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Exam 3: Confidence Intervals

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Question 31

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

A) SE = 0.056
B) SE = 0.067
C) SE = 0.072
D) SE = 0.079

E) A) and B)
F) None of the above

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Question 32

Multiple Choice

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A sample of size 46 with a mean of 13.6 is to be used to construct a confidence interval for ?. A bootstrap distribution based on 1,000 samples is created. Where will the bootstrap distribution be centered?

A) 46
B) 13.6
C) $\mu$
D) 1,000

E) None of the above
F) A) and B)

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Question 33

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

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, 18, 23

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. ‪ -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 answer the questions below: The sampling distribution shows sample means from samples of size n = 50. ‪ -Estimate the standard error of the sample means.

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. -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 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: 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. -Suppose you wish to 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. Which percentiles would you use?

Use the following to answer the questions below: In a recent 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 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. ‪ -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, ‪ 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 to answer the questions below: 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 to answer the questions below: 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 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: 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 a student collects pulse rates from a random sample of 200 students at her college and finds a 90% confidence interval goes from 65.5 to 71.8 beats per minute. Is the following statement an appropriate interpretation of this interval? If not, explain why not. "90% of the students at my college have mean pulse rates between 65.5 and 71.8 beats per minute."

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

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." -Suppose you wish to use the percentiles of your bootstrap distribution to provide a 95% confidence interval for the proportion of U.S. adults who have no confidence in the media. Which percentiles would you use?

Use the following to answer the questions below: Suppose that a 95% confidence interval for the slope of a regression line based on a sample of size n = 100 and the percentiles of the slopes for 1,000 bootstrap samples goes from 2.50 to 2.80. For each change described (with all else staying the same) , indicate which of the three confidence intervals would be the most likely result. -Increase the confidence level to 99%.

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 standard error is estimated to be 0.078 (based on 5,000 bootstrap samples) . Find a 95% confidence interval for the proportion of domestic cats that are "left-pawed". Round the margin of error to three decimal places.

Use the following to answer the questions below: The sampling distribution shows sample means from samples of size n = 50. ‪ -What does one dot on the sampling distribution represent?