Exam 3: Confidence Intervals

Use the following 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 The sampling distribution shows sample proportions from samples of size n = 35. -If samples of size n = 65 had been used instead of n = 35, which of the following would be true?

Use the following 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. -Two boxplots are shown. One boxplot corresponds to the yards/game for a random sample of n = 20 running backs. The other boxplot represents the values in a sampling distribution of 1,000 means of yards/game for samples of size n = 20. Which boxplot represents the sample? Which boxplot represents the sampling distribution? Briefly explain how you know.

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. -Use the estimate of the standard error to construct a 95% confidence interval for the mean amount of time (in minutes) U.S. adults spent watching election coverage on election night. Use three decimal places in your answer.

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. -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 create a confidence interval from a bootstrap distribution using percentiles, we keep the middle values and chop off a certain percentage from each tail. Indicate what percent of values must be chopped off from each tail for each confidence level. -95%

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 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"? Briefly explain.

Use the following Identify each of the following as either a parameter or a statistic, and give the correct notation. -Proportion of students at your university that smoke, based on data from your class.

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. -Describe how you would estimate the standard error from the bootstrap distribution.

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". -Percentiles of the bootstrap distribution (based on 5,000 samples) are provided. Use the percentiles to provide a 99% confidence interval for the parameter. Indicate the percentiles that you use.

Use the following 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. -Where should the bootstrap distribution be centered?

Use the following Identify if each of the following statements is a proper interpretation of a 95% confidence interval. -I am 95% sure that this interval will contain the population parameter.

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". -Suppose the parameter of interest is the proportion of U.S. adults who have "no confidence at all" in the media. Use the data to find an estimate of this parameter. Report your answer with two decimal places.

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 According to U.S. Census data, 71.6% of Americans are age 21 and over. The provided figure shows possible sampling distributions for the proportion of a sample age 21 and over, for samples of size n = 50, n = 125, and n = 250. Match the sample sizes (n = 50, n = 125, and n = 250) to their sampling distribution. -Sample C: n = _____________

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. -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 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 to use the data to construct a bootstrap distribution. What value should be recorded for each of the bootstrap samples.

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 confidence level to 99%.

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 to use the data to construct a bootstrap distribution. What value should be recorded for each of the bootstrap samples?

Use the following The sampling distribution shows sample means from samples of size n = 50. -If samples of size n = 30 had been used instead of n = 50, which of the following would be true?