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. -What is the population parameter of interest? Define using the appropriate notation.

Use the following A biologist collected data on a random sample of porcupines. She wants to estimate the correlation between the body mass of a porcupine (in grams) and the length of the porcupine (in cm). -Her sample consists of 20 porcupines. A bootstrap distribution for the correlation between body mass and length (based on 1,000 samples) is provided. Would it be appropriate to use this bootstrap distribution to estimate a 95% confidence interval for the correlation between body mass and length of porcupines? Explain briefly.

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". -Provide an interpretation of your 95% confidence interval in the context of this data situation.

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. -50%

Use the following Identify each of the following as either a parameter or a statistic, and give the correct notation. -Proportion of students at a university that are part-time, based on data on all students enrolled at the university.

Use the following The sampling distribution shows sample proportions from samples of size n = 35. -Using the sampling distribution, how likely is = 0.98?

Use the following 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.

A bootstrap distribution will be centered at the value of the original statistic.

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 technology to construct a bootstrap distribution with at least 1,000 samples and estimate the standard error.

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 A: n = _____________

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. -99%

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. -65%

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 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. -8 hours

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 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 A biologist collected data on a random sample of porcupines. She wants to estimate the correlation between the body mass of a porcupine (in grams) and the length of the porcupine (in cm). -The biologist noted that two of the porcupines were much smaller than the others, and thus they were likely not "adults". Since she is only interested in adult porcupines, the biologist wants to use the 18 adults to estimate the correlation between body mass and body length. The sample correlation is 0.407. Her bootstrap distribution is provided. The standard error is estimated to be 0.165. If appropriate, construct and interpret a 95% confidence interval for the correlation between body mass and body length for adult porcupines (with the margin of error rounded to three decimal places). If not appropriate, explain why not.

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 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. ‪ -If the parameter of interest is the difference in proportions, p_m - p_f, where p_m and p_f represent the proportion of smokers in each gender, find a point estimate for this difference in proportions based on the data in the table. Report your answer with two decimal places.

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. -88%