the following questions showing all work please. If you use Minitab Express include the appropriate output (copy + paste) along with an explanation. Round all answers to 3 decimal places. 1. For the following scenarios, write the appropriate null and alternative hypotheses. Use the appropriate symbols (Ho, Ha, , p). (20 points) A. The University wants to know if more than half of all undergraduate students are enrolled in an online course this summer. B. World Campus wants to know if more than two-thirds of their students work full-time. C. On a given weight-loss plan, is the average change in weight negative? D. Is the mean age of all Penn State first-year undergraduate students less than 22 years? E. Do students at XYZ High School do better than the national average of 500 on the Verbal section of the SAT? 2. Answer the following questions using the dataset SUMMER16STDATA.MTW Consider this data to be a sample that is representative of the population of all Penn State World Campus STAT 200 students. (50 points) A. At the .05 alpha level, is there evidence that the proportion of all World Campus STAT200 students who male is different from 50%? Use the five-step hypothesis testing procedure. B. In part A, is it possible that a Type I or Type II error was committed? Why? C. At the .05 alpha level, is there evidence that more than 30% of Penn State World Campus STAT 200 students have a cat? Use the five-step hypothesis testing procedure. D. Construct a 95% confidence interval for the population mean height. Assume that in the population this variable is normally distributed. E. At the .05 alpha level, is there evidence that the mean height is different from 67 inches? Assume that in the population this variable is normally distributed. Use the five-step hypothesis testing procedure. F. Compare your results from part D and part E. Explain how these two results could be used to answer the same research question. G. In terms of the scenario in part E, explain each of the following changes would impact power: i. Increase in sample size ii. Change in alpha from .05 to .10 iii. Decrease in sample mean iv. Decrease in sample standard deviation 3. A test prep company has developed a new intervention to improve SAT-Math scores. They will conduct a hypothesis test to determine if the average SAT-Math score of a student who has completed their program is greater than the known national average of 500. The program is very expensive at $4,800 per student. Use this scenario to answer the following questions. (30 points) A. Write out the null and alternative hypotheses using the appropriate symbols. B. In terms of this scenario, what would a Type I error be? C. In terms of this scenario, what would a Type II error be? D. The researchers used a sample size of n= 15,000 and found a sample mean of 502. Using your hypotheses from part A and the known population standard deviation of 100, what is the t test statistic? E. What is the p-value associated with the test statistic you computed in part D? F. Are the results of this study statistically significant? Why or why not. G. Are the results of this study practically significant? For example, if you were a parent, would you be convinced that you should spend $4,800 to send your child through this program? Explain why 4. For each of the following scenarios, which of the following hypothesis tests is most appropriate: one sample proportion, one sample mean, two independent proportions, two independent means, or two paired (dependent) means? Explain why. (30 points) A. The Graduate School's Admissions Office at Penn State wants to know if applicants to their M.Ed. programs have higher GRE-Verbal scores than applicants to their M.S. programs. B. A bakery advertises that their cupcakes weigh 90 grams including the frosting. A group of customers believe that this is false advertising and that the average weight of this bakery's cupcakes is really less than 90 grams (including frosting). C. The physics department at one college wants to know if physics majors' SATMath scores are higher than their SAT-Verbal scores. They take a simple random sample of 30 physics majors and ask each student for his or her SATMath and SAT-Verbal scores. D. Students at Penn State and Michigan State are arguing over which university's students have better SAT-Writing essay scores. They take a random sample of 50 students from each university and record their SATWriting essay scores. E. In the population of all Penn State World Campus students, 18.6% have military experience. An instructor at Penn State Harrisburg wants to know if the proportion of students at Penn State Harrisburg is different from 18.6%. She takes a random sample of 100 Penn State Harrisburg students and asks if they've had military experience. F. A group of developmental psychologists are conducting a study on male/female fraternal twins. They want to know if the female twins tend to have higher emotional intelligence scores than their male twin counterparts. They have a sample of 20 male/female fraternal twins and give each an emotional intelligence test. G. Nursing students want to compare the resting heart rates of college students who exercise regularly and college students who do not exercise regularly. They have a sample of 100 college students: 60 who claim to exercise regularly and 40 do not. They measure each individual's resting heart rate. H. The Department of Statistics wants to compare the proportion of men and women who pass STAT 200. They take a random sample of 500 students enrolled in STAT 200 and at the end of the semester record their gender and whether or not they passed the course. I. A pharmaceutical company wants to compare the LDL cholesterol levels of patients who have taken two different drugs (Drug A and Drug B). They randomly assign 30 patients to receive Drug A and 30 patients to receive Drug B. After taking 90 days they measure each patient's LDL cholesterol level. J. A group of students want to know if wives tend to have higher marital satisfaction levels than their husbands. They have a sample of 30 married heterosexual couples. The husband and wife each complete a test of marital satisfaction. Scores on the instrument are quantitative. 5. In Spring 2016 I wanted to compare my STAT 200 students' scores on the Midterm Practice Quiz and the Midterm Exam. In a sample of 33 students, the mean difference was 6.159 points with a standard deviation of 15.156. Scored tended to be higher on the practice quiz. Use Minitab Express to answer the following questions. You will have to enter in these statistics as \"summarized data.\" (20 points) A. Construct a 95% confidence interval for the mean difference between the Midterm Practice Quiz and Midterm Exam. B. Given the null hypothesis d = 0, and alternative hypothesis d 0, what is the p value? C. Is there evidence that students scored differently on the Midterm Practice Quiz and Midterm Exam? Why? 6. Open the SUMMER16STDATA.MTW dataset. Assume that this is a sample that is representative of the population of all World Campus STAT 200 students. We want to know if males and females differ in terms of their heights. (50 points) A. Write the null and alternative hypothesis using the appropriate symbols. B. What statistical procedure should be used to determine if there is a difference between the mean heights of males and females in the population of all World Campus STAT 200 students? Explain why C. For the height variable, are the standard deviations for males and females similar or different? (If one is more than twice of the other they are different.) D. Compute the appropriate test statistic. (I strongly encourage you do to this in Minitab Express and NOT by hand) E. What is the p value? F. Is your decision to reject or fail to reject the null hypothesis from part A? Explain why G. Is there statistical evidence that the mean heights of males and females are different in this population? H. How could you answer this research question using a confidence interval? (You don't have to actually do it, just explain what you could do. I. Construct a 95% confidence interval for the difference in the proportion of males and females who are dieting. J. Interpret the 95% confidence interval that you constructed in part I. K. A research team hypothesizes that people who are dieting are more likely to eat breakfast. Use the five-step hypothesis testing procedure to determine if there is evidence to support this claim. Step 1: Step 2: Step 3: Step 4: Step 5: Name Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Pennsylvania Dog No Yes Yes Yes Yes Yes No Yes No Yes Yes No No No Yes Yes Yes No Yes Yes No Yes No Yes No No Yes Yes No No No No Yes Yes No Yes No Yes Yes No Yes Yes No Yes Yes Yes Yes Yes No Yes Yes Yes No Yes Yes No Yes No No No No Yes Yes Yes Yes Yes No Yes No No No No Yes Yes Yes No Yes No No Yes Yes Yes Yes Yes Yes No No Yes No No Cat No No No No No No No Yes Yes No No No No No No Yes Yes No No No No No No No No No No Yes No No No No No No Yes No No Yes No No No No No No Biological SexHeight (incheShoe Size Female 59 7.5 Female 64 6 Female 64 6 Female 62 8 Male 70 12 Male 71 11 Female 66 10 Female 67 9 Male 67 9 Male 68 7.5 Female 62 7 Female 66 10 Male 74 12 Female 8 Male 75 13 Male 68 10.5 Female 66 8.5 Female 66 9 Female 62 7 Female 67 10 Female 67 9 Female 58 7 Female 66 10 Female 66 9 Female 67 7.5 Male 67 10 Female 63 8 Female 64 6 Male 71 10 Female 66 7 Male 76 13 Female 63 9 Female 58 5 Male 71 11.5 Female 64 8 Female 65 8 Female 63 7 Female 64 8 Female 63 8 Female 68 7 Male 68 12 Female 64 6 Female 62 6 Male 56 9.5 Male 71 10.5 Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous No Yes Yes Yes Yes Yes No No No No No Yes No No No No Yes Yes No No Yes No No Yes Yes Yes No No Yes Yes Yes No Yes No Yes No No Yes No No No Yes Yes No No Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes No No Yes Yes No Yes Yes Yes Yes Yes Yes No Yes No No Yes Yes No Yes Yes Yes No No No No No No No No No No No No No No No Yes No No No No Yes Yes Yes No Yes No Yes No Yes No No No Yes No Yes No No No No Yes No No Yes No No No Female Female Male Female Female Female Female Female Female Female Female Female Female Male Female Female Female Female Female Female Female Male Male Female Female Female Female Male Female Male Female Female Female Male Female Male Female Male Female Female Female Male Male Female Male Female 68 65 65 64 63 63 63 63 63 69 67 66 68 72 68 66.5 60 62 66 63 62 67 75 69 60 64 65 60 63 74 66 64 63 68 64 71 69 74 65 67 64 72 71 66 75 61 9 8 9 6 7.5 7.5 6 8.5 8 8.5 9 7 10 8.5 7.5 7.5 6.5 7 8 7 10 14 9 7 7 7.5 11 6 10.5 9 6.5 8 11 6.5 9 9 11 8 8.5 8 10 10 7 12 7 Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous No Yes Yes No Yes No Yes No No Yes No No No No Yes Yes Yes Yes Yes No Yes Yes Yes No No Yes No No No Yes No Yes No No No No Yes No Yes No No Yes No Yes Yes No No Yes Yes Yes Yes Yes Yes Yes Yes Yes No No No No Yes Yes Yes Yes Yes No Yes No No Yes No No No No No Yes No Yes Yes No No Yes Yes Yes Yes No Yes Yes Yes Yes Yes No No No Yes No No No No No No Yes Yes No Yes No Yes No No Yes Yes No No No Yes Yes No No Yes No No No No No No No No No Yes No No No Yes No No No No No 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Anonymous Anonymous No No Yes No No Yes Yes Yes No No Yes Yes No No Yes Yes No Yes Yes Yes Yes No Yes No Yes No No Yes No No Yes No Yes No No No No No No Yes Yes Yes No No Yes Yes No No Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes No No Yes Yes Yes Yes Yes No Yes No Yes Yes No Yes Yes Yes No No Yes No Yes No Yes Yes Yes No No Yes No No Yes Yes No Yes Yes Yes No No Yes No Yes No Yes Yes No No Yes No No No Yes Yes Yes No Yes No No No Yes Yes No No Yes No Yes No No No No No No No Yes No No Yes Yes Yes Female Female Female Male Male Female Male Female Female Male Female Female Female Male Male Male Female Female Female Female Female Female Female Female Female Male Female Female Female Male Male Male Female Male Female Female Male Male Female Male Female Male Male Female Female Female 60 67 69 71 69 70 75 71 62 72 63 65 67 69 70 69 64 64 65 66 62 66 66 65 64 72 67 60 62 73 72 66 63 68 68 64 70 72 68 70 63 62 68 71 62 65 8 7.5 10 10 9 8.5 12 10 6 12 7 8 10 11 12 11 7.5 8 8 9 8 8.5 8.5 6 8 10.5 7 6 7.5 12 11 10 8.5 9 10 8 10.5 10 9 10 6 10.5 10 7.5 8 Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous No No Yes No No Yes Yes Yes Yes No Yes Yes Yes Yes No No No Yes No No Yes Yes No Yes No No No Yes Yes No No Yes Yes Yes No Yes No No Yes No Yes No Yes Yes No No Yes Yes No Yes Yes No No No No Yes No Yes Yes Yes No No Yes No Yes Yes Yes Yes No Yes Yes No No No Yes No Yes Yes Yes Yes Yes No Yes No Yes No Yes No Yes Yes Yes No No No No Yes Yes No No No No No No No No No No No No Yes No No No No No Yes No No No Yes Yes No No No No No No No Yes No No No No No Yes No No No Female 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8.5 9 6.5 13.5 11.5 8.5 7.5 12.5 9 9.5 13 Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous No No No No No No No Yes No Yes No Yes No Yes Yes Yes Yes Yes No Yes Yes No No No Yes Yes No Yes Yes Yes No Yes Yes Yes Yes No Yes No Yes Yes Yes Yes No No No No Yes No Yes No Yes Yes No Yes Yes Yes No No Yes No Yes No Yes Yes Yes Yes No No No No Yes No Yes No Yes No Yes No No No No No Yes Yes No Yes Yes Yes No Yes Yes No Yes No No No Yes No Yes No No No No No Yes No Yes No No No No Yes Yes Yes No Yes No Yes No No Yes Yes No No No No Yes No No Yes Yes No No No No Yes No Yes Female Male Male 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Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Anonymous Yes Yes No No No No Yes Yes No Yes Yes No Yes Yes No Yes Yes Yes Yes No Yes Yes Yes No No Yes No No Yes No Yes Yes No No No No No Yes No Yes Yes Yes No No Yes No No Yes No No No No Yes No Yes No No Yes Yes Yes Yes Yes No No Yes Yes Yes No Yes Yes No No Yes No No No Yes No Yes Yes No Yes No No No Yes Yes No Yes No Yes Yes No Yes Yes No Yes No No Yes Yes Yes No No No No Yes No No No Yes No Yes Yes No No No No No Yes No No No No Yes No No No Yes No No Yes No No No No Yes No Female Female Male Female Female Male Male Female Female Male 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5 No 6 0 2 5 No 3 10 0 6 Yes 3 6 0 5 No 6 3 0 5 No 4 0 2 4 No 2 0 0 4 No 0 3 0 3 Yes 27 14 1 7 No 2 8 1 2 No 4 3 1 3 No 8 0 0 2 No 20 0 0 5 No 5 3 0 4 No 4 3 5 5 No 3 2 0 4 No 8 10 0 3 Yes 16 0 4 4 No 4 7 0 3 No 7 0 0 5 Yes 1 0 0 4 Yes 4 1 1 6 No 10 7 0 6 No 5 0 3 3 No 3 20 0 4 No 5 3 2 6 Yes 0 0 0 3 No 8 7 0 5 No 3 4 2 4 Yes 1.5 17 1 5 No 12 17 0 No No No No Yes No No No Yes Yes No No No Yes No No Yes Yes No Yes Yes No No No Yes Yes Yes No Yes No No Yes Yes Yes No No Yes Yes No No No No No Yes No No Yes No No Yes Yes Yes No No Yes No Yes Yes Yes Yes Yes No No No Yes Yes Yes No Yes Yes Yes No Yes No Yes No Yes No No Yes Yes Yes No Yes Yes Yes No Yes Yes Yes Yes Yes 4 No 4 No 4 No 5 Yes 3 No 5 No 4 No 6 No 3 Yes 3 Yes 3 Yes 4 No 5 No 4 No 5 No 2 No 2 No 2 No 4 No 4 No 4 Yes 3 No 5 No 3 No 6 Yes 4 Yes 3 No 4 Yes 5 No 4 No 5 No 3 Yes 4 No 4 Yes 6 Yes 3 No 2 Yes 4 No No 4 No 3 No 5 No 3 No 4 No 6 No 5 No 2 6 3 5 5 1 12 0 3 0 5 7 0 0 9 3 0 7 5 6 6 12 8 2 6 6 3 8 7 0 3 5 0 4 25 2 6 2 3 4 10 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0 3 0 2 2 2 0 0 0 0 0 1 0 0 0 1 0 0 0 2 0 0 2 3 0 55 0 3 1 0 0 2 0 0 0 Yes No Yes No No No Yes No No No No Yes No No Yes No Yes No Yes No No Yes Yes No No No No No No No No No No No No No No Yes Yes No No No No No Yes Yes Yes Yes No No Yes No Yes Yes Yes No No No Yes Yes No Yes Yes Yes Yes Yes No Yes No Yes Yes Yes No No Yes Yes No Yes Yes Yes Yes Yes No No Yes Yes No No No Yes Yes Yes 3 No 3 No 2 No 2 No 3 No 4 No 3 No 5 Yes 4 No 3 Yes 3 Yes 4 No 4 No 4 No 3 No 4 No 6 No 4 Yes 5 No 4 No 3 No 3 No 2 Yes 3 No 5 Yes 4 No 2 No 8 No 5 Yes 6 Yes 2 No 4 No 4 No 4 Yes 4 No 5 Yes 3 No 2 No 5 Yes 3 No No 3 No 7 No 3 No 5 Yes 5 Yes 0 0 2 3 5 0 8 9 2 7 20 3 0 5 4 7 10 3 5 0 0 5 5 2 15 5 5 7 3 30 10 7 10 12 4 0 5 1 8 10 14 5 0 1 8 7 0 6 0 0 20 12 0 1 21 10 2 7 10 2 3 4 6 5 5 0 5 0 1 14 5 0 7 6 12 14 0 2 0 4 0 2 0 10 7 0 0 3 3 7 30 0 0 1 0 0 2 0 1 0 0 2 2 0 1 0 0 0 2 2 1 0 0 0 0 0 0 0 1 0 0 0 0 3 0 8 1 0 0 5 0 0 0 4 0 3 1 No No Yes No No No No No No No Yes Yes Yes No No Yes No Yes Yes No No No Yes 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