Exam 6: Inference for Means and Proportions

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 boxplot displays the amount of time (in minutes) spent watching election coverage for a random sample of 25 U.S. adults. In this sample, the average time spent watching election coverage was 80.44 minutes with standard deviation of 43.99 minutes. -Is it reasonable to use the t-distribution to construct a confidence interval for the average amount of time spent watching election coverage by U.S. adults? Explain briefly.

Use the following Situations comparing two proportions are described. In each case, determine whether the situation involves comparing proportions for two groups or comparing two proportions from the same group. -Comparing proportion of milk chocolate M&M's that are blue to the proportion of milk chocolate M&M's that are green.

Use the following Students in a large lecture class want to know who has, on average, more Facebook friends, male or female students. The data for the students are displayed in the provided dotplots and summary statistics are available in the provided table. -Test, at the 5% level, if this sample provides evidence of a significant difference in the mean number of Facebook friends for male and female students at this university. Include all of the details of the test.

Use the following In an October 2012 survey of 7,786 randomly selected adults living in Germany, 5,840 said they exercised for at least 30 minutes three or more times per week. -Construct a 99% confidence interval for the proportion of Germans who exercise for 30 minutes three or more times a week. Use three decimal places in your margin of error.

Use the following In an October 2012 survey of 7,786 randomly selected adults living in Germany, 5,840 said they exercised for at least 30 minutes three or more times per week. -Provide an interpretation of your interval in the context of this data situation.

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. The responses are summarized in the provided dotplot. The average amount of time spent on the Internet per week was 7.2 hours, with a standard deviation of 7.9 hours. -Provide an interpretation of your interval in the context of this data situation.

Use the following Admissions records at a small university indicates that 6.7% of the students enrolled are international students. -What proportion of samples of 200 randomly selected students will have at least 8% international students? Use three decimal places when reporting your answer.

Use the following Consider taking random samples of size 50 from Population A with mean 15 and standard deviation 3 and random samples of size 75 from Population B with mean 10 and standard deviation 5. -Find the mean of the distribution of differences in sample means, .

Use the following On August 8, 2012, the national average price for a gallon of regular unleaded gasoline was $3.63. The prices for a random sample of n = 10 gas stations in the state of Illinois were recorded at that time. The mean price for the sampled gas stations was $3.975, with standard deviation $0.2266. A boxplot of the data is provided. -Test, at the 5% level, if there is evidence that the average gas price in Illinois (on August 8, 2012) was significantly higher than the national average. Include all of the details of the test.

Use the following Suppose that the makers of M&M's claim that 24% of their Milk Chocolate M&M's are blue. -Suppose you purchase a bag of Milk Chocolate M&M's from a vending machine and only 8 of your 55 candies are blue. Assuming that the sample proportions are normally distributed, what percent of vending machine bags (i.e., samples of size 55) will have a sample proportion smaller than 0.145? Use two decimal places when reporting your answer.

Use the following For each of the following, assume that the sample is a random sample from a distribution that is reasonably normally distributed and that we are doing inference for a population mean. -Find the area in a t-distribution to the right of 2.6 if the sample has size n = 16.

Use the following A confidence interval for a population proportion p is 0.640 to 0.675. -What , the best estimate of p ?

Use the following Consider taking samples of size 25 from a population with proportion 0.65. -Find the standard error of the distribution of sample proportions.

Use the following For each of the following, assume that the sample is a random sample from a distribution that is reasonably normally distributed and that we are doing inference for a population mean. -Find the area in a t-distribution to the right of 1.75 if the sample has size n = 4.

Use the following Every year since the 1957-58 academic year, the National Science Foundation (NSF) conducts its Survey of Earned Doctorates (SED) of all individuals receiving research doctoral degrees from accredited U.S. institutions. The results from the 2010 survey published on the NSF website indicate that 78.2% of individuals earning their doctorate in the physical sciences have no graduate debt while 48.3% of those earning their doctorate in the social sciences have no graduate debt. Of the 48,069 research doctorates granted in 2010, 93% completed the SED, thus the information collected by the NSF can be good approximations of the population parameters. -Suppose we take random samples of 100 individuals who earned a doctorate in the physical sciences (in 2010) and 100 individuals who earned a doctorate in the social sciences (in 2010). Find the mean and standard error (using four decimal places) of the distribution of differences in sample proportions ( ), and indicate if the sample sizes are large enough to use the Central Limit Theorem.

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"). The researchers were also interested in comparing the proportion of "left-pawed" cats for male and female cats. Of the 21 male cats in the sample, 19 were classified as "left-pawed" while only 1 of the 21 female cats were considered to be "left-pawed". Explain why it would not be appropriate to use the normal distribution to construct a confidence interval for the difference in the proportion of male and female cats that are "left-pawed".

Use the following A professor with a large introductory statistics class noticed that nearly half of his students missed class the day before a long break (like Thanksgiving Break or Spring Break). He randomly called on students and found 10 students in attendance and 10 students who had skipped class. Later in his office, he examined the current course grades for the 20 students he had selected. A plot of his findings and summary statistics are provided. Note that the grades were entered as proportions, and thus a grade of 0.925 is a 92.5% in the course. -Construct a 98% confidence interval for the difference between the mean grades for students attending and not attending class the day before break. Use four decimal places in your margin of error.

Use the following to answer questions : In a 2012 survey, Gallup asked a random sample of U.S. adults if they would prefer to have a job outside the home, or if they would prefer to stay home to care for the family and home. Of the 504 males they surveyed, 391 said that they would prefer to have a job outside of the home. Of the 473 females they surveyed, 254 said that they would prefer a job outside of the home. -Construct a 99% confidence interval for the difference between the proportion of men and women who would prefer to have a job outside the home. Use three decimal places when computing the sample proportions and margin of error.

Use the following to answer questions : In a 2012 survey, Gallup asked a random sample of U.S. adults if they would prefer to have a job outside the home, or if they would prefer to stay home to care for the family and home. Of the 504 males they surveyed, 391 said that they would prefer to have a job outside of the home. Of the 473 females they surveyed, 254 said that they would prefer a job outside of the home. -Verify that the sample size is large enough in each group to use the normal distribution to construct a confidence interval for a difference in proportions.

Use the following Admissions records at a small university indicates that 6.7% of the students enrolled are international students. -Find the mean and standard error of the sample proportion of international students in random samples of size 50. Use four decimal places when reporting the standard error.