Answer the below questions systematically ??

Heart rate variability of police officers. The heart rate variability (HRV) of police officers was the subject of research published in the American Journal of Human Biology (Jan. 2014). HRV is defined as the variation in the time intervals between heartbeats. A measure of HRV was obtained for each in a sample of 355 Buffalo, NY, police officers. (The lower the measure of HRV, the more susceptible the officer is to cardiovascular disease.) For the 73 officers diagnosed with hypertension, a 95% confidence interval for the mean HRV was (4.1, 124.5). For the 282 officers that are not hypertensive, a 95% confidence interval for the mean HRV was (148.0, 102.6). a. What confidence coefficient was used to generate the confidence intervals? b. Give a practical interpretation of both of the 95% confidence intervals. Use the phrase "95% confident" in your answer. c. When you say you are "95% confident, what do you mean? d. If you want to reduce the width of each confidence interval, should you use a smaller or larger confidence coefficient? Explain.Irrelevant speech effects. Refer to the Acoustical Science & Technology (Vol 35, 2014) study of irrelevant speech effects, Exercise 2.34 (pp. 40). Recall that subjects performed a memorization task under two conditions: (1) with irrelevant background speech and (2) in silence. The difference in the error rates for the two conditions-called the relative difference in error rate (RDER)-was computed for each subject. Descriptive statistics for the RDER values are reproduced in the following SAS printout. Suppose you want to estimate the average difference in error rates for all subjects who perform the memorization tasks. The MEANS Procedure Analysis Variable : RDER Mean Std Dev Minimum Maximum 71 78. 1885070 63 2429128 -19.2710000 254.1090000 a. Define the target parameter in words and in symbols. b. In Exercise 2.104b (p. 77), you computed the interval T + 2s. Explain why this formula should not be used as an interval estimate for the target parameter. c. Form a 98% confidence interval for the target parameter. Interpret the result. d. Explain what the phrase "98% confident" implies in your answer to part c. c. Refer to the histogram of the sample RDER values shown in Exercise 2.34 and note that the distribution is not symmetric. Consequently, it is likely that the pop- ulation of RDER values is not normally distributed. Does this compromise the validity of the interval esti- mate, part c? Explain. (Reference Exercise 2.34) Irrelevant speech effects. In a psychological study of short term memory, irrelevant speech effects refer to the degree to which the memorization process is impaired by irrelevant background speech (for example, trying to memorize a list of numbers while listening to a speech in an unfamiliar language). An analysis of irrelevant speech effects was carried out and published in Acoustical Science & Technology (Vol. 35, 2014). Subjects performed the memorization task under two conditions: (1) with irrelevant background speech and (2) in silence. The difference in the error rates for the two conditions-called the relative difference in error rate (RDER)-was computed for each subject. A MINITAB histogram summarizing the RDER values for 71 subjects is displayed here. Histogram of RDER 20- -15 43 225 a. Convert the frequency histogram into a relative frequency histogram. b. What proportion of the subjects had RDER values between 75 and 105? c. What proportion of the subjects had RDER values below 15?Latex allergy in health care workers. Health care workers who use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Symptoms of a latex allergy include conjunctivitis, hand eczema, nasal congestion, a skin rash, and shortness of breath. Each in a sample of 46 hospital employees who were diagnosed with latex allergy based on a skin-prick test reported on their exposure to latex gloves (Current Allergy& Clinical Immunology. March 2004). Summary statistics for the number of latex gloves used per week are 7 - 19.3 and s = 11.9. a. Give a point estimate for the average number of latex gloves used per week by all health care workers with a latex allergy. b. Form a 95% confidence interval for the average number of latex gloves used per week by all health care workers with a latex allergy. c. Give a practical interpretation of the interval you found in part b. d. Give the conditions required for the interval in part b to be valid.Lipid profiles of hypertensive patients. Hypertension is diagnosed if a patient's systolic blood pressure exceeds 140 mmig and diastolic blood pressure exceeds 90 mmig. A study of the lipid profiles of hypertensive patients was carried out and the results published in Biology and Medicine (Vol. 2, 2010). Data on fasting blood sugar (milligrams/ deciliter) and magnesium (milligrams/deciliter) in blood specimens collected from 50 patients diagnosed with hypertension were collected and are stored in the HYPER file. Biochemists used these data to establish a benchmark for fasting blood sugar (FBS) and magnesium (MAG) levels in hypertensive patients. The accompanying MINITAB printout gives 90% confidence intervals for the mean fasting blood sugar and mean magnesium level. a. Locate and interpret the 90% confidence interval for mean fasting blood sugar on the printout. b. Locate and interpret the 90% confidence interval for mean magnesium level on the printout. c. If the biochemists increase the confidence level to 957:, what will happen to the width of the intervals? d. If the biochemists increase the sample of hypertensive patients from 50 to 100, what will likely happen to the width of the intervals? Variable N Mean StDev SE Mean | 90% or FBS 50 101.62 34.13 4.83 (93.53, 109.75) MAG 1.94100 0.05507 0.00793 (1.82771, 1.95429)\fAlbedo of ice melt ponds. Refer to the National Snow and Ice Data Center (NSIDC) collection of data on the albedo, depth, and physical characteristics of ice-melt ponds in the Canadian Arctic, presented in Exercise. Albedo is the ratio of the light reflected by the ice to that received by it. (High albedo values give a white appearance to the ice.) Visible albedo values were recorded for a sample of 504 ice-melt ponds located in the Barrow Strait in the Canadian Arctic; these data are saved in the PONDICE file. a. Find a 90%% confidence interval for the true mean visible albedo value of all Canadian Arctic ice ponds. b. Give both a practical and a theoretical interpretation of the interval. c. Recall from Exercise that the type of ice for each pond was classified as first-year ice, multiyear ice, or landfast ice. Find 90% confidence intervals for the mean visible albedo for each of the three types of ice. Interpret the intervals. Characteristics of ice melt ponds. The National Snow and Ice Data Center (NSIDC) collects data on the albedo, depth, and physical characteristics of ice melt ponds in The FREQ Procedure ICETYPE Frequency | Percent | Cumulative Frequency | Cumulative Percent First-year 88 17.48 88 17.48 Landfast 196 38.89 284 58.35 Multi-year 220 43.75 504 100.00 ICE TYPE 20 90 50 the Canadian Arctic. Environmental engineers at the University of Colorado are using these data to study how climate affects the sea ice. Data on 504 ice melt ponds located in the Barrow Strait in the Canadian Arctic are saved in the PONDICE file. One variable of interest is the type of ice observed for each pond, classified as firstyear ice, multiyear ice, or landfast ice. An SAS summary table and a horizontal bar graph that describe the types of ice of the 504 melt ponds are shown at the bottom of page. a. Of the 504 melt ponds, what proportion had landfast ice? b. The University of Colorado researchers estimated that about 17%% of melt ponds in the Canadian Arctic have first-year ice. Do you agree? c. Convert the horizontal bar graph into a Pareto diagram. Interpret the graph.Evaporation from swimming pools. A new formula for estimating the water evaporation from occupied swimming pools was proposed and analyzed in the journal Heating/ Piping/Air Conditioning Engineering (Apr. 2013). The key components of the new formula are number of pool occupants, area of pool's water surface, and the density difference between room air temperature and the air at the pool's surface. Data were collected from a wide range of pools where the evaporation level was known. The new formula was applied to each pool in the sample, yielding an estimated evaporation level. The absolute value of the deviation between the actual and estimated evaporation level was then recorded as a percentage. The researchers reported the following summary statistics for absolute deviation percentage: I - 18,: - 20. Assume that the sample contained n = 500 swimming pools. 3. Estimate the true mean absolute deviation percentage for the new formula with a 90% confidence interval. b. The American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE) handbook also provides a formula for estimating pool evaporation. Suppose the ASHRAE mean absolute deviation percentage is *= 34%% (This value was reported in the article.) On average. is the new formula "better" than the ASHRAE formula? Explain.Use the applet entitled Confidence Intervals for a Proportion to investigate the effect of the sample size on the number of confidence intervals that contain the population proportion p for a value of p close to 0 or 1. a. Run the applet several times without clearing for p = .5 and n = 50. Record the proportion of the 90% confidence intervals containing p. b. Now set p =.1 and run the applet several times without clearing for n = 50. How does the proportion of the 09% confidence intervals containing p compare with that in part a? c. Repeat part b, keeping p =.1 and increasing the sample size by 50 until you find a sample size that yields a similar proportion of the 99% confidence intervals containing pas that in part a. d. Based on your results, describe how the value of p affects the sample size needed to guarantee a certain level of confidence.The mean and standard deviation of a random sample of n measurements are equal to 33.9 and 3.3. respectively. a. Find a 95%% confidence interval for A ifn = 100. b. Find a 95% confidence interval for A if n = 400. c. Find the widths of the confidence intervals you calculated in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?\f\f\f\f\fA random sample of 100 observations from a normally distributed population possesses a mean equal to 83.2 and a standard deviation equal to 8.4. a. Find a 95%% confidence interval for t. b. What do you mean when you say that a confidence coefficient is .95? c. Find a 90%% confidence interval for . d. What happens to the width of a confidence interval as the value of the confidence coefficient is increased while the sample size is held fixed? e. Would your confidence intervals of parts a and c be valid if the distribution of the original population were not normal? Explain.Shopping on Black Friday. The day after Thanksgiving- called Black Friday-is one of the largest shopping days in the United States. Winthrop University researchers conducted interviews with a sample of 38 women shopping on Black Friday to gauge their shopping habits and reported the results in the International Journal of Retail and Distribution Management (Vol. 30, 2011). One question was "How many hours do you usually spend shopping on Black Friday?" Data for the 38 shoppers are listed in the accompanying table. a. Describe the population of interest to the researchers. b. What is the quantitative variable of interest to the researchers? c. Use the information in the table to estimate the population mean number of hours spent shopping on Black Friday with a 95% confidence interval. d. Give a practical interpretation of the interval. e. A retail store advertises that the true mean number of hours spent shopping on Black Friday is 5.5 hours. Should the store be sued for false advertising? Explain. 16 4 4 5 6 6 5 5 4 4 7 12 6 10 10 11 Source: Thomas, I. R, and Peters, C. "An exploratory investigation of Black Friday consumption rituals." International Journal of Weird and Distribution Wowrgement, Vol. 19, No. 7. 2011 (Table I).Personality and aggressive behavior. How does personality impact aggressive behavior? A team of university psychologists conducted a review of studies that examined the relationship between personality and aggressive behavior ( Psychological Bulletin , Vol. 132, 2006). One variable of interest to the researchers was the difference between the aggressive behavior level of individuals in the study who scored high on a personality test and those who scored low on the test. This variable, standardized to be between -7 and 7, was called "effect size". (A large positive effect size indicates that those who score high on the personality test are more aggressive than those who score low.) The researchers collected the effect sizes for a sample of n = 109 studies published in psychology journals. This data is saved in the PERAGGR file. A dot plot and summary statistics for effect size are shown in the MINITAB printouts at the bottom of the page. Of interest to the researchers is the true mean effect size p for all psychological studies of personality and aggressive behavior. a. Identify the parameter of interest to the researchers. b. Examine the dot plot. Does effect size have a normal distribution? Explain why your answer is irrelevant to the subsequent analysis. c. Locate a 95%% confidence interval for p on the accompanying printout. Interpret the result. d. If the true mean effect size exceeds 0, then the researchers will conclude that in the population, those who score high on a personality test are more aggressive than those who score low. Can the researchers draw this conclusion? Explain.Colored string preferred by chickens. Animal behaviorists have discovered that the more domestic chickens 4 MINITAB Output for Variable | N Mean StDev SE Mean EffSize 109 0.8477 0.8906 peck at objects placed in their environment, the healthier the chickens seem to be. White string has been found to be a particularly attractive pecking stimulus. In one experiment, 72 chickens were exposed to a string stimulus. Instead of white string, blue string was used. The number of pecks each chicken took at the blue string over a specified interval of time was recorded. Summary statistics for the 72 chickens were Y - 1.13 pecks and s = 2.21 pecks ( Applied Animal Behaviour Science , October 2000). 3. Use a 90% confidence interval to estimate the population mean number of pecks made by chickens pecking at blue string. Interpret the result. b. Previous research has shown that p = 7.5 pecks if chickens are exposed to white string Based on the results you found in part a , is there evidence that chickens are more apt to peck at white string than blue string? Explain.Speed training in football. A key statistic used by football coaches to evaluate players is a player's 40-yard sprint time. Can a drill be developed for improving a player's speed in the sprint? Researchers at Northern Kentucky University designed and tested a speed-training program for junior varsity and varsity high school football players ( The Sport Joumal, Winter 2004). The training program included 50-yard sprints run at varying speeds, high knee running sprints, butt kick sprints. "crazy legs"straddle runs, quick feet drills, jumping. power skipping, and all-out sprinting. Each in a sample of 38 high school athletes was timed in a 40-yard sprint prior to the start of the training program and timed again after completing the program. The decreases in times (measured in seconds) are listed in the table and saved in the SPRINT file. [ Note: A negative decrease implies that the athlete's time after completion of the program was higher than his time prior to training ] The goal of the research is to demonstrate that the training program is effective in improving 40-yard sprint times -.01 .1 .24 .25 .05 .28 1.25 .2 1.14 .32 .34 .3 1.09 .05 0 .04 .17 0 .21 15 3 102 .12 1.14 .1 .08 .51 .36 .1 .01 34 38 44 10.8 Based on Gray, M.,& Sauerbeck, J. A. "Speed training program for high school football players." The Sport Joumal, Vol. 7, No. 1, Winter 2004 (Table). a. Find a 95%% confidence interval for the true mean decrease in sprint times for the population of all football players who participate in the speed-training program. b. Based on the confidence interval, is the training program really effective in improving the mean 40-yard sprint time of high school football players? Explain