STAT 200 QUIZ 3 Section 6361 Summer 2017 I have completed this assignment myself, working independently and not consulting anyone except the instructor. NAME_____________________________ INSTRUCTIONS The quiz is worth 40 points total. The quiz covers Week 5 and 6 materials. Make sure your answers are as complete as possible and show your work/argument. When there are calculations involved, you should show how you come up with your answers with critical work and/or necessary tables. You must show why you choose certain answer for true-or-false and multiple choice questions. Answers that come straight from program software packages will not be accepted. The quiz is open book and open notes. This means that you may refer to your textbook, notes, and online course materials for the current course, but you must work independently and may not consult anyone. The brief honor statement is on top of the exam. If you fail to put your name under the statement, your quiz will not be accepted. You may take as much time as you wish, provided you turn in your quiz via LEO by 11:59 pm EDT on Sunday, July 9. (For Questions 1 & 2) UMUC Stats Club conducted an online poll of 300 adults in May 2017. One question was \"Do you believe that the climate change is due to global warming?\". 210 adults answered \"Yes\". 1. (2 pts) Find a 95% confidence interval estimate of population proportion of adults who support the claim that climate change is due to global warming. (Explain how you get the critical value, show work and round the answer to three decimal places) 1 2. (5 pts) In a similar online poll conducted in 2016, 65% of adults supported the claim. In order to determine if the proportion of adults who support the claim in 2017 is higher than one year ago, we would like to perform the following hypothesis test: H 0 : p=0. 65 H a : p> 0.65 (a) (2 pts) Find the test statistic. (Show work and round the answer to two decimal places) (b) (2 pts) Determine the P-value for this test. (Show work and round the answer to three decimal places. If you use technology to find the P-value, you have to describe the steps) (c) (1 pt) Is there sufficient evidence to justify the rejection of H0 at the =0.01 level? Explain. 3. (5 points) The SAT math scores for all seniors in a high school are normally distributed with population standard deviation of 150. 100 seniors from the school are randomly selected, and their SAT math scores has a sample mean of 650. (a) (1 pt) What distribution will you use to determine the critical value for a confidence interval estimate of the mean SAT math score for the seniors in the high school? Why? (b) (3 pts) Construct a 90% confidence interval estimate of the mean SAT math score for the seniors in the high school. (Show work and round the answer to two decimal places) 2 (c) (1 pt) Is a 95% confidence interval estimate of the mean SAT math score wider than the 90% confidence interval estimate you got from part (b)? Why? [You don't have to construct the 95% confidence interval] 3 4. (7 points) Consider the hypothesis test given by H 0 : =650 H a : > 650 Assume the population is normally distributed. In a random sample of 25 subjects, the sample mean is found to be x =665 , and the sample standard deviation is s=30. (a) (1 pt) Is this test for population proportion, mean or standard deviation? What distribution should you apply for the critical value? Why? (b) (1 pt) Is the test a right-tailed, left-tailed or two-tailed test? (c) (2 pts) Find the test statistic. (Show work and round the answer to two decimal places) (d) (2 pts) Determine the P-value for this test. (Show work and round the answer to three decimal places if necessary. If you use technology to find the P-value, you have to describe the steps) 4 (e) (1 pt) Is there sufficient evidence to justify the rejection of Explain. 5 H0 at the =0.05 level? 5. (6 pts) Assume a population is normally distributed with population standard deviation of 100. Given a sample size of 64, with sample mean of 500, we perform the following hypothesis test. H 0 : =475 H a : 475 (a) (1 pt) Is this test for population proportion, mean or standard deviation? What distribution should you apply for the critical value? Why? (b) (2 pts) What is the test statistic? (Show work and round the answer to three decimal places) (c) (2 pts) What is the p-value? (Show work and round the answer to two decimal places. If you use technology to find the P-value, you have to describe the steps) (d) (1 pt) What is your conclusion of the test at the = 0.01 level? Why? (Show work) 6 6. (7 pts) A company claims that its new 3-month diet program is effective in weight loss. Five people on the program were selected at random. Their weights before and after the 3-month program were recorded. The data are recorded in the table below. We want to test if the weights, on average, are less after the program. Weight in pounds Subject 1 Subject 2 Subject 3 Subject 4 Subject 5 Weight before the program 150 220 180 200 190 Weight after the program 160 210 180 180 195 (a) (1 pt) Which of the following is the appropriate test and best distribution to use for the test? (i) Two independent means, normal distribution (ii) Two independent means, Student's t-distribution (iii) Matched or paired samples, normal distribution (iv) Matched or paired samples, Student's t-distribution (b) (1 pt) Let d be the population mean for the differences of weights (weight after the program - before the program). Fill in the correct symbol (=, , , >, , <) for the null and alternative hypotheses. (i) H0: d ________ 0 (ii) Ha: d ________ 0 (c) (2 pts) What is the test statistic? (Show work and round the answer to three decimal places) (d) (2 pts) What is the p-value? (Show work and round the answer to three decimal places) (e) (1 pt) What is your conclusion of the test at the = 0.10 level? Why? (Show work) 7 7. (2 pts) In a two-tailed test, the test statistic is 1.5. We know the test statistic follows a distribution which is symmetric to 0, and P(T > 1.5) = 0.03. What is the p-value for this test? (Justify for full credit) (a) 0.03 (b) 0.97 (c) 0.06 (d) 0.94 8. (2 pts) Five hundred students took a chemistry test. You sampled 200 students to estimate the average score and the standard deviation. How many degrees of freedom were there in the estimation of the standard deviation? (Justify for full credit) (a) 199 (b) 200 (c) 499 (d) 500 9. (2 pts) True or False: If a 90% confidence interval for a population mean contains 1, then the 95% confidence interval for the same parameter must contain 1. (Justify for full credit) 10. (2 pts) True or False: It is easier to reject the null hypothesis in a hypothesis testing at significance level of 0.05 than at significance level of 0.10. (Justify for full credit) 8