I would like to solve all of them:-
\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.Shell lengths of sea turtles. Refer to the Aquatic Biology (Vol. 9, 2010) study of green sea turtles inhabiting the Grand Cayman South Sound lagoon, Exercise. The data on curved carapace (shell) length, measured in centimeters, for 76 captured turtles are displayed in the table and saved in the TURTLES file. Environmentalists want to estimate the true mean shell length of all green sea turtles in the lagoon. 33.96 |30.37 32.57 31.50 36.46 35.54 36.16 |35.32 35.90 39.55 44.33 42.73 42.15 42.43 49.96 46.04 48.75 47.78 45.81 40.05 49.65 49.71 54.20 52.01 51.15 54.42 52.62 53.27 54.07 50.40 53.69 51.30 54.29 54.58 55.11 57.65 56.35 55.68 58.40 58.06 57.79 65.98 8 57.03 57.64 59.27 64.79 61.95 60.08 62.34 63.84 60.24 64.91 60.35 62.63 63.33 63.00 64.55 60.03 64.75 60.61 69.01 65.07 65.77 65.30 68.24 65.28 67.54 68.49 56.54 65.67 70.26 70.94 70.52 72.01 74.34 81.63 a. Define the parameter of interest to the environmentalists. b. Use the data in the TURTLES file to find a point estimate of the target parameter. c. Compute a 95% confidence interval for the target parameter. Interpret the result. d. Suppose a biologist claims that the mean shell length of all green sea turtles in the lagoon is 60 cm. Make an inference about the validity of this claim. Shell lengths of sea turtles. Aquatic Biology (Vol. 9, 2010) reported on a study of green sea turtles inhabiting the Grand Cayman South Sound lagoon. The data on curved carapace (shell) length (in centimeters) for 76 captured turtles are saved in the TURTLES file. Descriptive statistics for the data are shown on the accompanying MINITAB printout. Descriptive Statistics: Length Variable N Mean n StDev | Variance | Minimum | Maximum Range Length 76 55.47 11.34 128.57 30.37 81.83 51.26 a. Locate the range of the shell lengths on the printout. b. Locate the variance of the shell lengths on the printout. c. Locate the standard deviation of the shell lengths on the printout. d. If the target of your interest is these specific 78 captured turtles, what symbols would you use to represent the variance and standard deviation?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.
