Exam 3: Confidence Intervals

A bootstrap distribution, based on 1,000 bootstrap samples is provided. Use the distribution to estimate a 99% confidence interval for the population mean. Explain how you arrived at your answer.

Use the following The sampling distribution shows sample proportions from samples of size n = 35. -Using the sampling distribution, how likely is = 0.45?

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. -The standard error is estimated to be 1.511 (based on 5,000 bootstrap samples). Find a 95% confidence interval for the difference in the mean number of hours spent watching television for males and females at this university. Round the margin of error to two decimal places.

Use the following 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. -Percentiles of the bootstrap distribution are provided. Use the percentiles to report a 90% confidence interval for the 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". -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. -What does one dot on the sampling distribution represent?

Use the following A sample of 148 college students reports sleeping an average of 6.85 hours on weeknights, with a margin of error of 0.35 hours. Based on this information, identify each of the following as plausible or not for the average amount of sleep college students get on weeknights. -6.6 hours

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 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". -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 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 sample statistic.

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 relevant statistic?

Use the following Identify each of the following as either a parameter or a statistic, and give the correct notation. -Average commute time for employees at a small company, based on interviews with all employees.

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". -Where should the bootstrap distribution be centered?

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. -Interpret your 95% confidence interval in the context of this data situation.

Use the following The sampling distribution shows sample means from samples of size n = 50. -Using the sampling distribution, how likely is = 68.7?

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

Use the following The sampling distribution shows sample means from samples of size n = 50. -Estimate the population mean from the dotplot.

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 percentiles of your bootstrap distribution 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 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. -Interpret the confidence interval from (b).

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 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.