Exam 3: Confidence Intervals

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. -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 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 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. ‪ -Use percentiles of your bootstrap distribution to provide a 98% confidence interval for the difference in the proportion of smokers between male and female students. State which percentiles you are using.

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. ‪ -Use the estimate of the standard error to construct a 95% confidence interval for the difference in the proportion of smokers between male and female students, p_m - p_f. Round the margin of error to three decimal places. Provide an interpretation of the interval in the context of this data situation.

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. -Use percentiles of your bootstrap distribution 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 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. -Use the estimate of the standard error to construct 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 The sampling distribution shows sample means from samples of size n = 50. -Estimate the standard error of the sample means.

Use the following The sampling distribution shows sample proportions from samples of size n = 35. -What does one dot on the sampling distribution represent?

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 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. -96%

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. -The standard error is estimated to be 0.056. Find and interpret (in the context of this data situation) a 95% confidence interval for the difference in the proportion of smokers between male and female students, p_m - p_f. Round the margin of error to three 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. -The standard error is estimated to be 8.769 (based on 5,000 bootstrap samples). Find a 95% confidence interval for the mean amount of time (in minutes) U.S. adults spent watching election coverage on election night. Round the margin of error to two decimal places.

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

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?

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 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 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 B: n = _____________

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

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. -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 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%