1 Data Analysis Assignment 4 Make sure you do the following. Points will be taken off if you do not. (For an example of formatting, see the sample solutions document posted in Blackboard.) 1.Type your name on your paper. 2.Under your name, put STAT 250 with your correct section number (e.g. STAT 250-xxx). 3.Type Data Analysis Assignment 4 centered on Page 1. 4.Number your pages across your entire solutions document. 5.Number and letter the answers to each problem and each part of each problem accordingly. Keep the problems (and parts of each problem) in order. 6.Use complete and coherent sentences to answer the explanation questions. Generate all requested graphs using StatCrunch. Place a copy of any requested graph in your solutions document. 7.Title and label all of your graphs \"correctly\" (as demonstrated in lecture notes). 8.Unless explicitly stated in the problem, you DO NOT need to include ALL StatCrunch output. You just need to include the part of the output that answers the question (i.e., the specifically requested statistics and/or graphs). 9. Upload your solutions document onto Blackboard as a Word document. 10. Please note that there is no specific data files posted on our group in StatCrunch to use to answer the following problems. However, StatCrunch will be used to answer these problems. Problem 1: Is Starbucks coffee overpriced? (25 Points) A 2010 article reported that 93% of Americans feel Starbucks coffee is overpriced. Consider the population of all Americans. a) A random sample of n = 100 couples will be selected from this population and , the p proportion of Americans who believe Starbucks is overpriced will be computed. What are the mean and standard error of the sampling distribution of the sample proportion ? p b) Is it reasonable to assume that the sampling distribution of the sample proportion p is approximately Normal for random samples of size n = 100? Explain. c) Suppose that the sample size is n = 200 rather than n = 100 as in Part b. Does the change in sample size change the mean and standard error of the sampling distribution of the sample proportion ? If so, what are the new values for the mean and standard error? If p not, explain why not. d) Is it reasonable to assume that the sampling distribution of the sample proportion approximately Normal for random samples of size n = 200? Explain. p is 2 e) When n = 200, what is the approximate probability that the sample proportion of Americans who believe Starbucks is overpriced will be greater than 0.90? Show your work (i.e., z-score and value obtained from table). f) Verify your answer to Part e using StatCrunch. Copy the StatCrunch results (graph plus answer) into your solutions document. g) When n = 200, what is the approximate probability that the sample proportion will fall within 1.5 standard errors of the population proportion. Show your work (i.e., z-scores and values obtained from table). h) Verify your answer to Part g using StatCrunch. Copy the StatCrunch results (graph plus answer) into your solutions document. Problem 2: Got Milk (15 Points) According to the U.S. Department of Agriculture, 58.8% of males between 20 and 39 years old consume the minimum daily requirement of calcium. After an aggressive \"Got milk\" advertising campaign, the USDA conducted a survey of 55 randomly selected males between the ages of 20 and 39 and found that 36 of them consume the recommended daily allowance of calcium. a) Construct a 99% confidence interval for the above data. Show your work using the formulas and verify your work using StatCrunch. b) Interpret the above confidence interval as we learned in class. c) Construct a 90% confidence interval for the above data. Show your work using the formulas and verify your work using StatCrunch. d) Explain why the widths of the two confidence intervals are different. Problem 3: Explore the Confidence Interval Applet (25 Points) a) Start in StatCrunch by clicking Applets Confidence intervals for a proportion. Choose any value for the population proportion between 0.01 and 0.99. Enter this value in the box following p:under Population: / Proportion with characteristic Set the Initial confidence level: to any value between 0.90 and 0.99. Choose a sample size n that is at least large enough so that np 10 and n(1 - p) 10 where p is the chosen value for the population proportion. Enter this in the box under Initial sample size: Click Compute! 3 Then, once your first 100 intervals have been constructed, click the 1000 intervals button near the top of the graph. You will now have 1100 total intervals. Copy and paste your graph of many confidence intervals. (Your graph will represent intervals 1001 to 1100.) Discuss the percentage capturing p listed under Prop. contained in relation to the correct confidence interval interpretation discussed in class. b) Repeat Part a (using the same population proportion and confidence level) but with a small enough sample size that either np < 10 or n(1 - p) < 10. Again, copy and paste your graph of many confidence intervals. (Your graph will represent intervals 1001 to 1100.) Discuss the percentage capturing p listed under Prop. contained in relation to the correct confidence interval interpretation discussed in class. Problem 4: Smoking Bans (15 points) On November 3 - 5, 2010, the Gallup Organization surveyed 1028 adult Americans and found that 463 said they supported a ban on smoking in public places. More recently, on October 15 - 17, 2014, the Gallup Organization surveyed 997 adult Americans and found that 550 supported a ban on smoking in public places. a) Construct a 93% confidence interval for the above data. Show your work using the formulas and verify your work using StatCrunch. b) Construct a 98% confidence interval for the above data. Show your work using the formulas and verify your work using StatCrunch. c) Interpret the confidence interval calculated in part (b) as we learned in class. Problem 5: Mercury in Freshwater Fish (20 points) Experts believe that 20% of all freshwater fish in the United States have such a high level of mercury that they are dangerous to eat. Suppose a fish market has 250 fish tested and 60 of them have dangerous levels of mercury. Test the hypothesis that this sample is not from a population with 20% dangerous fish. Use = 0.10. i. ii. iii. iv. v. vi. State the null and alternative hypotheses. State the significance level for this problem. List the conditions that allow you to use the test statistic, and, if appropriate, calculate the test statistic. Calculate the p-value and include the probability notation statement. State whether you reject or do not reject the null hypothesis. State your conclusion in context of the problem (i.e. interpret your results). 4 vii. Use StatCrunch to verify your test statistic and p-value. Note: To add formulas to a Word document, go above to Insert object Microsoft Equation 3.0. You can also copy and paste the following formulas when you need them (double click on the formula to replace the letters with numbers). p z * z p1 p n p p0 p 0 1 p 0 n ( p1 p 2 ) z * p1 1 p1 p 2 1 p 2 n1 n2