Exam 3: Confidence Intervals

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. ‪ -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 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. -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 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." -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 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. -72%

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. -Where should the bootstrap distribution be centered?

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." -Use technology to construct a bootstrap distribution with at least 1,000 samples. Use the percentiles of your bootstrap distribution to provide a 99% confidence interval for the parameter. Indicate the percentiles that you use. A) 0.262 to 0.667 (using the 0.5%- and 99.5%-iles) B) 0.286 to 0.643 (use 1%- and 99%-iles) C) 0.310 to 0.619 (use 2.5%- and 97.5%-iles) D) 0.357 to 0.595 (use 5%- and 95%-iles)

Use the following to answer the questions below: Identify if each of the following statements is a proper interpretation of a 95% confidence interval. -95% of the population values will fall within this interval.

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. -Percentiles of the bootstrap distribution are provided. Use the percentiles to report a 95% confidence interval for the parameter.

Use the following to answer the questions below: The sampling distribution shows sample means from samples of size n = 50. ‪ -Using the sampling distribution, how likely is = 64.2?

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. -Proportion of students at your university that smoke, based on data from your class.

Use the following to answer the questions below: 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 to answer the questions below: Identify whether each of the following samples is a possible bootstrap sample from this original sample: 20, 24, 19, 23, 18 -20, 24, 21, 19, 18

Use the following to answer the questions below: In a poll conducted before a Massachusetts city's mayoral election, 134 of 420 randomly chosen likely voters indicated that they planned to vote for the Democratic candidate. -Suppose that an article describing the poll says that the margin of error for the statistic is 0.045. Use this information to find an interval estimate and interpret the confidence interval.

Recently, the Centers for Disease Control and Prevention estimated 9.4% of children under the age of 18 had asthma. They reported the standard error to be 0.35%. Assuming that the sampling distribution is symmetric and bell-shaped, find a 95% confidence interval.

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. -Describe how to use the data to select one bootstrap sample. What statistic is recorded from this sample?

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." -Construct a 95% confidence interval for the proportion of U.S. adults who have no confidence in the media. Provide an interpretation of your 95% confidence interval in the context of this data situation.

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." -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 to answer the questions below: In a poll conducted before a Massachusetts city's mayoral election, 134 of 420 randomly chosen likely voters indicated that they planned to vote for the Democratic candidate. -Suppose that an article describing the poll says that the margin of error for the statistic is 0.045 and an interval estimate is found.What quantity is the interval estimate in trying to capture? Identify with appropriate notation and words.

Use the following to answer the questions below: 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 A: n = ________

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