Population variability.

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Complete the following exercises located at the end of each chapter and put them into a Word document to be submitted as directed by the instructor. Show all relevant work; use the equation editor in Microsoft Word when necessary.
9.7 Define the sampling distribution of the mean
9.8 Specify three important properties of the sampling distribution of the mean.
9.9 Indicate whether the following statements are true or false. If we took a random sample of 35 subjects from some population, the associated sampling distribution of the mean would have the following properties:
(a) Shape would approximate a normal curve.
(b) Mean would equal the one sample mean.
(c) Shape would approximate the shape of the population.
(d) Compared to the population variability, the variability would be reduced by a factor equal to the square root of 35. (e) Mean would equal the population mean.
(f) Variability would equal the population variability.
9.13 Given a sample size of 36, how large does the population standard deviation have to be in order for the standard error to be
(a) 1 ?
(b) 2 ?
(c) 5 ?
(d) 100 ?
9.14 (a) A random sample of size 144 is taken from the local population of grade-school children. Each child estimates the number of hours per week spent watching TV. At this point, what can be said about the sampling distribution?
(b) Assume that a standard deviation, σ, of 8 hours describes the TV estimates for the local population of schoolchildren. At this point, what can be said about the sampling distribution?
(c) Assume that a mean, µ, of 21 hours describes the TV estimates for the local population of schoolchildren. Now what can be said about the sampling distribution?
(d) Roughly speaking, the sample means in the sampling distribution should deviate, on average, about ___ hours from the mean of the sampling distribution and from the mean of the population.
(e) About 95 percent of the sample means in this sampling distribution should be between ___ hours and ___ hours.
10.9 The normal range for a widely accepted measure of body size, the body mass index (BMI), ranges from 18.5 to 25. Using the midrange BMI score of 21.75 as the null hypothesized value for the population mean, test this hypothesis at the .01 level of significance given a random sample of 30 weight-watcher participants who show a mean BMI = 22.2 and a standard deviation of 3.1.
10.10 Let’s assume that, over the years, a paper and pencil test of anxiety yields a mean score of 35 for all incoming college freshmen. We wish to determine whether the scores of a random sample of 20 new freshmen, with a mean of 30 and a standard deviation of 10, can be viewed as coming from this population. Test at the .05 level of significance.
10.11 According to the California Educational Code (http://www.cde.ca.gov/ls/fa/sf/pegui-demidhi.asp), students in grades 7 through 12 should receive 400 minutes of physical education every 10 school days. A random sample of 48 students has a mean of 385 minutes and a standard deviation of 53 minutes. Test the hypothesis at the .05 level of significance that the sampled population satisfies the requirement
10.12 According to a 2009 survey based on the United States census (http://www.census.gov/prod/2011pubs/acs-15.pdf), the daily one-way commute time of U.S. workers averages 25 minutes with, we’ll assume, a standard deviation of 13 minutes. An investigator wishes to determine whether the national average describes the mean commute time for all workers in the Chicago area. Commute times are obtained for a random sample of 169 workers from this area, and the mean time is found to be 22.5 minutes. Test the null hypothesis at the .05 level of significance
11.11 Give two reasons why the research hypothesis is not tested directly.
11.19 How should a projected hypothesis test be modified if you’re particularly concerned about
(a) the type I error?
(b) the type II error?
11.20 Consult the power curves in Figure 11.7 to estimate the approximate detection rate, rounded to the nearest tenth, for each of the following situations:
(a) a four-point effect, with a sample size of 13
(b) a ten-point effect, with a sample size of 29
(c) a seven-point effect with a sample size of 18 (Interpolate)
12.8 In Review Question 11.12 on page 218, instead of testing a hypothesis, you might prefer to construct a confidence interval for the mean weight of all 2-pound boxes of candy during a recent production shift.
(a) Given a population standard deviation of .30 ounce and a sample mean weight of 33.09 ounces for a random sample of 36 candy boxes, construct a 95 percent confidence interval
(b) Interpret this interval, given the manufacturer’s desire to produce boxes of candy that, on the average, exceed 32 ounces.

 

 

 

 

 

Sample Solution

Population variability

A sampling distribution is a probability distribution of a statistic obtained from a larger number of samples drawn from a specific population. It describes a range of possible outcomes that of a statistic, such as the mean or mode of some variable, as it truly exists a population. The sampling distribution of the sample mean can be thought of as “for a sample of size n, the sample mean will behave according to this distribution.” Any random draw from that sampling distribution would be interpreted as the mean of a sample of n observations from the original population.

Franklin Delano Roosevelt, known to many as FDR, was not only a leader for his time, but a leader for all times. Not only did FDR successfully lead his nation through possibly the two most dramatic, and consequential world events of the 20th century, the Great Depression and WW2; he is also responsible for spearheading the creation of the United Nations, as well as the series of programs, projects, policies and laws that came to be known as the “New Deal”. Through his experimentation and willingness to listen and learn from others, FDR demonstrated that he was the man to lead America forward. FDR’s actions throughout his presidency shaped not only the way Americans lived their lives, but how the world perceived America for decades to come. Throughout his presidency, FDR was able to display his brilliance in leadership. However, what was the greatest achievement in each of his four terms? And perhaps most interesting of all, what was his greatest failure? For his brilliance in leadership, as well as a lack of competent competitors, the American people rewarded him with an unprecedented four terms in office. In his first term he successfully tiptoed around the edge of the precipice, leading the American people from the turmoil caused by the Great Depression. In his second term, perhaps his most undervalued achievement was the packing of the supreme court, for it was here where you can see the long lasting impact. His third term was dominated by World War Two and the successes enjoyed by the allies. In his fourth term, despite the brevity of it, he was able to establish the foundations of the modern United Nations. Truly a leader for all times. From the moment FDR won the governorship of New York State, to the moment he became president of the United States of America, you see an unparalleled level of political victories. In his first presidential campaign, the elites of the democratic party thought that they could control him. In the end, their underestimation of FDRs coolness proved costly, with him ultimately using it to his advantage. History tells us that the world was overall, a better place because of his actions, but what exactly did he do to transform America in specific, and

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