incoming election results during the primetime hours. The provided table displays the amount of time (in minutes) spent watching election coverage for a random sample of 25 U.S. adults. -What is the population parameter of interest? Define using the appropriate notation.

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μ = mean amount of t...

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Question 53

Multiple Choice

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Use the following to answer the questions below: An Internet provider contacts a random sample of 300 customers and asks how many hours per week the customers use the Internet. It found the average amount of time spent on the Internet per week to be about 7.2 hours. -The standard error is about 0.458. Find a 95% confidence interval for the parameter. Round the margin of error to two decimal places.

Use the following to answer the questions below: Identify each of the following as either a parameter or a statistic, and give the correct notation. -Average gas price in Minnesota, based on prices at randomly selected gas stations throughout the state.

Use the following to answer the questions below: In a survey of 7,786 randomly selected adults living in Germany, 5,840 said they exercised for at least 30 minutes three or more times per week. -Identify, with the proper notation, the quantity being estimated.

Use the following to answer the following questions: A study to investigate the dominant paws in cats was described in the scientific journal Animal Behaviour. The researchers used a random sample of 42 domestic cats. In this study, each cat was shown a treat (5 grams of tuna), and while the cat watched, the food was placed inside a jar. The opening of the jar was small enough that the cat could not stick its head inside to remove the treat. The researcher recorded the paw that was first used by the cat to try to retrieve the treat. This was repeated 100 times for each cat (over a span of several days). The paw used most often was deemed the dominant paw (note that one cat used both paws equally and was classified as "ambidextrous"). Of the 42 cats studied, 20 were classified as "left-pawed." -The researchers were also interested in comparing the proportion of "left-pawed" cats for male and female cats. Of the 21 male cats in the sample, 19 were classified as "left-pawed" While only 1 of the 21 female cats was considered to be "left-pawed." A bootstrap distribution (based on 1,000 bootstrap samples) for difference in the proportion of "left-pawed" Cats is provided. Would it be appropriate to use this bootstrap distribution to construct a confidence interval for the difference in the proportion of male and female cats that are "left-pawed"?

Use the following to answer the questions below: November 6, 2012 was election day. Many of the major television networks aired coverage of the incoming election results during the primetime hours. The provided table displays the amount of time (in minutes) spent watching election coverage for a random sample of 25 U.S. adults. -What is the population parameter of interest? Define using the appropriate notation.

Use the following to answer the questions below: There are 24 students enrolled in an introductory statistics class at a small university. As an in-class exercise the students were asked how many hours of television they watch each week. Their responses, broken down by gender, are summarized in the provided table. Assume that the students enrolled in the statistics class are representative of all students at the university. ‪ -Describe how to use the data to construct a bootstrap distribution. What value should be recorded for each of the bootstrap samples?

Use the following to answer the questions below: A study to investigate the dominant paws in cats was described in the scientific journal Animal Behaviour. The researchers used a random sample of 42 domestic cats. In this study, each cat was shown a treat (5 grams of tuna), and while the cat watched, the food was placed inside a jar. The opening of the jar was small enough that the cat could not stick its head inside to remove the treat. The researcher recorded the paw that was first used by the cat to try to retrieve the treat. This was repeated 100 times for each cat (over a span of several days). The paw used most often was deemed the dominant paw (note that one cat used both paws equally and was classified as "ambidextrous"). Of the 42 cats studied, 20 were classified as "left-pawed." -What is the population parameter of interest? Define using the appropriate notation.

Use the following to answer the questions below: In a survey conducted by the Gallup organization, 1,017 adults were asked "In general, how much trust and confidence do you have in the mass media - such as newspapers, TV, and radio - when it comes to reporting the news fully, accurately, and fairly?" 81 said that they had a "great deal" of confidence, 325 said they had a "fair amount" of confidence, 397 said they had "not very much" confidence, and 214 said they had "no confidence at all." -The estimate of the standard error is 0.013. Use the estimate of the standard error to construct a 95% confidence interval for the proportion of U.S. adults who have no confidence in the media. Round the margin of error to three decimal places.

Use the following to answer the questions below: A random sample of 200 students shows that 62% of students use the Student Health Center at some point during their time on campus, with a margin of error of ± 4%. Based on this information, identify each of the following as plausible or not for the percent of the entire student body that use the Student Health Center at some point during their time on campus. -60%

Use the following to answer the questions below: According to ESPN.com, the average number of yards per game for all NFL running backs with at least 50 attempts in the 2011 season was 49 yards/game. A sample of 20 running backs from the 2011 season averaged 46.54 yards/game. -Is 49 yards/game a parameter or statistic?

Use the following to answer the questions below: November 6, 2012 was election day. Many of the major television networks aired coverage of the incoming election results during the primetime hours. The provided table displays the amount of time (in minutes) spent watching election coverage for a random sample of 25 U.S. adults. -Percentiles of the bootstrap distribution (based on 5,000 samples) are provided. Use the percentiles to provide a 92% confidence interval for the mean amount of time (in minutes) U.S. adults spent watching election coverage on election night. Indicate which percentiles you are using.

Use the following to answer the questions below: There are 24 students enrolled in an introductory statistics class at a small university. As an in-class exercise the students were asked how many hours of television they watch each week. Their responses, broken down by gender, are summarized in the provided table. Assume that the students enrolled in the statistics class are representative of all students at the university. ‪ -If the parameter of interest is the difference in means, - where and are the mean number of hours spent watching television for males and females at this university, find a point estimate of the parameter based on the available data. Report your answer with two decimal places.

Use the following to answer the questions below: In a recent Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over) , 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. They also report that the "margin of sampling error is plus or minus 4%." -What is the population of interest?

Use the following to answer the questions below: Suppose we are interested in comparing the proportion of male students who smoke to the proportion of female students who smoke. We have a random sample of 150 students (60 males and 90 females) that includes two variables: Smoke = "yes" or "no" and Gender = "female (F)" or "male (M)." The two-way table below summarizes the results. -Describe how you would estimate the standard error from the bootstrap distribution.

Use the following to answer the questions below: The sampling distribution shows sample proportions from samples of size n = 35. ‪ -Estimate the population proportion from the dotplot.

Use the following to answer the questions below: In a survey of 7,786 randomly selected adults living in Germany, 5,840 said they exercised for at least 30 minutes three or more times per week. -Using the correct notation, give the value of the best estimate of the population parameter. Round your answer to two decimal places.

Use the following to answer the questions below: November 6, 2012 was election day. Many of the major television networks aired coverage of the incoming election results during the primetime hours. The provided table displays the amount of time (in minutes) spent watching election coverage for a random sample of 25 U.S. adults. -Use the data from the sample to estimate the parameter of interest. Report your answer with two decimal places.

Use the following to answer the following questions: A study to investigate the dominant paws in cats was described in the scientific journal Animal Behaviour. The researchers used a random sample of 42 domestic cats. In this study, each cat was shown a treat (5 grams of tuna), and while the cat watched, the food was placed inside a jar. The opening of the jar was small enough that the cat could not stick its head inside to remove the treat. The researcher recorded the paw that was first used by the cat to try to retrieve the treat. This was repeated 100 times for each cat (over a span of several days). The paw used most often was deemed the dominant paw (note that one cat used both paws equally and was classified as "ambidextrous"). Of the 42 cats studied, 20 were classified as "left-pawed." -Construct a 99% confidence interval and provide an interpretation of it in the context of this data situation.