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statistics for experimentert

Introductory Statistics 10th Global Edition Neil A. Weiss - Solutions

Shortleaf Pines. The data from Exercise 15.43 for volume, in cubic feet, and diameter at breast height, in inches, for 70 shortleaf pines are on the WeissStats site.
Body Fat. In the paper “Total Body Composition by DualPhoton (153Gd) Absorptiometry” (American Journal of Clinical Nutrition, Vol. 40, pp. 834–839), R. Mazess et al. studied methods for quantifying body composition. Eighteen randomly selected adults were measured for percentage of body fat,
Tax Efficiency. Following are the data on percentage of investments in energy securities and tax efficiency from Exercise 15.22.x 3.1 3.2 3.7 4.3 4.0 5.5 6.7 7.4 7.4 10.6 y 98.1 94.7 92.0 89.8 87.5 85.0 82.0 77.8 72.1 53.5a. Obtain a point estimate for the mean tax efficiency of all mutual fund
Corvette Prices. Following are the age and price data for Corvettes from Exercise 15.23.x 6662254514 y 290 280 295 425 384 315 355 328 425 325a. Obtain a point estimate for the mean price of all 4-year-old Corvettes.b. Determine a 90% confidence interval for the mean price of all 4-year-old
Homes for Sale. Following are the size and price data for resale homes from Exercise 15.24.x 2500 1346 5000 1250 1700 1937 2200 2249 2500 y 458.5 447.0 695.0 114.9 158.8 349.9 369.0 425.0 469.0a. Determine a point estimate for the mean price of all homes with 2000-sq. ft. living room size.b. Find a
Plant Emissions. Following are the data on plant weight and quantity of volatile emissions from Exercise 15.25.x 57 85 57 65 52 67 62 80 77 53 68 y 8.0 22.0 10.5 22.5 12.0 11.5 7.5 13.0 16.5 21.0 12.0a. Obtain a point estimate for the mean quantity of volatile emissions of all (Solanum tuberosum)
Crown-Rump Length. Following are the data on age of fetuses and length of crown-rump from Exercise 15.26.x 10 10 13 13 18 19 19 23 25 28 y 66 66 108 106 161 166 177 228 235 280a. Determine a point estimate for the mean crown-rump length of all 19-week-old fetuses.b. Find a 90% confidence interval
Study Time and Score. Following are the data on total hours studied over 2 weeks and test score at the end of the 2 weeks from Exercise 15.27.x 12 24 10 9 15 17 9 18 16 22 y 84 79 81 90 81 85 82 84 83 75a. Determine a point estimate for the mean test score of all beginning calculus students who
Birdies and Score. The data from Exercise 15.34 for number of birdies during a tournament and final score of 63 women golfers are on the WeissStats site. Specified value of the predictor variable:12 birdies.
U.S. Presidents. The data from Exercise 15.35 for the ages at inauguration and of death of the presidents of the United States are on the WeissStats site. Specified value of the predictor variable: 53 years.
Movie Grosses. The data from Exercise 15.36 on domestic and overseas grosses for a random sample of 50 movies are on the WeissStats site. Specified value of the predictor variable:$100 million.
Acreage and Value. The data from Exercise 15.37 for lot size (in acres) and assessed value (in thousands of dollars) of a sample of homes in a particular area are on the WeissStats site. Specified value of the predictor variable: 2.5 acres.
Home Size and Value. The data from Exercise 15.38 for home size (in square feet) and assessed value (in thousands of dollars)for the same homes as in Exercise 15.101 are on the WeissStats site.Specified value of the predictor variable: 3000 sq. ft.
High and Low Temperature. The data from Exercise 15.39 for average high and low temperatures in January of a random sample of 50 cities are on the WeissStats site. Specified value of the predictor variable: 55◦F.
PCBs and Pelicans. The data from Exercise 15.40 for shell thickness and concentration of PCBs of 60 Anacapa pelican eggs are on the WeissStats site. Specified value of the predictor variable: 220 ppm.
Gas Guzzlers. The data from Exercise 15.41 for gas mileage and engine displacement of 121 vehicles are on the WeissStats site.Specified value of the predictor variable: 3.0 L.
Estriol Level and Birth Weight. The data from Exercise 15.42 for estriol levels of pregnant women and birth weights of their children are on the WeissStats site. Specified value of the predictor variable: 18 mg/24 hr.
Shortleaf Pines. The data from Exercise 15.43 for volume, in cubic feet, and diameter at breast height, in inches, of 70 shortleaf pines are on the WeissStats site. Specified value of the predictor variable: 11 inches.
Body Fat. The data from Exercise 15.80 for age and body fat of 18 randomly selected adults are on the WeissStats site. Specified value of the predictor variable: 30 years.Extending the Concepts and Skills Margin of Error in Regression.
Age and Price of Orions. Refer to the data on age and price of a sample of 11 Orions given in Table 15.4 on page 701.a. For each age between 2 and 7 years, obtain a 95% confidence interval for the mean price of all Orions of that age. Plot the confidence intervals against age and discuss your
Refer to the confidence interval and prediction interval formulas in Procedures 15.3 and 15.4, respectively.a. Explain why, for a fixed confidence level, the margin of error for the estimate of the conditional mean of the response variable increases as the value of the predictor variable moves
Is ρ a parameter or a statistic? What about r? Explain your answers.In each of Exercises 15.115–15.117, fill in the blank.
If ρ = 0, then the two variables under consideration are linearly .
If two variables are positively linearly correlated, one of the variables tends to increase as the other .
If two variables are linearly correlated, one of the variables tends to decrease as the other increases.
Tax Efficiency. Following are the data on percentage of investments in energy securities and tax efficiency from Exercise 15.22.x 3.1 3.2 3.7 4.3 4.0 5.5 6.7 7.4 7.4 10.6 y 98.1 94.7 92.0 89.8 87.5 85.0 82.0 77.8 72.1 53.5 At the 2.5% significance level, do the data provide sufficient evidence to
Corvette Prices. Following are the age and price data for Corvettes from Exercise 15.23.x 6662254514 y 290 280 295 425 384 315 355 328 425 325 At the 5% level of significance, do the data provide sufficient evidence to conclude that age and price of Corvettes are negatively linearly correlated?
Homes for Sale. Following are the size and price data for resale homes from Exercise 15.24.x 2500 1346 5000 1250 1700 1937 2200 2249 2500 y 458.5 447.0 695.0 114.9 158.8 349.9 369.0 425.0 469.0 At the 5% significance level, do the data provide sufficient evidence to conclude that, for resale homes,
Plant Emissions. Following are the data on plant weight and quantity of volatile emissions from Exercise 15.25.x 57 85 57 65 52 67 62 80 77 53 68 y 8.0 22.0 10.5 22.5 12.0 11.5 7.5 13.0 16.5 21.0 12.0 Do the data suggest that, for the potato plant Solanum tuberosum, weight and quantity of volatile
Crown-Rump Length. Following are the data on age of fetuses and length of crown-rump from Exercise 15.26.x 10 10 13 13 18 19 19 23 25 28 y 66 66 108 106 161 166 177 228 235 280 At the 10% significance level, do the data provide sufficient evidence to conclude that age and crown-rump length are
Study Time and Score. Following are the data on total hours studied over 2 weeks and test score at the end of the 2 weeks from Exercise 15.27.x 12 24 10 9 15 17 9 18 16 22 y 84 79 81 90 81 85 82 84 83 75a. At the 1% significance level, do the data provide sufficient evidence to conclude that a
Birdies and Score. The data from Exercise 15.34 for number of birdies during a tournament and final score of 63 women golfers are on the WeissStats site. Do the data provide sufficient evidence to conclude that, for women golfers, number of birdies and score are negatively linearly correlated?
U.S. Presidents. The data from Exercise 15.35 for the ages at inauguration and of death of the presidents of the United States are on the WeissStats site. Do the data provide sufficient evidence to conclude that, for U.S. presidents, age at inauguration and age at death are positively linearly
Movie Grosses. The data from Exercise 15.36 on domestic and overseas grosses for a random sample of 50 movies are on the WeissStats site. Do the data provide sufficient evidence to conclude that domestic and overseas grosses are positively linearly correlated?
Acreage and Value. The data from Exercise 15.37 for lot size (in acres) and assessed value (in thousands of dollars) of a sample of homes in a particular area are on the WeissStats site. Do the data provide sufficient evidence to conclude that, for homes in this particular area, lot size and
Home Size and Value. The data from Exercise 15.38 for home size (in square feet) and assessed value (in thousands of dollars)for the same homes as in Exercise 15.137 are on the WeissStats site.Do the data provide sufficient evidence to conclude that, for homes in this particular area, home size and
High and Low Temperature. The data from Exercise 15.39 for average high and low temperatures in January of a random sample of 50 cities are on the WeissStats site. Do the data provide sufficient evidence to conclude that, for cities, average high and low temperatures in January are linearly
PCBs and Pelicans. The data from Exercise 15.40 for shell thickness and concentration of PCBs of 60 Anacapa pelican eggs are on the WeissStats site. Do the data provide sufficient evidence to conclude that concentration of PCBs and shell thickness are linearly correlated for Anacapa pelican eggs?
Gas Guzzlers. The data from Exercise 15.41 for gas mileage and engine displacement of 121 vehicles are on the WeissStats site.Do the data provide sufficient evidence to conclude that engine displacement and gas mileage are negatively linearly correlated?
Estriol Level and Birth Weight. The data from Exercise 15.42 for estriol levels of pregnant women and birth weights of their children are on the WeissStats site. Do the data provide sufficient evidence to conclude that estriol level and birth weight are positively linearly correlated?
Shortleaf Pines. The data from Exercise 15.43 for volume, in cubic feet, and diameter at breast height, in inches, of 70 shortleaf pines are on the WeissStats site. Do the data provide sufficient evidence to conclude that diameter at breast height and volume are positively linearly correlated for
Body Fat. The data from Exercise 15.80 for age and body fat of 18 randomly selected adults are on the WeissStats site.a. Do the data provide sufficient evidence to conclude that, for adults, age and percentage of body fat are positively linearly correlated?b. Remove the potential outlier and repeat
use and understand the formulas in this chapter.
state the assumptions for regression inferences.
understand the difference between the population regression line and a sample regression line.
estimate the regression parameters β0, β1, and σ.
determine the standard error of the estimate.
perform a residual analysis to check the assumptions for regression inferences.
perform a hypothesis test to decide whether the slope, β1, of the population regression line is not 0 and hence whether x is useful for predicting y.
obtain a confidence interval for β1.
determine a point estimate and a confidence interval for the conditional mean of the response variable corresponding to a particular value of the predictor variable.
determine a predicted value and a prediction interval for the response variable corresponding to a particular value of the predictor variable.
understand the difference between the population correlation coefficient and a sample correlation coefficient.
perform a hypothesis test for a population linear correlation coefficient.
Suppose that x and y are two variables of a population and that the assumptions for regression inferences are met with x as the predictor variable and y as the response variable.a. What statistic is used to estimate the slope of the population regression line?b. What statistic is used to estimate
Suppose that you perform a hypothesis test for the slope of the population regression line with the null hypothesis H0: β1 = 0 and the alternative hypothesis Ha: β1 = 0. If you reject the null hypothesis, what can you say about the utility of the regression equation for making predictions?
Generally speaking, what is the difference between a confidence interval and a prediction interval?
Fill in the blank: x¯ is to μ as r is to .
Identify the relationship between two variables and the terminology used to describe that relationship ifa. ρ > 0.b. ρ = 0.c. ρ < 0.Applying the Concepts and Skills
Dropout Rates. Dropout rate — the percentage of entering as freshmen but leaving before graduating and what influences it is a concern in U.S. colleges and universities. In the article “America’s Awful College Dropout Rates, in Four Charts”, data is given for dropout rate as a function of
25 12.0 20
21 19.2 25
26 12.1 22
21 17.9 24
20 22.3 Discuss what satisfying the assumptions for regression inferences would mean with average age as the predictor variable and dropout rate as the response variable.
Dropout Rates. Refer to Problem 11.a. Determine the regression equation for the data.b. Compute and interpret the standard error of the estimate.c. Presuming that the assumptions for regression inferences are met, interpret your answer to part (b).
Dropout Rates. Refer to Problems 11 and 12. Perform a residual analysis to decide whether considering the assumptions for regression inferences to be met by the variables average age and dropout rate is reasonable.For Problems 14–17, presume that the variables student-to-faculty ratio and
Dropout Rates. Refer to Problems 11 and 12.a. At the 5% significance level, do the data provide sufficient evidence to conclude that average age is useful as a predictor of dropout rate?b. Determine a 95% confidence interval for the slope , β1, of the population regression line that relates
Dropout Rates. Refer to Problems 11 and 12.a. Find a point estimate for the mean dropout rate of all universities that have an average age of 21 years.b. Determine a 95% confidence interval for the mean dropout rate of all universities that have an average age of 21 years.
Dropout Rates. Refer to Problems 11 and 12.a. Find the predicted graduation rate for a university that has an average age of 21 years.b. Find a 95% prediction interval for the dropout rate of a university that has an average age of 21 years.c. Explain why the prediction interval in part (b) is
Dropout Rates. Refer to Problem 11. At the 2.5% significance level, do the data provide sufficient evidence to conclude that the variables average age and dropout rate are negatively linearly correlated?
IMR and Life Expectancy. From the International Data Base, published by the U.S. Census Bureau, we obtained data on infant mortality rate (IMR) and life expectancy (LE), in years, for a sample of 60 countries. The data are presented on the WeissStats site.For the estimations and predictions, use an
High Temperature and Precipitation. The National Oceanic and Atmospheric Administration publishes temperature and precipitation information for cities around the world in Climates of the World. Data on average high temperature (in degrees Fahrenheit) in July and average precipitation (in inches) in
Fill in the blank. The graph of a linear equation with one independent variable is a .
Answer true or false to each statement, and explain your answers.a. The graph of a linear equation slopes upward unless the slope is 0.b. The value of the y-intercept has no effect on the direction that the graph of a linear equation slopes.4.23 Rental-Car Costs. During one month, the Avis
Air-Conditioning Repairs. Richard’s Heating and Cooling in Prescott, Arizona, charges $55 per hour plus a $30 service charge.Let x denote the number of hours required for a job, and let y denote the total cost to the customer.a. Find the equation that expresses y in terms of x.b. Determine b0 and
Measuring Temperature. Two of the most commonly used scales for measuring temperature are the Celsius and Kelvin scales.If you let y denote Celsius temperature and x denote Kelvin temperature, you can express the relationship between those two scales with the linear equation y = x − 273.15.a.
A Law of Physics. A ball is thrown straight up in the air with an initial velocity of 10 (m/sec). According to the laws of physics, if you let y denote the velocity of the ball after x seconds, y = 10 − 9.81x.a. Determine b0 and b1 for this linear equation.b. Determine the velocity of the ball
Rental-Car Costs. Refer to Exercise 14.23. The linear equation is y = 68.22 + 0.25x.
Air-Conditioning Repairs. Refer to Exercise 14.24. The linear equation is y = 30 + 55x.
Measuring Temperature. Refer to Exercise 14.25. The linear equation is y = x − 459.67.
A Law of Physics. Refer to Exercise 14.26. The linear equation is y = 10 − 9.81x.Extending the Concepts and Skills
Hooke’s Law. According to Hooke’s law for springs, developed by Robert Hooke (1635–1703), the force exerted by a spring that has been compressed to a length x is given by the formula F = −k(x − x0), where x0 is the natural length of the spring and k is a constant, called the spring
Vertical Lines. In this section, we stated that any nonvertical line can be described by an equation of the form y = b0 + b1x.a. Explain in detail why a vertical line can’t be expressed in this form.b. What is the form of the equation of a vertical line?c. Does a vertical line have a slope?
Regarding the line that best fits a set of data points,a. what is that line called?b. what is the equation of that line called?
Tax Efficiency. Tax efficiency is a measure, ranging from 0 to 100, of how much tax due to capital gains stock or mutual funds investors pay on their investments each year; the higher the tax efficiency, the lower is the tax. In the article “At the Mercy of the Manager” (Financial Planning,
Corvette Prices. The Kelley Blue Book provides information on wholesale and retail prices of cars. Following are age and price data for 10 randomly selected Corvettes between 1 and 6 years old.Here, x denotes age, in years, and y denotes price, in hundreds of dollars. For part (g), predict the
Homes for Sale. RE/MAX, an acronym for ‘‘Real Estate Maximums’’, is a real estate organization in Canada, specializing in buying and selling of properties, with over 5,000 sales associates.A random sample of nine custom homes, currently listed for sale, provided the following information on
Plant Emissions. Plants emit gases that trigger the ripening of fruit, attract pollinators, and cue other physiological responses.N. Agelopolous et al. examined factors that affect the emission of volatile compounds by the potato plant Solanum tuberosum and published their findings in the paper
Crown-Rump Length. In the article “Fetal Crown Length:Re-evaluation of relation to menstrual age with high- resolution realtime Ultra-Sound.” (Radiology, Vol. 182, Issue 2), F. P. Hadlock et al. evaluated the relationship between crown-rump length and menstrual age of fetuses in a population of
An instructor asked a random sample of eight students to record their study times at the beginning of a course. She then made a table for total hours studied (x) over 2 weeks and test score (y) at the end of the 2 weeks. The table is given below. Complete parts (a)through (f).x 12 13 12 21 9 15 14
Tax Efficiency. In Exercise 14.58, you determined a regression equation that relates the variables percentage of investments in energy securities and tax efficiency for mutual fund portfolios.a. Should that regression equation be used to predict the tax efficiency of a mutual fund portfolio with
Corvette Prices. In Exercise 14.59, you determined a regression equation that can be used to predict the price of a Corvette, given its age.a. Should that regression equation be used to predict the price of a 4-year-old Corvette? a 10-year-old Corvette? Explain your answers.b. For which ages is use
Anscombe’s Quartet. In the article “Graphs in Statistical Analysis” (American Statistician, Vol. 27, Issue 1, pp 17–21), F. Anscombe presented four sets of data points with almost identical basic statistical properties (means, standard deviations, regression lines, etc.) but quite different
Study Time and Score. The negative relation between study time and test score found in Exercise 14.63 has been discovered by many investigators. Provide a possible explanation for it.
Age and Price of Orions. In Table 14.2, we provided data on age and price for a sample of 11 Orions between 2 and 7 years old. On the WeissStats site, we have given the ages and prices for a sample of 31 Orions between 1 and 11 years old.a. Obtain a scatterplot for the data.b. Is it reasonable to
Wasp Mating Systems. In the paper “Mating System and Sex Allocation in the Gregarious Parasitoid Cotesia glomerata” (Animal Behaviour, Vol. 66, pp. 259–264), H. Gu and S. Dorn reported on various aspects of the mating system and sex allocation strategy of the wasp C. glomerata. One part of
Birdies and Score. How important are birdies (a score of one under par on a given golf hole) in determining the final total score of a woman golfer? From the U.S. Women’s Open website, we obtained data on number of birdies during a tournament and final score for 63 women golfers. The data are
U.S. Presidents. The Information Please Almanac provides data on the ages at inauguration and of death for the presidents of the United States. We give those data on the WeissStats site for those presidents who are not still living at the time of this writing.
Movie Grosses. Box Office Mojo collects and posts data on movie grosses. For a random sample of 50 movies, we obtained both the domestic (U.S.) and overseas grosses, in millions of dollars. The data are presented on the WeissStats site.

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