Exam 6: Inference for Means and Proportions

Use the following to answer the questions below: 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 to answer the questions below: 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 200. Use four decimal places when reporting the standard error.

Use the following to answer the questions below: In a given year, the average score on the Mathematics portion of the ACT for males was 21.3 with standard deviation 5.3. The average score on the Mathematics portion of the ACT for females was 20.2 with standard deviation 4.8. -If random samples are taken with 60 males and 60 females, find the standard error of the distribution of differences in sample means, where and represent the sample means for males and females, respectively. Report the standard error with four decimal places.

Use the following to answer the questions below: Consider taking random samples of size 100 from Population A with mean 85 and standard deviation of 15 and random samples of size 60 from Population B with mean 78 and standard deviation 12. -Find the mean of the distribution of differences in sample means,

Use the following to answer the questions below: In May 2012 President Obama made history by revealing his support of gay marriage. Around that time the Gallup Organization polled 1,024 U.S. adults about their opinions on gay/lesbian relations and gay marriage. They found that 54% of those sampled viewed gay/lesbian relations as "morally acceptable." -What sample size would we need to reduce the margin of error to ± 1.5%?

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. 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. ‪ -Construct a 95% confidence interval for the average amount of time customers of this Internet provider spend on the Internet each week. Provide an interpretation of your interval in the context of this data situation.

Use the following to answer the questions below: For each of the following, find the standard error of the distribution of sample means. Use two decimal places when reporting your standard error. -Samples of size 25 from a population with mean 10 and standard deviation 2.

Use the following to answer the questions below: 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. -How many degrees of freedom should be used when conducting inference for with samples of this size?

Use the following to answer the questions below: As part of a course project, a statistics student surveyed random samples of 50 student athletes and 50 student non-athletes at his university, with the goal of comparing the heights of the two groups. His summary statistics are displayed in the provided table. -Test, at the 5% level, if student athletes at this university are significantly taller, on average, than student non-athletes. Include all of the details.

Use the following to answer the questions below: 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 endpoints of a t-distribution with 3% beyond them in each tail if the sample has size

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?" Of the 1,017 respondents, 214 said they had "no confidence at all." -Test, at the 5% level, if this sample provides evidence that the proportion of U.S. adults who have no confidence in the media differs significantly from 25%. Verify that the sample size is large enough to use the normal distribution to compute the p-value for this test and include all of the details of the test.

Use the following to answer the questions below: Many major television networks air coverage of the incoming election results during 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?

Use the following to answer the questions below: In a recent study, the Centers for Disease Control and Prevention reported that in a sample of 4,349 African Americans 31% were Vitamin D deficient. Overall, it is believed that Vitamin D deficiency affects 8% of all U.S. adults. -Verify that the sample size is large enough to use a normal distribution to conduct a test comparing the population proportion of African Americans with Vitamin D deficiency to the overall rate of 8%.

-What is the test statistic for this test?

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." -Construct a 95% confidence interval for the proportion of domestic cats that are "left-pawed." Provide an interpretation of your interval in the context of this data situation.

Use the following to answer the questions below: 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. -Is it reasonable to use a t-distribution for inference about the difference in mean number of Facebook friends for male and female students at this university?

Use the following to answer questions 18-21: In a 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. Provide an interpretation of your interval in the context of this data situation.

Use the following to answer the questions below: 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. -Test, at the 5% level, if there is evidence that students who attended class before break have, on average, a significantly higher course grade than those who skipped. Include all of the details of the test.

Use the following to answer the questions below: February 12, 2009 marked the anniversary of Charles Darwin's birth. To celebrate, Gallup, a national polling organization, surveyed 1,018 randomly selected American adults about their education level and their beliefs about the theory of evolution. In their sample, 325 of their respondents had some college education and 228 were college graduates. Among the 325 respondents with some college education, 133 said that they believed in the theory of evolution. Among the 228 respondents who were college graduates, 121 said that they believed in the theory of evolution. -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 to answer the questions below: Turkey is a staple at most traditional Thanksgiving dinners. A random sample of 12 grocery store customers were asked about the size of the turkey they were purchasing for Thanksgiving. The average weight was 13.9 pounds with a standard deviation of 2.2 pounds. The boxplot displays the distribution of the sample turkey weights. ‪ -What sample size would we need to reduce the margin of error to ±1 pound?