Exam 6: Inference for Means and Proportions

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. -Which data analysis method is more appropriate in this situation: paired data difference in means or difference in means with two separate groups?

Use the following to answer the questions below: 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 25 individuals who earned a doctorate in the physical sciences (in 2010) and 50 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.

Use the following to answer the questions below: In a 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. -Test, at the 5% level, if this sample provides evidence that the proportion of Americans who are dissatisfied with education in kindergarten through grade 12 differs significantly from 50%. Be sure to verify that it is appropriate to use a normal distribution to compute the p-value and include all of the details of the test.

Use the following to answer the questions below: Students in a small statistics class were asked to count the number of scars both on their "dominant" hand (the one they use most often) and on their "off" hand. The summary statistics are provided. It is of interest to compare the average number of scars on the dominant and off hands. -Construct a 90% confidence interval for the difference in mean number of scars on dominant and off hands. Round your margin of error to two decimal places.

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 50 from a population with mean 450 and standard deviation 75.

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. -Test, at the 10% level, if there is evidence that the proportion of college graduates that believe in evolution differs significantly from the proportion of individuals with some college education that believe in evolution. Include all of the details of the test.

Use the following to answer the questions below: Suppose that the makers of M&M's claim that 24% of their Milk Chocolate M&M's are blue. -Assume that Fun-Size bags of Milk Chocolate M&M's hold 20 candies. Find the standard error of the distribution of sample proportions of blue candies for Fun-Size bags (i.e., samples of size 20). Use four decimal places when reporting the standard error.

Use the following to answer the questions below: In a 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. -Suppose you want to estimate the proportion of local adults who are dissatisfied with the education students receive in kindergarten through grade 12 with 95% confidence and a 5% margin of error. If you suspect that local adults won't differ drastically from those Gallup used, how many people should you sample?

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." -Construct a 90% confidence interval for the proportion of U.S. adults who find gay/lesbian relations to be "morally acceptable." Round the margin of error to three decimal places.

Use the following to answer the questions below: According to a National Science Foundation study, individuals who graduated with a doctoral degree had an average of $14,115 graduate debt. Assume that the standard deviation of graduate debt is $26,400. If we take lots of samples of individuals who graduated with a doctoral degree, what would you expect the standard error of the distribution of sample mean graduate debt amounts to be in each case? In each case, use two decimal places when reporting your standard error. -n = 200 individuals

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. -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: 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 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. ‪ -Is it reasonable to use the t-distribution to construct a confidence interval for the average weight of turkeys purchased at this store?

Use the following to answer the questions below: A 1997 study described in the European Journal of Clinical Nutrition compares the growth of vegetarian and omnivorous children, ages 7 - 11, in Northwest England. In the study, each of the 50 vegetarian children in the study was matched with an omnivorous child of the same age with similar demographic characteristics. One of the aspects on which the children were compared was their body mass index (BMI). The differences in BMI for each pair of children (one vegetarian and one omnivore) was computed as vegetarian BMI minus omnivore BMI. -Report the test statistic (with two decimal places), p-value, and conclusion for a test of versus using the paired data provided in the following table. Use a 5% significance level. Assume that the results come from random samples from populations that are approximately normal and that the differences are computed using

Use the following to answer the questions below: 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 to answer the questions below: 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 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. -Is it reasonable to use the t-distribution to perform a test about the average gas price in Illinois (on August 8, 2012)?

Use the following to answer the questions below: A study published in the American Journal of Health Promotion by researchers at the University of Minnesota (U of M) found that 124 out of 1,923 U of M females had over $6,000 in credit card debt while 61 out of 1,236 males had over $6,000 in credit card debt. -Test, at the 5% level, if there is evidence that the proportion of female students at U of M with more than $6,000 credit card debt is greater than the proportion of males at U of M with more than $6,000 credit card debt. Include all details of the test.

Use the following to answer the questions below: 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 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 to answer the questions below: Consider taking random samples of size 50 from Population A with proportion 0.45 and random samples of size 40 from Population B with proportion 0.38. -Find the mean of the distribution of differences in sample proportions, - .

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 the area in a t-distribution to the right of 1.75 if the sample has size