Exam 3: Confidence Intervals

In 2010, 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 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. -60%

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. -Percentiles of the bootstrap distribution (based on 5,000 samples) are provided. Use the percentiles 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 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 you would estimate the standard error from the bootstrap distribution.

Use the following 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 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". -Use the percentiles of your bootstrap distribution to provide a 99% confidence interval for the parameter. Indicate the percentiles that you use.

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

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

Use the following 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. -The standard error is about 0.458. Find and interpret a 95% confidence interval for the parameter. Round the margin of error to two decimal places.

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". -The estimate of the standard error is 0.013. Use the estimate of the standard error to construct a 95% confidence interval for the proportion of U.S. adults who have no confidence in the media. Round the margin of error to three 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 -24, 19, 24, 20,23

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

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?

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

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. -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, find a point estimate of the parameter based on the available data. Report your answer with two decimal places.

Use the following According to ESPN.com, the average number of yards per game for all NFL running backs with at least 50 attempts in the 2011 season was 49 yards/game. A sample of 20 running backs from the 2011 season averaged 46.54 yards/game. -Is 49 yards/game a parameter or statistic?

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, 24, 21, 19, 18

Use the following 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. -Define the parameter of interest, using the proper notation.

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.