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Questions and Answers of Statistics

Researchers conducted an experiment to test the effects of alcohol. The errors were recorded in a test of visual and motor skills for a treatment group of 22 people who drank ethanol and another
If we use the body temperatures from 8 A.M. on Day 2 as listed in Data Set 3 in Appendix B, we get the statistics given in the accompanying table. Use these data with a 0.05 significance level to
Magnet Treatment of Pain Researchers conducted a study to determine whether magnets are effective in treating back pain, with results given below (based on data from €œBipolar Permanent Magnets
Researchers measured skulls from different time periods in an attempt to determine whether interbreeding of cultures occurred. Results are given below (based on data from Ancient Races of the The
Listed below are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from Pennsylvania residents and New York residents born
Listed below are the numbers of years that popes and British monarchs (since 1690) lived after their election or coronation (based on data from Computer-Interactive Data Analysis, by Lunn and McNeil,
Listed below are heights (cm) of randomly selected females and males taken from Data Set 1 in Appendix B. Use a 0.05 significance level to test the claim that females and males have heights with the
Listed below are weights (kg) of randomly selected females and males taken from Data Set 1 in Appendix B. Use a 0.05 significance level to test the claim that males have weights with more variation
Listed below are weights (kg) of randomly selected females and males taken from Data Set 1 in Appendix B. Use a 0.05 significance level to test the claim that males have weights with more variation
M&Ms Refer to Data Set 20 in Appendix B and use the weights (g) of the red M&Ms and the orange M&Ms. Use a 0.05 significance level to test the claim that the two samples are from populations with the
Use the original weights of pre-1964 quarters and post-1964 quarters listed in Data Set 21 in Appendix B. Instead of using the A test, use the following procedure for a €œcount five€ test of
Use the weights (g) of pre-1964 quarters and post-1964 quarters listed in Data Set 21 of Appendix B. Use the Levene-Brown-Forsythe test with a 0.05 significance level to test the claim that weights
Carpal tunnel syndrome is a common wrist complaint resulting from a compressed nerve, and it is often caused by repetitive wrist movements. In a randomized controlled trial, among 73 patients treated
Construct a confidence interval suitable for testing the claim from Exercise 1. What feature of the resulting confidence interval leads to the same conclusion from Exercise 1?
In a study of the effectiveness of airbags in cars, 11,541 occupants were observed in car crashes with airbags available, and 41 of them were fatalities. Among 9853 occupants in crashes with airbags
Listed below are the costs (in dollars) of flights from New York (JFK) to San Francisco for US Air, Continental, Delta, United, American, Alaska Airlines, and Northwest. Use a 0.01 significance level
As part of the National Health and Nutrition Examination Survey conducted by the Department of Health and Human Services, self-reported heights and measured heights were obtained for females aged 12
Does stress affect the recall ability of police eyewitnesses? This issue was studied in an experiment that tested eyewitness memory a week after a nonstressful interrogation of a cooperative suspect
Construct a confidence interval suitable for testing the claim from Exercise 6. What feature of the resulting confidence interval leads to the same conclusion from Exercise 6?
Among 13,200 submitted abstracts that were blindly evaluated (with authors and institutions not identified), 26.7% were accepted for publication. Among 13,433 abstracts that were not blindly
The baseline characteristics of different treatment groups are often included in journal articles. In one study, 49 subjects treated with raw garlic had LDL cholesterol measurements with a mean of
Use the sample data from Exercise 9 to test the claim that the two populations have LDL levels with the same standard deviation. Use a 0.05 significance level. The baseline characteristics of
Use the following heights (in.) of mothers, fathers, and their adult daughters. The data are matched so that each column consists of heights from the same family.a. Are the three samples independent
Construct a scatter plot of the paired mother/daughter heights. What does the result suggest? Use the following heights (in.) of mothers, fathers, and their adult daughters. The data are matched so
Construct a 95% confidence interval estimate of the mean height of daughters. Write a brief statement that interprets the confidence interval.Use the following heights (in.) of mothers, fathers, and
Use a 0.05 significance level to test the claim that there is no significant difference between the heights of mothers and the heights of their daughters.Use the following heights (in.) of mothers,
Refer to the accompanying normal quantile plot and determine whether the sample of heights of daughters appears to be from a normally distributed population.Use the following heights (in.) of
In a survey of 1032 Americans, respondents were asked what they miss most when electrical power is lost. Of the respondents 134 indicated their computer and/or Internet access (based on results from
Late-night talk show host David Lettermen made jokes about the name “Juke” for a Nissan motor vehicle. (It is kind of funny.) If you have been commissioned to conduct a survey of American drivers
Based on the measurements in Data Set 1 of Appendix B, assume that heights of women are normally distributed with a mean of 162.0 cm and a standard deviation of 6.6 cm. a. If a woman is randomly
Another (clearly inferior) statistics textbook includes an exercise in which students are given the mean income for each of the 50 states. The students are then asked to compute the mean of those 50
For each of several randomly selected years, the sunspot number and the high value of the Dow Jones Industrial Average are recorded. The sunspot number is a measure of sunspot activity on the sun,
A physics experiment consists of recording paired data consisting of the time (seconds) elapsed since the beginning of the experiment and the distance (cm) of a robot from its point of origin. Using
Some studies have shown that there is a correlation between consumption of salt and blood pressure. As more salt is consumed, blood pressure tends to rise. A reporter reads one of these studies and
In a test of the Weight Watchers weight loss program, weights of 40 subjects are recorded before and after the program. Assume that the before/ after weights result in r = 0.876. Is there sufficient
For 40 eruptions of the Old Faithful geyser in Yellowstone National Park, duration times (sec) were recorded along with the time intervals (min) to the next eruption. The paired durations and
For 40 eruptions of the Old Faithful geyser in Yellowstone National Park, duration times (sec) were recorded along with the heights (ft) of the eruptions. The paired duration and height measurements
The heights (in inches) of a sample of 10 father/son pairs of subjects were measured. Minitab results are shown below (based on data from the National Health Examination Survey). Is there sufficient
The amounts of sugar (grams of sugar per gram of cereal) and calories (per gram of cereal) were recorded for a sample of 16 different cereals. TI-83/84 Plus calculator results are shown here. Is
a. Construct a scatterplot.b. Find the value of the linear correlation coefficient r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two
a. Construct a scatterplot.b. Find the value of the linear correlation coefficient r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two
Refer to the accompanying Minitab-generated scatterplot.a. Examine the pattern of all 10 points and subjectively determine whether there appears to be a correlation between x and y.b. After
Refer to the following Minitab-generated scatterplot. The four points in the lower left corner are measurements from women, and the four points in the upper right corner are from men.a. Examine the
Listed below are annual data for various years. The data are weights (metric tons) of lemons imported from Mexico and U.S. car crash fatality rates per 100,000 population. Is there sufficient
Listed below are PSAT scores and SAT scores from prospective college applicants. The scores were reported by subjects who responded to a request posted by the Web site talk.collegeconfidential.com.
Listed below are numbers of enrolled students (in thousands) and numbers of burglaries for randomly selected large colleges in a recent year. Is there sufficient evidence to conclude that there is a
Listed below are altitudes (thousands of feet) and outside air temperatures (degrees Fahrenheit) recorded by the author during Delta Flight 1053 from New Orleans to Atlanta. Is there sufficient
Town Courts Listed below are amounts of court fine revenue and salaries paid to the town justices (based on data from the Poughkeepsie Journal). All amounts are in thousands of dollars, and all of
The author is a member of the board of directors of a nonprofit organization that held a fund-raising auction. He recorded the opening bids suggested by the auctioneer and the final winning bids for
The table below lists measured amounts of redshift and the distances (billions of light-years) to randomly selected clusters of galaxies (based on data from The Cosmic Perspective by Bennett et ah,
The table below lists weights (carats) and prices (dollars) of randomly selected diamonds. All of the diamonds are round with ratings of €œvery good€ cut, they all have a color rating of F
Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. The purpose of the study was to determine if weights of seals could be determined
Listed below are repair costs (in dollars) for cars crashed at 6 mi/h in full-front crash tests and the same cars crashed at 6 mi/h in full-rear crash tests. The cars are the Toyota Canary, Mazda 6,
Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. Is there sufficient evidence to conclude that there is a linear correlation between right and left arm
One classic application of correlation involves the association between the temperature and the number of times a cricket chirps in a minute. Listed below are the numbers of chirps in 1 min and the
Gas prices have been very volatile in recent years. The table below lists gas prices (dollars per gallon) at randomly selected Connecticut stations at the time of this writing. Is there sufficient
Repeat the preceding exercise using the prices of regular gas and the prices of mid-grade gas. Gas Prices Gas prices have been very volatile in recent years. The table below lists gas prices (dollars
Diameters (cm), circumferences (cm), and volumes (cm3) from balls used in different sports are listed in the table below. Is there sufficient evidence to conclude that there is a linear correlation
Repeat the preceding exercise using diameters and volumes.Sports Diameters (cm), circumferences (cm), and volumes (cm3) from balls used in different sports are listed in the table below. Is there
Refer to Data Set 6 in Appendix B and use the paired data consisting of brain volume (cm3) and IQ score. Use the data from Appendix B to construct a scatterplot, find the value of the linear
Refer to Data Set 15 in Appendix B and use the departure delay times and the arrival delay times. Use the data from Appendix B to construct α a scatterplot, find the value of the linear correlation
Refer to Data Set 17 in Appendix B and use the word counts measured from men and women in couple relationships listed in the first two columns of Data Set 17.Use the data from Appendix B to construct
Refer to Data Set 16 in Appendix B and use the magnitudes and depths from the earthquakes. Use the data from Appendix B to construct α a scatterplot, find the value of the linear correlation
In addition to testing for a linear correlation between x and y, we can often use transformations of data to explore other relationships. For example, we might replace each x value by x2 and use the
Table A-6 lists critical values of r for selected values of n and a. More generally, critical r values can be found by using the formulaWhere the t value is found from the table of critical t values
Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.
Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.
Refer to the Minitab-generated scatterplot given in Exercise 11 of Section 10-2.a. Using the pairs of values for all 10 points, find the equation of the regression line. b. After removing the point
Refer to the Minitab-generated scatterplot given in Exercise 12 of Section 10-2.a. Using the pairs of values for all 8 points, find the equation of the regression line. b. Using only the pairs of
Find the best predicted crash fatality rate for a year in which there are 500 metric tons of lemon imports.Find the regression equation using Î± = 0.05, letting the first variable be the predictor
One subject not included in the given table had a PSAT score of 229. Find the best predicted SAT score for this student. Is the result close to the reported value of 2400? Given that the data are
Find the best predicted number of burglaries for Ohio State, which had an enrollment of 51,800 students. Is the predicted value close to 329, which was the actual number of burglaries?Find the
At 6327 ft (or 6.327 thousand feet), the author recorded the temperature. Find the best predicted temperature at that altitude. How does the result compare to the actual recorded value of 48°F?Find
The court for the town of Beekman had income of $83,941 (or $83,941 thousand). Find the best predicted salary for the justice. Is the result close to the actual salary of $26,088?Find the regression
An item not included in the table is a pair of New York Knicks tickets. The auctioneer started the bidding at $300. Find the best predicted winning bid. Is the result close to the actual winning bid
The cluster Hydra has a measured redshift of 0.0126. Find the best predicted distance to that cluster. Is the result close to the actual distance of 0.18 billion light-years?Find the regression
Not included in the table below is a diamond with a weight of 1.50 carats. Find the best predicted price for this diamond. Is the result close to the actual price of $16,097? What is wrong with
Find the best predicted weight of a seal if the overhead width measured from a photograph is 2 cm. Can the prediction be correct? What is wrong with predicting the weight in this case?Find the
Find the best predicted repair costs for a full-rear crash for a Volkswagon Passat, given that its repair cost from a full-front crash is $4594. How does the result compare to the $982 actual repair
Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 100 mm Hg.Find the regression equation using Î± = 0.05, letting the first
Find the best predicted temperature at a time when a cricket chirps 3000 times in 1 minute. What is wrong with this predicted value?Find the regression equation using Î± = 0.05, letting the first
One gas station not included in the table below had a listed price of $2.78 for regular gas. Find the best predicted price of premium gas at this station. Is the result close to the actual price of
Using the data from the preceding exercise, find the best predicted price for mid-grade gas for a station that posted $2.78 as the price of regular gas. Is the result close to the actual price of
Find the best predicted circumference of a marble with a diameter of 1.50 cm. How does the result compare to the actual circumference of 4.7 cm?Find the regression equation using Î± =
Using the data from the preceding exercise, find the best predicted volume of a marble with a diameter of 1.50 cm. How does the result compare to the actual volume of 1.8 cm3?Find the regression
Refer to Data Set 6 in Appendix B and use the paired data consisting of IQ score and brain volume (cm3). Find the best predicted IQ score for someone with a brain volume of 1000 cm3.In each case,
Refer to Data Set 15 in Appendix B and use the departure delay times and the arrival delay times. Find the best predicted arrival delay time for a flight with no departure delay.In each case, find
Refer to Data Set 17 in Appendix B and use the word counts measured from men and women in couple relationships listed in the first two columns of Data Set 17. Find the best predicted word count for a
Refer to Data Set 16 in Appendix B and use the magnitudes and depths from the earthquakes. Find the best predicted depth of an earthquake with a magnitude of 1.50.In each case, find the regression
Explain why a test of the null hypothesis H0: p = 0 is equivalent to a test of the null hypothesis H0: β1 = 0, where p is the linear correlation coefficient for a population of paired data, and β1
According to the least-squares property, the regression line minimizes the sum of the squares of the residuals. Refer to the data in Table 10-1.a. Find the sum of squares of the residuals.b. Show
Using Data Set 1 from Appendix B, if we let the predictor variable x represent heights of males and let the response variable y represent weights of males, the sample of 10-4 Prediction Intervals and
Using the heights and weights described in Exercise 1, a height of 180 cm is used to find that the predicted weight is 88.0 kg, and the 95% prediction interval is displayed by Minitab as (50.7,
Using the heights and weights described in Exercise 1, the linear correlation coefficient r is 0.356. Find the value of the coefficient of determination. What practical information does the
A sample of 12 different statistics textbooks is obtained and their weights are measured in kilograms and in pounds. Using the 12 paired weights (kg, lb), what is the value of se? For a Triola
r — 0.933 (x = weight of male, y = waist size of male) Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that
r = 0.963 (x = chest size of a bear, y = weight of a bear) Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation
r = —0.793 (x = weight of a car, y = highway fuel consumption) Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total
r — 0.751 (x = weight of discarded plastic, y = household size) Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total
Use the information provided in the display to determine the value of the linear correlation coefficient. Given that there are 40 pairs of data, is there sufficient evidence to support a claim of a

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