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##### PART VI. Solve each of the following problems. (...

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PART VI. Solve each of the following problems. (8 points - 2 pts each) 1. A large number of simple random samples of size n = 85 are obtained from a large population of birth weights having a mean of 3420 g and a standard deviation of 495 g. The sample mean is calculated for each sample. A) What is the approximate shape of the distribution of the sample means? ________________________________ B) Determine the expected mean and the expected standard deviation of the sample means. Mean________________________________ Std dev ________________________ 2. In a poll of 600 randomly selected subjects, 240 answered ?yes? when asked if they planned to vote in a state election. A) Construct a 95% confidence interval estimate of the proportion of all who plan to vote in that election. ________________________________ B) Construct a 99% confidence interval estimate of the proportion of all who plan to vote in that election. ________________________________ 3. Find the sample size required to estimate the mean age of registered drivers in the United States. Assume that we want 95% confidence that the sample mean is within ? year of the true mean age of the population. Also assume that the standard deviation of the population is known to be 12 years. ________________________________ 4. In a Pew Research Center poll of 800 randomly selected adults, 600 said that it is morally wrong to not report all income on tax returns. Construct a 90% confidence interval estimate of the percentage of all adults who have the belief, and then write a statement interpreting the confidence interval. ________________________________ PART VII. Solve each of the following problems. (15 points - 5 pts each) 1. In a study of incomes of individual adults in the United States, it is observed that many people have no income or very small incomes, while there are very few people with extremely large incomes, so a graph of the incomes is skewed instead of being symmetric. A researcher states that because are a normal occurrence, the distribution of incomes is a normal distribution. Is that statement correct? ___________ Why or why not? (Explain)_________________________________________________________________________ ________________________________________________________________________________________________________ _________________________________________________________________________________________________________ 2. If you conduct a poll by surveying all of your friends that you see during the next week, which of the following terms best describes the type of sampling used: random, systematic, cluster, convenience, voluntary response? ______________________________________________________ Is the sample likely to be representative of the population?__________ Explain _______________________________________________________________________________________________ ________________________________________________________________________________________________________ _________________________________________________________________________________________________________ 3. Jane Doe learns that the Newland Agency has hired only 15 women among its last 40 new employees. She also learns that the pool of applicants is very large, with an equal number of qualified men and women. A) Find the probability that among 40 such applicants, the number of women is 15 or fewer. ________________________________ B) Based on the result, is there strong evidence to charge that the Newland Agency is discriminating against women? ________________________________ PART VIII. Solve each of the following problems. (12 points ? 4 pts each) 1. At a local college, two professors, Saber and Tooth, are each teaching large sections of introductory statistics with 500 students in each section. They decide to compare the results from their first exam. It would be too cumbersome to compare all 1000 students, so they decide to select a random sample of 50 students from each section. They want to find out whether or not the mean scores of students? performance in these two sections is comparable for this one exam. A) State the null hypothesis and alternative hypothesis. Null Hyp________________________________ Alt Hyp________________________________ Indicate the type of test to be performed (left-tailed, right-tailed, or two-tailed). ________________________________ B) Provide a statement in terms of the hypothesis testing process in this problem that would signify a Type I Error has been committed. ____________________________________________________________________ C) Provide a statement in terms of the hypothesis testing process in this problem that would signify a Type II Error has been committed. ___________________________________________________________________ 2. The effectiveness of treating respiratory infections with herbal remedies was studied. ?Days of fever? was used to measure effects. Among 233 children treated with herbal remedies, the mean number of days with fever was 0.36, with a standard deviation of 1.53 days. Among 293 children given a placebo, the mean was 0.77, with a standard deviation of 1.14 days. Do not assume the population standard deviations are equal. A) State the null hypothesis and alternative hypothesis. Null Hyp________________________________ Alt Hyp________________________________ Indicate the type of test to be performed (left-tailed, right-tailed, or two-tailed). ________________________________ B) Provide a statement in terms of the hypothesis testing process in this problem that would signify a Type I Error has been committed. ____________________________________________________________________ C) Provide a statement in terms of the hypothesis testing process in this problem that would signify a Type II Error has been committed. ___________________________________________________________________ 3. A genetic experiment with peas resulted in one sample of offspring that consisted of 438 green peas and 159 yellow peas. A) Construct a 90% confidence interval to estimate the percentage of yellow peas ________________________________ B) It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectation?_______ Why?_________________________________________________________________________________________________ ________________________________________________________________________________________________________,it's me again

Paper#11475 | Written in 18-Jul-2015

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