Discussion: Elementary Statistics

Discussion: Elementary Statistics ORDER NOW FOR CUSTOMIZED AND ORIGINAL ESSAY PAPERS ON Discussion: Elementary Statistics Chapter 7 Confidence Intervals 1. Confidence Interval – proportion -A study by the University of Michigan found that one in five 13 and 14 years olds is a sometime smoker. To see how the smoking rate of the students at a large school district compared to the national rate, the superintendent surveyed two hundred 13 and 14 year old students and found that 23% said they were sometimes smokers. Find the 95% confidence interval of the true proportion and compare this with the University of Michigan’s study. a) What is p? ______ b) Find ??? and ???. c) Find critical value, ?. ?????? d) Find margin of error: ?? = ????/2 ? ?? e) Find the confidence interval: CI = P ±??. f) Write the conclusion. 2. In a Gallop Poll of 1005 individuals, 452 thought they were worse off financially than a year ago. Find the 95% confidence interval for the true proportion of individuals that feel they are worse off. Write the same steps as shown in #1. 3. Confidence Interval – Mean ?? ??????????, ???? ?? ? ?? A random sample of 48 days taken at a large hospital shows that an average of 38 patients were treated in the emergency room per day. The standard deviation of the population is 4. Find the 99% confidence interval of the mean number of ER patients treated each day at the hospital. a) Find the critical value:??. b) Find the margin of error: E = ????/2 ?? ??? c) Find the confidence interval: CI = ??? ± ??. d) Write the conclusion. Discussion: Elementary Statistics 4. A telecommunications company wants to estimate the mean length of time (in minutes) that 18 to 24 year olds spend text messaging each day. In a random sample of twenty seven 18 to 24 year olds, the mean length of time spent texting was 29 minutes. From past studies the ?? is 4.5 minutes. Find the 90% confidence interval. Write the same steps as shown in #3. 5. Confidence Interval, ?? is not known or n<30. For a group of 20 students taking a final exam, the mean heart rate was 96 beats per minute and the standard deviation was 5. Find the 95% confidence interval of the true mean. e) Find the critical value:??. f) Find the margin of error: E = ????/2 ?? ??? g) Find the confidence interval: CI = ??? ± ??. h) Write the conclusion. 6. A county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 45 miles per hour. A random sample of 25 vehicles has a mean speed of 48 miles per hour and a standard deviation of 5.4 mph. Find the 95% confidence interval for the speed limit. Write the same steps as shown in #5. Chapter 8 – Hypothesis Testing Class Exercises A. Complete the following hypothesis test where x is a normal random variable and ? is known. 1. Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took glucose readings and found a sample mean of ??? = 93.8. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that ? = 12.5. The mean glucose for horses should be µ = 85 mg/100ml. Doe these data indicate that Gentle Ben has an overall average glucose level higher than 85. Use a 0.05 level of significance.Discussion: Elementary Statistics B. Complete the following hypothesis test where ? is unknown 2. USA Today reported that the state with the longest mean life span is Hawaii, where the population mean life span is 77 years. A random sample of 20 obituary notices in the Honolulu Advertizer had a mean of ??? = 71.4 years and a standard deviation, s = 20.65 yrs. Assuming that life span in Honolulu is approximately normally distributed, does this information indicate that the population life span for Honolulu residents is less than 77 years? Use a 5% level of significance. C. Complete the following hypothesis test for a proportion 3. Women athletes at the University of Colorado have a long-term graduation rate of 67%. Over the past several years, a random sample of 38 women athletes at the school showed that 21 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the University of Colorado is now less than 67%? Use a 5% level of significance. CH 10 Correlation Group Correlation Exercise: Air Force servicemen and servicewomen were tested for maximal oxygen use in a 12 min distance run versus a 1.5 mile run. The participant runs on a level terrain for the prescribed distance. Discussion: Elementary Statistics The technicians records the participant’s time to the closet second, the heart rate for 15 s immediately after the participant crosses the finish line and then estimate the VO 2 max consumption using a Wilmore and Bergfeld fitness table. Below is listed the data for both the 12 min and the 1.5 mile run with the corresponding VO2 maximum oxygen levels. Data 1.5 Mile Run (n=29) X y Time (min) VO2Max(ml/kg.min) 8.1 59.2 8.2 60.0 9.0 49.7 9.5 59.9 9.8 51.2 10.0 48.5 10.3 49.5 10.5 49.5 10.9 50.0 11.0 47.5 11.1 40.0 11.9 45.1 12.0 44.0 12.3 49.1 12.4 50.0 12.5 40.0 12.6 40.0 12.5 43.0 13.0 38.8 13.1 40.0 13.8 32.0 13.9 36.1 14.5 39.8 14.8 38.1 15.0 37.5 15.5 30.0 15.9 32.0 16.8 30.0 17.3 24.5 Data 12 Min Distance (n=25) x y Miles VO2Max(ml/kg.min) 1.1 23.2 1.15 30.0 1.2 30.0 1.15 32.5 1.25 36.3 1.26 37.0 1.28 40.0 1.31 32.3 1.3 35.0 1.38 40.0 1.4 45.1 1.43 47.5 1.45 50.0 1.5 46.2 1.6 41.0 1.65 46.4 1.67 49.0 1.67 50.0 1.7 48.0 1.8 47.5 1.85 51.5 1.9 59.8 2.0 49.8 2.15 60.0 2.2 59.0 Data One: 1.5 mile run Time vs. VO2Max ____________________________________________ Name 1. Make a scatter diagram for these pairs of data. Sketch below. 2. According to the scatter plot, as the time increases, what happens to the oxygen consumed? _________ 3. Does this indicate a positive or negative correlation? __________________ 4. Complete the steps to find the correlation coefficient, the line of fit and the values for the linear regression equation. 5. Does the line of fit, fit reasonably well? ______________ 6. What is the correlation coefficient, r, for the 1.5 mile run? r= _______ 7. Does the correlation coefficient, r, substantiate your conclusion above? _________ 8. What does the r value tell you about the data values x and y? ___________________________________ 9. Write the equation of the least-squares line( line of fit).__________________________________ 10. What is the slope of the line of fit(regression line)? ______________________ 11. What is the marginal change for the 1.5 mile run time to one ml/kg.min. versus maximal oxygen consumption? 12. If the 1.5 mile run time is 7 minutes, what is the amount of oxygen consumed?_____________, __________ Data Two: 12 Min distance vs. VO2 Consumed 1. Make a scatter diagram for these pairs of data. Sketch below. 2. According to the scatter plot, as the distance increases, what happens to the oxygen consumed? _________ 3. Does this indicate a positive or negative correlation? ________________ 4. Complete the steps to find the correlation coefficient, the line of fit and the values for the linear regression equation. 5. Does the line of fit, fit reasonably well? ________________ 6. What is the correlation coefficient, r, for 12 min. distance run? r= _______ 7. What does the r value tell you about the data values x and y? ___________________________________ 8. Does the correlation coefficient, r, substantiate your conclusion above? ___________ 9. Write the equation of the least-squares line( line of fit). Discussion: Elementary Statistics ______________________________________ 10. What is the slope of the line of fit?_____________________ 11. What is the marginal change for the 1 min of distance to one ml/kg.min. of oxygen consumption? If the 12 min distance is 2.3 miles, what is the amount of oxygen consumed? (Please show all steps: Null and alternate Hypothsis, diagram, critical value, test statistic, Reject or Do not Reject, Conclusion) (protest) (z-test) (t-test) Chapter 7 Confidence Intervals 1. Confidence Interval – proportion -A study by the University of Michigan found that one in five 13 and 14 years olds is a sometime smoker. To see how the smoking rate of the students at a large school district compared to the national rate, the superintendent surveyed two hundred 13 and 14 year old students and found that 23% said they were sometimes smokers. Find the 95% confidence interval of the true proportion and compare this with the University of Michigan’s study. a) What is p? ______ b) Find ??? and ???. c) Find critical value, ?. ?????? d) Find margin of error: ?? = ????/2 ? ?? e) Find the confidence interval: CI = P ±??. f) Write the conclusion. 2. In a Gallop Poll of 1005 individuals, 452 thought they were worse off financially than a year ago. Find the 95% confidence interval for the true proportion of individuals that feel they are worse off. Write the same steps as shown in #1. 3. Confidence Interval – Mean ?? ??????????, ???? ?? ? ?? A random sample of 48 days taken at a large hospital shows that an average of 38 patients were treated in the emergency room per day. The standard deviation of the population is 4. Find the 99% confidence interval of the mean number of ER patients treated each day at the hospital. a) Find the critical value:??. b) Find the margin of error: E = ????/2 ?? ??? c) Find the confidence interval: CI = ??? ± ??. d) Write the conclusion. 4. A telecommunications company wants to estimate the mean length of time (in minutes) that 18 to 24 year olds spend text messaging each day. In a random sample of twenty seven 18 to 24 year olds, the mean length of time spent texting was 29 minutes. From past studies the ?? is 4.5 minutes. Find the 90% confidence interval. Write the same steps as shown in #3. 5. Confidence Interval, ?? is not known or n<30. For a group of 20 students taking a final exam, the mean heart rate was 96 beats per minute and the standard deviation was 5. Find the 95% confidence interval of the true mean. e) Find the critical value:??. f) Find the margin of error: E = ????/2 ?? ??? g) . Find the confidence interval: CI = ??? ± ??. h) Write the conclusion. 6. A county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 45 miles per hour. A random sample of 25 vehicles has a mean speed of 48 miles per hour and a standard deviation of 5.4 mph. Find the 95% confidence interval for the speed limit. Write the same steps as shown in #5. Chapter 8 – Hypothesis Testing Class Exercises A. Complete the following hypothesis test where x is a normal random variable and ? is known. 1. Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took glucose readings and found a sample mean of ??? = 93.8. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that ? = 12.5. The mean glucose for horses should be µ = 85 mg/100ml. Doe these data indicate that Gentle Ben has an overall average glucose level higher than 85. Use a 0.05 level of significance. B. Complete the following hypothesis test where ? is unknown 2. USA Today reported that the state with the longest mean life span is Hawaii, where the population mean life span is 77 years. A random sample of 20 obituary notices in the Honolulu Advertizer had a mean of ??? = 71.4 years and a standard deviation, s = 20.65 yrs. Assuming that life span in Honolulu is approximately normally distributed, does this information indicate that the population life span for Honolulu residents is less than 77 years? Use a 5% level of significance. C. Complete the following hypothesis test for a proportion Discussion: Elementary Statistics 3. Women athletes at the University of Colorado have a long-term graduation rate of 67%. Over the past several years, a random sample of 38 women athletes at the school showed that 21 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the University of Colorado is now less than 67%? Use a 5% level of significance. CH 10 Correlation Group Correlation Exercise: Air Force servicemen and servicewomen were tested for maximal oxygen use in a 12 min distance run versus a 1.5 mile run. The participant runs on a level terrain for the prescribed distance. The technicians records the participant’s time to the closet second, the heart rate for 15 s immediately after the participant crosses the finish line and then estimate the VO 2 max consumption using a Wilmore and Bergfeld fitness table. Below is listed the data for both the 12 min and the 1.5 mile run with the corresponding VO2 maximum oxygen levels. Data 1.5 Mile Run (n=29) X y Time (min) VO2Max(ml/kg.min) 8.1 59.2 8.2 60.0 9.0 49.7 9.5 59.9 9.8 51.2 10.0 48.5 10.3 49.5 10.5 49.5 10.9 50.0 11.0 47.5 11.1 40.0 11.9 45.1 12.0 44.0 12.3 49.1 12.4 50.0 12.5 40.0 12.6 40.0 12.5 43.0 13.0 38.8 13.1 40.0 13.8 32.0 13.9 36.1 14.5 39.8 14.8 38.1 15.0 37.5 15.5 30.0 15.9 32.0 16.8 30.0 17.3 24.5 Data 12 Min Distance (n=25) x y Miles VO2Max(ml/kg.min) 1.1 23.2 1.15 30.0 1.2 30.0 1.15 32.5 1.25 36.3 1.26 37.0 1.28 40.0 1.31 32.3 1.3 35.0 1.38 40.0 1.4 45.1 1.43 47.5 1.45 50.0 1.5 46.2 1.6 41.0 1.65 46.4 1.67 49.0 1.67 50.0 1.7 48.0 1.8 47.5 1.85 51.5 1.9 59.8 2.0 49.8 2.15 60.0 2.2 59.0 Data One: 1.5 mile run Time vs. VO2Max ____________________________________________ Name 1. Make a scatter diagram for these pairs of data. Sketch below. 2. According to the scatter plot, as the time increases, what happens to the oxygen consumed? _________ 3. Does this indicate a positive or negative correlation? __________________ 4. Complete the steps to find the correlation coefficient, the line of fit and the values for the linear regression equation. 5. Does the line of fit, fit reasonably well? ______________ 6. What is the correlation coefficient, r, for the 1.5 mile run? r= _______ 7. Discussion: Elementary Statistics Does the correlation coefficient, r, substantiate your conclusion above? _________ 8. What does the r value tell you about the data values x and y? ___________________________________ 9. Write the equation of the least-squares line( line of fit).__________________________________ 10. What is the slope of the line of fit(regression line)? ______________________ 11. What is the marginal change for the 1.5 mile run time to one ml/kg.min. versus maximal oxygen consumption? 12. If the 1.5 mile run time is 7 minutes, what is the amount of oxygen consumed?_____________, __________ Data Two: 12 Min distance vs. VO2 Consumed 1. Make a scatter diagram for these pairs of data. Sketch below. 2. According to the scatter plot, as the distance increases, what happens to the oxygen consumed? _________ 3. Does this indicate a positive or negative correlation? ________________ 4. Complete the steps to find the correlation coefficient, the line of fit and the values for the linear regression equation. 5. Does the line of fit, fit reasonably well? ________________ 6. What is the correlation coefficient, r, for 12 min. distance run? r= _______ 7. What does the r value tell you about the data values x and y? ___________________________________ 8. Does the correlation coefficient, r, substantiate your conclusion above? ___________ 9. Write the equation of the least-squares line( line of fit). ______________________________________ 10. What is the slope of the line of fit?_____________________ 11.Discussion: Elementary Statistics What is the marginal change for the 1 min of distance to one ml/kg.min. of oxygen consumption? If the 12 min distance is 2.3 miles, what is the amount of oxygen consumed? (Please show all steps: Null and alternate Hypothsis, diagram, critical value, test statistic, Reject or Do not Reject, Conclusion) (protest) (z-test) (t-test) …Discussion: Elementary Statistics Get a 10 % discount on an order above $ 100 Use the following coupon code : NURSING10