Exam 3: Confidence Intervals

Use the following A 2009 study to investigate the dominant paws in cats was described in Animal Behaviour (Volume 78, Issue 2). 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 standard error is estimated to be 0.078 (based on 5,000 bootstrap samples). Find a 95% confidence interval for the proportion of domestic cats that are "left-pawed". Round the margin of error to three decimal places.

Use the following Suppose that a 95% confidence interval for the slope of a regression line based on a sample of size n = 100 and the percentiles of the slopes for 1,000 bootstrap samples goes from 2.50 to 2.80. For each change described (with all else staying the same), indicate which of the three confidence intervals would be the most likely result. -Decrease the sample size to n = 60.

Use the following 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. -Percentiles of the bootstrap distribution (based on 5,000 samples) are provided. Use the percentiles 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. Indicate which percentiles you are using.

Use the following 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. -Interpret your 92% confidence interval in the context of this data situation.

Use the following A 2009 study to investigate the dominant paws in cats was described in Animal Behaviour (Volume 78, Issue 2). 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 In a survey conducted by the Gallup organization September 6-9, 2012, 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". -Percentiles of the bootstrap distribution (based on 5,000 samples) are provided. Use the percentiles to provide a 95% confidence interval for the proportion of U.S. adults who have no confidence in the media. Indicate the percentiles that you use.

Use the following A 2009 study to investigate the dominant paws in cats was described in Animal Behaviour (Volume 78, Issue 2). 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 In a survey conducted by the Gallup organization September 6-9, 2012, 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". -Use technology to construct a bootstrap distribution with at least 1,000 samples and estimate the standard error.

Use the following In an October 2012 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 In an August 2012 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 A 2009 study to investigate the dominant paws in cats was described in Animal Behaviour (Volume 78, Issue 2). 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". -Use the data from the sample to estimate the parameter of interest. Round your answer to three decimal places.

In a dotplot of a bootstrap distribution, the number of dots should match the size of the original sample.

Use the following 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 Suppose that a 95% confidence interval for the slope of a regression line based on a sample of size n = 100 and the percentiles of the slopes for 1,000 bootstrap samples goes from 2.50 to 2.80. For each change described (with all else staying the same), indicate which of the three confidence intervals would be the most likely result. -Increase the number of bootstrap samples to 5,000

A sample of n = 10 Illinois gas stations taken on August 8, 2012 had an average price of $3.975 per gallon. The national average at this time was $3.63. If we want to use the sample data to construct a 95% confidence interval for the average gas price in Illinois (on August 8, 2012), where would the bootstrap distribution be centered?

Use the following In a poll conducted before the Republican presidential primary in Michigan, 134 of 420 randomly chosen likely voters indicated that they planned to vote for Mitt Romney. -Compute a sample statistic from these data. Use appropriate notation to label your statistic. Report your answer with three decimal places.

Use the following Identify each of the following as either a parameter or a statistic, and give the correct notation. -Correlation between height and armspan (distance from fingertip to fingertip when arms are extended to the sides) for all players on the Chicago Bulls basketball team, using data from all players currently on the team

Use the following The sampling distribution shows sample proportions from samples of size n = 35. -Estimate the standard error of the sample proportions.

Use the following In a survey conducted by the Gallup organization September 6-9, 2012, 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". -Describe how you would estimate the standard error from the bootstrap distribution.

Use the following In a poll conducted before the Republican presidential primary in Michigan, 134 of 420 randomly chosen likely voters indicated that they planned to vote for Mitt Romney. -What quantity is the interval estimate in (b) trying to capture? Identify with appropriate notation and words.