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statistics
elementary statistics a step by step approach

Questions and Answers of Elementary Statistics A Step By Step Approach

The data in Table 19.5 originate from the 1991 edition of the Historical Loss Development Study, published by the Reinsurance Association of American. These data have been widely used to illustrate
The data in Table 19.8 are from Gamage et al. (2007). These data are for 36 months of medical-care payments, from January 2001 through December 2003, inclusive. These are payments for medical-care
Determinants of CEO Compensation. Chief executive officer (CEO) compensation varies significantly from firm to firm. For this exercise, you will report on a sample of firms from a survey by Forbes
Two Population Poissons. We can express the two population problem in a regression context using one explanatory variable. Specifically, suppose that \(x_{i}\) only takes on the values of zero and
Verify the log-likelihood in equation (16.4) for the Tobit model. In L = = In { 1-0 (x-di)} 1:y=di 122. + (y; - x) 02 (16.4) i:y;>di
Verify the likelihood in equation (16.5) for the two-part model. n2. (16.5) -(-)-(-2)/02 L = [] {(p;)" (1 p; )'-'} [[ ( i=1 ri=1
Derive the likelihood for the tobit type II model. Show that your likelihood reduces to equation (16.5) in the case of uncorrelated disturbance terms. n2. (16.5) -(-)-(-2)/02 L = [] {(p;)" (1 p;
A Perfect Relationship, yet Zero Correlation. Consider the quadratic relationship \(y=x^{2}\), with dataa. Produce a rough graph for this dataset.b. Check that the correlation coefficient is \(r=0\).
Consider two variables, \(y\) and \(x\). Do a regression of \(y\) on \(x\) to get a slope coefficient that we call \(b_{1, x, y}\). Do another regression of \(x\) on \(y\) to get a slope coefficient
a. Show that\[s_{y}^{2}=\frac{1}{n-1} \sum_{i=1}^{n}\left(y_{i}-\bar{y}\right)^{2}=\frac{1}{n-1}\left(\sum_{i=1}^{n} y_{i}^{2}-n \bar{y}^{2}\right) .\]b. Follow the same steps to show
. Consider a fictitious dataset of \(n=100\) observations with \(s_{y}=80\). We run a regression with three explanatory variables to get \(s=50\). We also geta. Determine the standard error of
As an actuarial analyst, you are working with a large insurance company to help it understand claims distribution for private passenger automobile policies. You have available claims data for a
Suppose that you are an employee benefits actuary working with a medium-sized company in Wisconsin. This company is considering offering, for the first time in its industry, hospital insurance
Like other businesses, insurance companies seek to minimize expenses associated with doing business to enhance profitability. To study expenses, this exercise examines a random sample of 500
Who is doing health care right? Health-care decisions are made at the individual, corporate, and government levels. Virtually every person, corporation, and government has a different perspective on
On what distribution does one-way ANOVA rely?
For what is one-way ANOVA used?
A CNN/USA TODAY poll conducted by Gallup asked a sample of employed Americans the following question: “Which do you enjoy more, the hours when you are on your job, or the hours when you are not on
A CNN/USA TODAY poll conducted by Gallup asked a sample of employed Americans the following question: “Which do you enjoy more, the hours when you are on your job, or the hours when you are not on
A CNN/USA TODAY poll conducted by Gallup asked a sample of employed Americans the following question: “Which do you enjoy more, the hours when you are on your job, or the hours when you are not on
A CNN/USA TODAY poll conducted by Gallup asked a sample of employed Americans the following question: “Which do you enjoy more, the hours when you are on your job, or the hours when you are not on
We have given the number of possible values for two variables of a population. For each exercise, determine the maximum number of expected frequencies that can be less than 5 in order that Assumption
We have given the number of possible values for two variables of a population. For each exercise, determine the maximum number of expected frequencies that can be less than 5 in order that Assumption
We have given the number of possible values for two variables of a population. For each exercise, determine the maximum number of expected frequencies that can be less than 5 in order that Assumption
We have given the number of possible values for two variables of a population. For each exercise, determine the maximum number of expected frequencies that can be less than 5 in order that Assumption
We have given the number of possible values for two variables of a population. For each exercise, determine the maximum number of expected frequencies that can be less than 5 in order that Assumption
The U.S. Census Bureau compiles information on the money income of people by type of residence and publishes its finding in Current Population Reports. Independent simple random samples of people
There is convincing evidence that breastmilk containing antioxidants is important in the prevention of diseases in infants. Researchers A. Xavier et al. studied the effects of storing breastmilk on
In Exercise, we have provided a sample mean, sample standard deviation, and sample size. In each case, use the one-mean t-test to perform the required hypothesis test at the 5% significance level.x̄
The U.S. Department of Justice, Office of Justice Programs, and Bureau of Justice Statistics provides information on prison sentences in the document National Corrections Reporting Program. A random
With the advent of high-speed computing, new procedures have been developed that permit statistical inferences to be performed under less restrictive conditions than those of classical procedures.
In Example 7.9, we conducted a simulation to check the plausibility of the central limit theorem. The variable under consideration there is household size, and the population consists of all U.S.
Use the technology of your choice toa. Decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate. If so, then also do parts (b) and (c).b. Obtain
Use the technology of your choice to perform the following tasks.a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)–(d).b. Obtain the coefficient
Following are the data on age and crown-rump length for fetuses from Exercises 4.62 and 4.102.Exercise 4.62Crown-Rump Length. In the article “The Human Vomeronasal Organ. Part II: Prenatal
Following are the data on study time and score for calculus students from Exercise 4.63.Use the technology of your choice to perform the following tasks.a. Decide whether finding a regression line
Following are the data on age and crown-rump length for fetuses from Exercise 4.62.a. Compute SST, SSR, and SSE, using Formula 4.2b. Compute the coefficient of determination, r 2.c. Determine the
Use the technology of your choice to do the following tasks.a. Decide whether you can reasonably apply the conditional mean and predicted value t-interval procedures to the data. If so, then also do
In Exercises,a. Compute the three sums of squares, SST, SSR, and SSE, using the defining formulas.b. Verify the regression identity, SST = SSR + SSE.c. Compute the coefficient of determination.d.
In Exercises,a. Compute the three sums of squares, SST, SSR, and SSE, using the defining formulas.b. Verify the regression identity, SST = SSR + SSE.c. Compute the coefficient of determination.d.
In Exercises,a. Compute the three sums of squares, SST, SSR, and SSE, using the defining formulas.b. Verify the regression identity, SST = SSR + SSE.c. Compute the coefficient of determination.d.
The ability to estimate the volume of a tree based on a simple measurement, such as the tree’s diameter, is important to the lumber industry, ecologists, and conservationists. Data on volume, in
On the Weiss Stats site are data on home size (in square feet) and assessed value (in thousands of dollars) for the same homes as in Exercise 4.73.Exercise 4.73The document Arizona Residential
An instructor at Arizona State University asked a random sample of eight students to record their study times in a beginning calculus course. She then made a table for total hours studied (x) over 2
In the article “The Human Vomeronasal/ Organ. Part II: Prenatal Development”, T. Smith and K. Bhatnagar examined the controversial issue of the human vomeronasal organ, regarding its structure,
Identify the statistic that is used to estimatea. a population means.b. a population standard deviation.
In an article titled “Great White, Deep Trouble” (National Geographic, Vol. 197(4), pp. 2–29), Peter Benchley—the author of JAWS—discussed various aspects of the Great White Shark
An F-curve has df = (12, 5). In each case, find the F-value having the specified area to its right.a. 0.01 b. 0.05 c. 0.005
we provide data from independent simple random samples from several populations. In each case,a. Compute SST, SSTR, and SSE by using the computing formulas given in Formula 13.1b. Compare your
we provide data from independent simple random samples from several populations. In each case,a. Compute SST, SSTR, and SSE by using the computing formulas given in Formula 13.1b. Compare your
we provide data from independent simple random samples from several populations. In each case,a. Compute SST, SSTR, and SSE by using the computing formulas given in Formula 13.1b. Compare your
we repeat the data and provide the sample regression equations.a. Determine the standard error of the estimate.b. Construct a residual plot.c. Construct a normal probability plot of the residuals.
We repeat the information from exercise.a. Decide, at the 10% significance level, whether the data provide sufficient evidence to conclude that x is useful for predicting y.b. Find a 90% confidence
We repeat the information from exercise.a. Decide, at the 10% significance level, whether the data provide sufficient evidence to conclude that x is useful for predicting y.b. Find a 90% confidence
We repeat the information from exercise.a. Decide, at the 10% significance level, whether the data provide sufficient evidence to conclude that x is useful for predicting y.b. Find a 90% confidence
We repeat the information from exercise.a. Decide, at the 10% significance level, whether the data provide sufficient evidence to conclude that x is useful for predicting y.b. Find a 90% confidence
We repeat the data from and specify a value of the predictor variable.a. Determine a point estimate for the conditional mean of the response variable corresponding to the specified value of the
We repeat the data and specify an alternative hypothesis for a correlation t-test. For each exercise, decide, at the 10% significance level, whether the data provide sufficient evidence to reject the
We repeat the data and specify an alternative hypothesis for a correlation t-test. For each exercise, decide, at the 10% significance level, whether the data provide sufficient evidence to reject the
We repeat the data from and specify a value of the predictor variable.a. Determine a point estimate for the conditional mean of the response variable corresponding to the specified value of the
We repeat the data and specify an alternative hypothesis for a correlation t-test. For each exercise, decide, at the 10% significance level, whether the data provide sufficient evidence to reject the
We repeat the data and specify an alternative hypothesis for a correlation t-test. For each exercise, decide, at the 10% significance level, whether the data provide sufficient evidence to reject the
We repeat the data and specify an alternative hypothesis for a correlation t-test. For each exercise, decide, at the 10% significance level, whether the data provide sufficient evidence to reject the
In Exercises,a. Obtain and interpret the quartiles.b. Determine and interpret the interquartile range.c. Find and interpret the five-number summary.d. Identify potential outliers, if any.e. Construct
We repeat the data from and specify a value of the predictor variable.a. Determine a point estimate for the conditional mean of the response variable corresponding to the specified value of the
We repeat the data from and specify a value of the predictor variable.a. Determine a point estimate for the conditional mean of the response variable corresponding to the specified value of the
We repeat the data and specify an alternative hypothesis for a correlation t-test. For each exercise, decide, at the 10% significance level, whether the data provide sufficient evidence to reject the
We repeat the data from and specify a value of the predictor variable.a. Determine a point estimate for the conditional mean of the response variable corresponding to the specified value of the
We repeat the data from and specify a value of the predictor variable.a. Determine a point estimate for the conditional mean of the response variable corresponding to the specified value of the
We repeat the data from and specify a value of the predictor variable.a. Determine a point estimate for the conditional mean of the response variable corresponding to the specified value of the
We repeat the data from and specify a value of the predictor variable.a. Determine a point estimate for the conditional mean of the response variable corresponding to the specified value of the
We repeat the information from exercise.a. Decide, at the 10% significance level, whether the data provide sufficient evidence to conclude that x is useful for predicting y.b. Find a 90% confidence
We repeat the information. Presuming that the assumptions for regression inferences are met, decide at the specified significance level whether the data provide sufficient evidence to conclude that
Apply Procedure 14.2 to find and interpret a confidence interval, at the specified confidence level, for the slope of the population regression line that relates the response variable to the
Apply Procedure 14.2 to find and interpret a confidence interval, at the specified confidence level, for the slope of the population regression line that relates the response variable to the
Apply Procedure 14.2 to find and interpret a confidence interval, at the specified confidence level, for the slope of the population regression line that relates the response variable to the
We repeat the data from and specify a value of the predictor variable.a. Determine a point estimate for the conditional mean of the response variable corresponding to the specified value of
We repeat the information. Presuming that the assumptions for regression inferences are met, decide at the specified significance level whether the data provide sufficient evidence to conclude that
Presuming that the assumptions for regression inferences are met, decide at the specified significance level whether the data provide sufficient evidence to conclude that the predictor variable is
Apply Procedure 14.2 to find and interpret a confidence interval, at the specified confidence level, for the slope of the population regression line that relates the response variable to the
Apply Procedure 14.2 to find and interpret a confidence interval, at the specified confidence level, for the slope of the population regression line that relates the response variable to the
We repeat the information from exercise.a. Decide, at the 10% significance level, whether the data provide sufficient evidence to conclude that x is useful for predicting y.b. Find a 90% confidence
We repeat the information from exercise.a. Decide, at the 10% significance level, whether the data provide sufficient evidence to conclude that x is useful for predicting y.b. Find a 90% confidence
We repeat the information from exercise.a. Decide, at the 10% significance level, whether the data provide sufficient evidence to conclude that x is useful for predicting y.b. Find a 90% confidence
We repeat the information from exercise.a. Decide, at the 10% significance level, whether the data provide sufficient evidence to conclude that x is useful for predicting y.b. Find a 90% confidence
In Exercises,a. Obtain and interpret the quartiles.b. Determine and interpret the interquartile range.c. Find and interpret the five-number summary.d. Identify potential outliers, if any.e. Construct
In Exercises,a. Obtain and interpret the quartiles.b. Determine and interpret the interquartile range.c. Find and interpret the five-number summary.d. Identify potential outliers, if any.e. Construct
In Exercises,a. Obtain and interpret the quartiles.b. Determine and interpret the interquartile range.c. Find and interpret the five-number summary.d. Identify potential outliers, if any.e. Construct
In the Exercise, we have provided simple data sets for you to practice finding the descriptive measures discussed in this section. For each data set,a. Obtain the quartiles.b. Determine the
In Exercises,a. Obtain and interpret the quartiles.b. Determine and interpret the interquartile range.c. Find and interpret the five-number summary.d. Identify potential outliers, if any.e. Construct
In Exercises,a. Obtain and interpret the quartiles.b. Determine and interpret the interquartile range.c. Find and interpret the five-number summary.d. Identify potential outliers, if any.e. Construct
In Exercises,a. Obtain and interpret the quartiles.b. Determine and interpret the interquartile range.c. Find and interpret the five-number summary.d. Identify potential outliers, if any.e. Construct
In Exercises,a. Obtain and interpret the quartiles.b. Determine and interpret the interquartile range.c. Find and interpret the five-number summary.d. Identify potential outliers, if any.e. Construct
In the Exercise, we have provided simple data sets for you to practice finding the descriptive measures discussed in this section. For each data set,a. Obtain the quartiles.b. Determine the
In the Exercise, we have provided simple data sets for you to practice finding the descriptive measures discussed in this section. For each data set,a. Obtain the quartiles.b. Determine the
In the Exercise, we have provided simple data sets for you to practice finding the descriptive measures discussed in this section. For each data set,a. Obtain the quartiles.b. Determine the
A data set consists of 2m2 − 1 zero, one −m, and one m.a. Compute x̄ and s for this data set.b. How many standard deviations from the mean is the observation m?c. Assuming that m ≥ 4, what
Malnutrition and Poverty. R. Reifen et al. studied various nutritional measures of Ethiopian school children and published their findings in the paper “Ethiopian-Born and Native Israeli School
As reported by the U.S. Census Bureau in Educational Attainment in the United States, the percentage of adults each state and the District of Columbia who have completed a bachelor’s degree
The Federal Reserve System publishes weekly figures of M2 money supply in the document Money Stock Measures. M2 includes such things as cash in circulation, deposits in checking accounts, nonbank

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