Lesson 7: Confidence Intervals NAME Lab Activity Answer the following questions showing all work. I strongly suggest using Minitab Express to answer questions when possible, as opposed to hand calculations. This will save you time and reduce mathematical errors. When you use Minitab Express, include the appropriate output (copy + paste) along with an explanation. 1. For each of the following, compute the correct degrees of freedom and find the correct t multiplier for constructing a confidence interval for a population mean. You may use the t table or Minitab Express. [20 points] A. Confidence level 80%, n=9, df = _____, t* = ______ B. Confidence level 80%, n=101, df = _____, t* = ______ C. Confidence level 95%, n=9, df = _____, t* = ______ D. Confidence level 95%, n=101, df = _____, t* = ______ E. How does the t multiplier change as the confidence level changes? Why? F. How does the t multiplier change as the sample size changes? Why? G. How does the t multiplier change as the population size changes? Why? 2. For the following scenarios, if you were to construct a confidence interval, what would be the appropriate multiplier? (State whether z* or t* AND look up the number) [16 points] A. You want to estimate the proportion of Penn State students who own a Mac with 95% confidence. You take a simple random sample of 56 Penn State students. B. You want to estimate the average weight of male golden retrievers with 98% confidence. You have a sample of 26 male golden retrievers. C. You want to construct a 90% confidence interval for the mean number of credits completed by students enrolled in STAT 200 this semester across all campuses. You take a random sample of 600 students. D. You want to construct an 80% confidence interval for the proportion of registered Pennsylvanian voters who plan to vote for Candidate A. You take a random sample of 21 registered voters in Pennsylvania. Lesson 7: Confidence Intervals NAME Lab Activity 3. During the first week of class data were collected from a sample of World Campus STAT 200 students. This data can be found in the file SP16STUDENTDATA.MTW. Use this data to answer the following questions. Copy + paste all relevant Minitab Express output. Clearly identify your answers. [32 points] A. What proportion of students in this sample said that they were dieting? B. Compute a 95% confidence interval for the proportion of the population of all World Campus STAT 200 students who are dieting. Use the normal approximation method. C. Interpret the confidence interval that you constructed in part (B). D. In this sample, what were the mean and standard deviation for the variable of height in inches? E. Compute an 80% confidence interval for the mean height in inches in the population of all World Campus STAT 200 students. F. Interpret the confidence interval that you constructed in part (E) G. Compute a 99% confidence interval for the mean height in inches in the population of all World Campus STAT 200 students. H. Which is wider, the 80% confidence interval in part (E) or the 99% confidence interval in part (G)? Explain why. Lesson 7: Confidence Intervals NAME Lab Activity 4. You have collected data concerning SAT-Math scores from a sample of 27 Penn State statistics majors. Your sample has a mean of 720 and a standard deviation of 40. [20 points] A. Construct a 95% confidence interval for the mean SAT-Math score of all Penn State statistics majors. B. In the general population (i.e., students who are not statistics majors), the mean SAT-Math score is 500. Given your results from part (A), is there evidence that Penn State statistics majors are different from the general population in terms of their average SAT-Math score? Explain why. C. If you wanted to construct a 95% confidence interval for SAT-Math score in all Penn State statistics majors with a margin of error of 10 points, what sample size would you need? D. If you wanted to construct a 95% confidence interval for SAT-Math score in all Penn State statistics majors with a margin of error of 5 points, what sample size would you need? E. Compare your results from part (C) and part (D). Which is larger? Explain why? Lesson 7: Confidence Intervals NAME Lab Activity 5. The graphics below were published in an NPR article on January 30, 2016. These data were collected just days before the Iowa caucuses. Use these to answer the following questions. For the entire article, see http://www.npr.org/2016/01/30/465000699/hillaryclinton-donald-trump-narrowly-ahead-in-final-poll-before-iowa [12 points] A. The article states, \"Hillary Clinton and Donald Trump lead narrowly just two days before the Iowa caucuses in the final Des Moines Register/Bloomberg poll, considered the \"global standard\" of Iowa polling. But Clinton's 3-point lead over Vermont Sen. Bernie Sanders is within the margin of error.\" How would you explain what it means to be \"within the margin of error\" to a friend who in interested in political polling but who has never taken a statistics course? B. If the only information that you had was the graphs above, would you be convinced that Clinton was going to beat Sanders in the Iowa caucus? Why or why not? (Assume that the sample is representative.) C. Given only the information in the graphs above, is there evidence that in the population of all Iowa voters more would select Trump as their first choice than Rubio? (Assume that the sample is representative.) D. In terms of the actual results, for the republicans, Cruz won with 27.6% of votes and for the democrats Clinton won with 49.9% of votes. Why are these Lesson 7: Confidence Intervals NAME Lab Activity numbers different from the ones presented in the graphs from the NPR article? 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Yes Female 67 8 No Male 69 10 No Male 71 10.5 No Breakfast Coffee (in Exercise (i TV (in hourLanugages Winter SpoIdeal Marriag No 0 1 3 1 Figure skat 18 Yes 0 3 6 4 Figure skat 28 Yes 0 5 10 1 Ice hockey 27 Yes 0 0 2 1 Figure skat 34 Yes 0 5 5 1 Ice hockey 28 No 0 0 1 2 Figure skat 25 Yes 2 2 5 1 Figure skat 31 Yes 1 0 10 1 Ice hockey 25 No 0 0 15 2 Curling 30 Yes 2 1 10 1 Curling 26 No 0 0 10 1 Figure skat 25 Yes 1 4 0 1 Figure skat 30 Yes 0 15 2 3 Ice hockey 30 Yes 0 0 8 1 Figure skat 25 Yes 6 5 10 1 Ice hockey 30 Yes 0 7 10 1 Ice hockey 26 No 2 2 8 1 Figure skat 30 Yes 0 0 5 2 Ice hockey 27 Yes 5 10 5 1 Ice hockey 30 Yes 1 8 5 1 Figure skat 29 No 1 2 20 1 Ice hockey 30 Yes 2 10 4 1 Ice hockey 26 Yes 2 3 2 1 Ice hockey 25 Yes 1 8 3 1 Ice hockey 25 No 1 2 2 2 Figure skat 25 Yes 2 5 5 1 Ice hockey 34 No 0 4 15 1 Yes 5 6 12 1 Ice hockey 18 No 0 5 14 1 Ice hockey 30 No 2 10 2 1 Ice hockey 27 Yes 2 5 5 1 Figure skat 25 No 1 0 2 2 Ice hockey 25 No 3 4 2 1 Figure skat 24 Yes 0 0 15 1 Figure 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No 5 Yes 3 Yes 3 Yes 2 Yes No No Yes No No No No No No No No No No No No No No Yes Yes Yes No Yes No No Yes No No Yes No No Yes No No No No No Yes No No Yes No Yes No Yes No Yes No No No Yes Yes No No No Yes No Yes No No Yes No No No No No No No No No Yes No No No No Yes No No Yes No No Yes No No No Yes Male Male Female Male Female Male Female Male Male Male Male Male Female Female Male Female Female Male Female Female Female Female Male Male Male Male Male Male Female Male Female Male Female Male Male Female Male Female Female Female Male Female Female Female Female Male Female Male Female Female Male Male Female Female Male Male Female Female Male Male Male Female Male Male Male Male Female Male Male Male Female Female Male Female Female Male Female Female Female Male Male Male Female Female Female 75 70 67 73 61 71.5 64 69 72 72 64 73 64 64 69 66 63 74 67 63 62 68 73 71 69 67 72 72 62 70 68 69 65 74 70 69 68 68 64 63 71 65 64 68 67 71 67 71 62 63 71 73 69 63 71 69 65 66 71 74 72 63 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2 2 0 1 2 0 1 2 0 0 0 0 2 0 1 0 0 0 0 0 0 0 2 2 1 2 2 0 0 0 3 0 4 0 0 1 1 1 0 6 2 1 0 0 1 0 0 0 0 3 2 5 2 7 5 23 0 2 2 5 8 5 2 12 5 15 8 0.5 1 15 1 0 4 0 5 7.5 10 0 5 8 0 4 6 2 3 2 4 2 2 0 1 3 3 12 12 10 0 4 0 10 6 10 0 2 5 1 8 0 3 4 0 4 2 8 0 4 20 4 3 0 10 0 2.5 5 10 4 4 4 1 3 1 0 5 10 10 8 2 10 20 4 6 4 9 10 0 7 8 6 0 1 0 2 2 10 2 5 5 3 2 45 4.5 18 7 5 8 2 6 6 3 3 3 10 8 4 2 5 10 4 7 4 20 3 0 0 10 10 10 5 3 3 42 18 1 1 0 15 10 0 7 3 5 1 0 5 0 10 6 14 2 4 4 10 2 12 5 5 15 1 Ice hockey 2 Ice hockey 1 Ice hockey 1 Ice hockey 1 Figure skat 1 Ice hockey 3 Figure skat 1 Ice hockey 1 Ice hockey 2 Ice hockey 1 Ice hockey 1 Ice hockey 1 Figure skat 1 Ice hockey 1 Ice hockey 1 Figure skat 2 Figure skat 1 Ice hockey 1 Figure skat 1 Ice hockey 1 Figure skat 1 Figure skat 1 Curling 1 Ice hockey 1 Ice hockey 1 Curling 1 Ice hockey 1 Ice hockey 1 Figure skat 1 Ice hockey 1 Ice hockey 1 Ice hockey 1 Figure skat 1 Ice hockey 1 Ice hockey 1 Figure skat 1 Curling 1 Ice hockey 2 Figure skat 1 Ice hockey 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Female Male Female Male Male Female Female Male Female 69 68 60 68.5 63 65 64 65 62 64 68 64 72 73 68 72 71 73 64 69 68 74 70 67 65 68 70 63 72 62 70 68 63 66 60 74 70 73 63 64 66 66 64 71 62 62 65 65 70 63 72 73 71 64.5 62 66 68.9 67 74 63 69 63 64 69 75 66 54 69 64 74 65 67 69 67 70 66.3 68 68 65 72 64 70 70 63 11 Yes 9.5 No 6 Yes 10.5 No 8.5 Yes 10 Yes 8 No 8.5 No 6 No 6.5 No 9 No 8.5 No 11.5 No 12 Yes 11 Yes 13 No 14 Yes 11.5 No 13 Yes 9.5 Yes 9 Yes 12 No 10.5 No 10 Yes 8 Yes 9 Yes 12 No 8 Yes 11 Yes 5.5 No 12 No 10 Yes 7 No 9 Yes 6 Yes 12 No 11 No 10 No 7.5 No 9 Yes 8 No 7.5 No 7 No 12 No 8 No 7 Yes 7 Yes 9 No 10 Yes Yes 11 Yes 10.5 No 11 No 8 No 6 Yes 6.5 No 11 Yes 9.5 No 9.5 No 6 No 9.5 No 6 No 9 No 11 No 12 No 6 No 8 No 8 No 8.5 No 11 No 10 Yes 10 No 9 No 8 No 11 No 12 No 9.5 No 12 Yes 10 No 10 Yes 11.5 No 8.5 Yes 9 Yes 10 No 7 No Yes Yes Yes No Yes No Yes No No Yes No Yes Yes No Yes Yes Yes Yes No Yes Yes Yes No No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes 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7.5 Yes 11 No 10 No 7 Yes 8 No 7.5 Yes 9 Yes 9 Yes 10.5 Yes 12 No 9.5 No 9 Yes 7 No 8.5 No 10.5 No 8.5 Yes 14 No 11 No 15 No 10 No 7 No 8 No 10 Yes 10 No 9 No 11 No 10.5 Yes 8 No 7 Yes 6 Yes 13 Yes 8 Yes 8 Yes 8 Yes 7.5 No 7 Yes 8 Yes 7 Yes 11 No 7.5 No 8.5 No 10 Yes 11 No 13 No 11.5 No 9 No 13 Yes 13 No 8 No 11 No 8.5 No 10 No 13 Yes 10 No 8 Yes 9.5 No 6.5 Yes 6 No 7 No 9 Yes 8 No 10.5 No 9 No 10 Yes Yes No Yes Yes Yes No Yes No Yes Yes Yes Yes No No Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes No No Yes Yes Yes Yes No Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No No Yes Yes Yes Yes No Yes Yes Yes No No Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes No No No Yes Yes No No No 0 1 0 2 4 3 2 0 0 1 1 0 0 0 3 0 1 5 0 2 0 0 0 1 0 0 1 3 1 0 0 0 0 0 1 1 0 2 3 0 0 0 2 2 1 3 0 3 1 1 0 2 1 0 4 2 4 2 1 9 0 1 5 2 0 0 1 2 4 1 0 0 3 4 1 0 3 0 0 1 0 1 4 0 0 6 0 6 5 3 5 0 0 1 0 5 0 1 8 0 5 10 0 3 0 0 3 7 4 3 2.5 3 4 2 8 2 10 0 0 0 8 8 7.5 5 0 0 7 2 10 5 1 4 5 10 4 15 13 5 6 3 1 5 4 0 15 1.5 5 7 5 0 2 5 5 1.5 0 0 0 7 10 0 2 9 5 10 15 0 10 2 5 0 4 5 4 14 25 0 2 5 5 21 12 10 4 4 10 60 5 24 5 12 0 6 8 10 10 1 6 4 1 2 12 15 15 4 3 7 0 2 12 15 4 10 3 10 14 10 6 7 10 3 3 2 3 15 8 3 3 12 3 14 1 25 6 10 0 14 12 12 12 10 0 12 10 3 25 7 5 3 10 5 10 18 0 2 10 1 Ice hockey 1 Ice hockey 1 Figure skat 1 Ice hockey 1 Ice hockey 1 Figure skat 1 1 Ice hockey 2 Ice hockey 1 Figure skat 1 Figure skat 1 Figure skat 1 Ice hockey 1 Ice hockey 1 Ice hockey 1 Ice hockey 1 Ice hockey 1 Figure skat 2 Figure skat 1 Ice hockey 1 Curling 2 Figure skat 3 Ice hockey 1 Ice hockey 1 Figure skat 1 Figure skat 1 Figure skat 1 Ice hockey 1 Figure skat 1 Ice hockey 1 Ice hockey 1 Figure skat 1 Ice hockey 1 Ice hockey 1 Figure skat 2 Ice hockey 1 Ice hockey 1 Ice hockey 1 Ice hockey 1 Ice hockey 1 Ice hockey 1 Figure skat 1 Ice hockey 1 Ice hockey 1 Ice hockey 1 Figure skat 1 Ice hockey 1 Curling 2 Figure skat 1 Figure skat 1 Figure skat 1 Ice hockey 1 Figure skat 1 Ice hockey 1 Figure skat 1 Ice hockey 1 Figure skat 1 Figure skat 1 Ice hockey 2 Figure skat 1 Ice hockey 1 Curling 1 Figure skat 1 Ice hockey 1 Curling 2 Curling 1 Ice hockey 1 Ice hockey 1 Ice hockey 1 Figure skat 1 Ice hockey 1 Ice hockey 1 Ice hockey 1 Curling 1 Ice hockey 1 Figure skat 1 Curling 1 Ice hockey 2 Ice hockey 3 Figure skat 1 Ice hockey 1 Figure skat 1 Ice hockey 1 Ice hockey 1 Ice hockey 25 25 25 25 29 24 30 25 32 35 25 35 25 28 25 28 33 26 27 25 49 35 30 25 25 25 25 21 30 30 30 27 30 25 30 28 25 30 28 24 35 29 27 29 35 25 27 24 24 25 34 30 28 30 29 30 26 28 45 24 22 23 30 24 18 40 30 26 27 27 26 30 28 28 30 23 18 26 30 24 26 30 25 33 AnonymouNo AnonymouYes AnonymouNo AnonymouNo AnonymouYes AnonymouYes AnonymouNo AnonymouNo AnonymouYes AnonymouYes AnonymouNo AnonymouYes AnonymouYes AnonymouNo 0 No 0 No 0 No 3 Yes 1 Yes 1 Yes 2 Yes 3 Yes 2 Yes 6 Yes 2 Yes 0 No 2 Yes 0 No No No No Yes No No No Yes Yes Yes Yes No No No Male Male Female Female Female Female Male Female Female Male Female Female Male Male 73 71 62 48 61 64 69 71 75 67 66 70 70 11 Yes 11.5 No 6 Yes 6 No 6 No 8 No 8.5 Yes 8.5 Yes 9 No 11.5 No 9.5 Yes 6.5 No 12 No 11 Yes No Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes 1 1 2 4 0 4 0 0 0 6 0 0 0 2 0 0 1 3 0 4 12 0 2 2 7 0 5 4 2 5 10 4 10 10 20 8 4 1 14 5 4 10 1 Ice hockey 1 Curling 1 Figure skat 3 Figure skat 1 Figure skat 1 Ice hockey 2 Ice hockey 1 Figure skat 1 Curling 1 Figure skat 1 Figure skat 1 Ice hockey 1 Ice hockey 1 Ice hockey 24 28 25 35 25 28 27 28 26 19 25 25 28 28 iage Age Lesson 8: Hypothesis Testing NAME Lab Activity Answer the following questions showing all work. For questions that require Minitab Express, include the appropriate output (copy + paste) along with an explanation. 1. For the following scenarios, write the appropriate null and alternative hypotheses. Use the appropriate symbols (Ho, Ha, , p). (15 points) A. The University wants to know if, on average, World Campus students are enrolled in more than 9 credits this semester. B. World Campus wants to know if more than 50% of students plan to enroll in courses this summer. C. An article reports that the majority of people lose weight on a certain diet. You want to provide evidence that the article is wrong. D. Is the mean age of University Park freshman less than 20 years? E. Do students at State College Area High School do better than the national average of 500 on the Verbal section of the SAT? Lesson 8: Hypothesis Testing NAME Lab Activity 2. Answer the following questions using the dataset SP16STUDENTDATA.MTW Consider this data to be a sample that is representative of the population of all Penn State World Campus STAT 200 students. (55 points) A. At the .05 alpha level, is there evidence that the proportion of all World Campus STAT200 students who are dieting is different from 30%? 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 of the variable ideal marriage age. Assume that in the population this variable is normally distributed. E. At the .05 alpha level, is there evidence that the mean ideal marriage age is different from 28? 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: Increase in sample size Change in alpha from .05 to .15 Lesson 8: Hypothesis Testing NAME Lab Activity Decrease in sample mean 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 SATMath score of a student who has completed their program is greater than the known national average of 500. The program is very expensive ($2,800 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= 10,500 and found a sample mean of 504. 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 $2,800 to send your child through this program? Explain why. Lesson 8: Hypothesis Testing NAME Lab Activity Answer the following questions showing all work. For questions that require Minitab Express, include the appropriate output (copy + paste) along with an explanation. 1. For the following scenarios, write the appropriate null and alternative hypotheses. Use the appropriate symbols (Ho, Ha, , p). (15 points) A. The University wants to know if, on average, World Campus students are enrolled in more than 9 credits this semester. B. World Campus wants to know if more than 50% of students plan to enroll in courses this summer. C. An article reports that the majority of people lose weight on a certain diet. You want to provide evidence that the article is wrong. D. Is the mean age of University Park freshman less than 20 years? E. Do students at State College Area High School do better than the national average of 500 on the Verbal section of the SAT? Lesson 8: Hypothesis Testing NAME Lab Activity 2. Answer the following questions using the dataset SP16STUDENTDATA.MTW Consider this data to be a sample that is representative of the population of all Penn State World Campus STAT 200 students. (55 points) A. At the .05 alpha level, is there evidence that the proportion of all World Campus STAT200 students who are dieting is different from 30%? 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 of the variable ideal marriage age. Assume that in the population this variable is normally distributed. E. At the .05 alpha level, is there evidence that the mean ideal marriage age is different from 28? 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: Increase in sample size Change in alpha from .05 to .15 Lesson 8: Hypothesis Testing NAME Lab Activity Decrease in sample mean 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 SATMath score of a student who has completed their program is greater than the known national average of 500. The program is very expensive ($2,800 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= 10,500 and found a sample mean of 504. 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 $2,800 to send your child through this program? Explain why