Exam 3: Confidence Intervals

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." -In a dotplot of a bootstrap distribution, the number of dots should match the size of the original sample.

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. -Use the information from the sample to give the best estimate of the population 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 = 55.6?

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. -If the parameter of interest is the difference in means, - where and are the mean number of hours spent watching television for males and females at this university, use technology to construct a bootstrap distribution with at least 1,000 samples and estimate the standard error. A) SE = 1.511 B) SE = 2.283 C) SE = 3.022 D) SE = 18.132

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

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. -Interpret your 92% confidence interval in the context of this data situation.

Use the following to answer the questions below: 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 to answer the questions below: 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 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. -Estimate the standard error and 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 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." -Percentiles of the bootstrap distribution (based on 5,000 samples) are provided. Use the percentiles to provide a 99% confidence interval for the parameter. Provide an interpretation of your 99% confidence interval in the context of this data situation.

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. -Correlation between price of a textbook and the number of pages, based on 25 textbooks selected from the bookstore.

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 you would estimate the standard error from the bootstrap distribution.

Use the following to answer the questions below: 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 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. -Use technology to construct a bootstrap distribution with at least 1,000 samples and estimate the standard error.

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. Report your answer with three decimal places.

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 -24, 19, 24, 20,23

Use the following to answer the questions below: 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 to answer the questions below: 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%

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 a university that are part-time, based on data on all students enrolled at the university.

Use the following to answer the questions below: 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. ‪ -You wish to provide a 98% confidence interval for the difference in the proportion of smokers between male and female students. State which percentiles of your bootstrap distribution you would use.