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Elementary Statistics A Step By Step Approach 10th Edition Allan G. Bluman - Solutions
What is meant by the unexplained variation? How is it computed?
What is the general form of the multiple regression equation? What does a represent? What do the b’s represent?
At a large department store customers were asked to rate the service and the materials purchased on a scale from 1 to 10, with 10 being the highest rating. Then the amount that they spent was recorded. Is there evidence of a relationship between the rating and the amount that they spent? Rating x 2
What is meant by the statement that two variables are related?
What is meant by the explained variation? How is it computed?
Explain the similarities and differences between simple linear regression and multiple regression.
What two things should be done before one performs a regression analysis?
If there is a significant difference between p1 and p2 and between p2 and p3, can you conclude that there is a significant difference between p1 and p3?
The average earnings of year-round full-time workers with bachelor’s degrees or more is $88,641 for men and $58,000 for women—a difference of slightly over $30,000 a year. One hundred of each were randomly sampled, resulting in a sample mean of $90,200 for men, and the population standard
The percentage of males 18 years and older who have never married is 30.4. For females the percentage is 23.6. Looking at the records in a particular populous county, a random sample of 250 men showed that 78 had never married and 58 of 200 women had never married. At the 0.05 level of
A researcher claims that students in a private school have exam scores that are at most 8 points higher than those of students in public schools. Random samples of 60 students from each type of school are selected and given an exam. The results are shown. At α = 0.05, test the claim.Private school
According to the U.S. Bureau of Labor Statistics, approximately equal numbers of men and women are engaged in sales and related occupations. Although that may be true for total numbers, perhaps the proportions differ by industry. A random sample of 200 salespersons from the industrial sector
According to the almanac, the average sales price of a single-family home in the metropolitan Dallas/Ft. Worth/Irving, Texas, area is $215,200. The average home price in Orlando, Florida, is $198,000. The mean of a random sample of 45 homes in the Texas metroplex was $216,000 with a population
A company owned two small Bath and Body Goods stores in different cities. It was desired to see if there was a difference in their mean daily sales. The following results were obtained from a random sample of daily sales over a six-week period. At α = 0.01, can a difference in sales
The mean travel time to work for Americans is 25.3 minutes. An employment agency wanted to test the mean commuting times for college graduates and those with only some college. Thirty-five college graduates spent a mean time of 40.5 minutes commuting to work with a population variance of 67.24.
Why is the critical region always on the right side in the use of the F test?
Find p̂ and q̂ for each.a. n = 36, X = 20b. n = 50, X = 35c. n = 64, X = 16d. n = 200, X = 175e. n = 148, X = 16
What three assumptions must be met when you are using the z test to test differences between two means when σ1 and σ2 are known?
As an aid for improving students€™ study habits, nine students were randomly selected to attend a seminar on the importance of education in life. The table shows the number of hours each student studied per week before and after the seminar. At α = 0.10, did attending the
What are the two different degrees of freedom associated with the F distribution?
A recent study of 20 individuals found that the average number of therapy sessions a person takes for a shoulder problem is 9.6. The standard deviation of the sample was 2.8. A study of 25 individuals with a hip problem found that they had a mean of 10.3 sessions. The standard deviation for this
Find each X, given p̂.a. p̂ = 0.60, n = 240b. p̂ = 0.20, n = 320c. p̂ = 0.60, n = 520d. p̂ = 0.80, n = 50e. p̂ = 0.35, n = 200
Show two different ways to state that the means of two populations are equal.
Find each X, given p̂.a. p̂ = 0.24, n = 300b. p̂ = 0.09, n = 200c. p̂ = 88%, n = 500d. p̂ = 40%, n = 480e. p̂ = 32%, n = 700
A researcher wishes to see if there is a difference between the mean number of hours per week that a family with no children participates in recreational activities and a family with children participates in recreational activities. She selects two random samples and the data are shown. At
A medical researcher wishes to see if he can lower the cholesterol levels through diet in 6 people by showing a film about the effects of high cholesterol levels. The data are shown. At α = 0.05, did the cholesterol level decrease on average? 1 3 5 6. Patient 222 206 219 Before After
Using Table H, find the critical value for each.a. Sample 1: s21 = 140, n1 = 25Sample 2: s22 = 125, n2 = 14Two-tailed α = 0.05b. Sample 1: s21 = 43, n1 = 12Sample 2: s22 = 56, n2 = 16Right-tailed α = 0.10c. Sample 1: s21 = 516, n1 = 21Sample 2: s22 = 472, n2 = 18Right-tailed α = 0.01
Teachers€™ Salaries New York and Massachusetts lead the list of average teacher€™s salaries. The New York average is $76,409 while teachers in Massachusetts make an average annual salary of $73,195. Random samples of 45 teachers from each state yielded the following.At
Find p̅ and q̅.a. X1 = 6, n1 = 15, X2 = 9, n2 = 15b. X1 = 21, n1 = 100, X2 = 43, n2 = 150c. X1 = 20, n1 = 80, X2 = 65, n2 = 120d. X1 = 15, n1 = 50, X2 = 3, n2 = 12e. X1 = 24, n1 = 40, X2 = 18, n2 = 36
A statistics class was given a pretest on probability (since many had previous experience in some other class). Then the class was given a six-page review handout to study for two days. At the next class they were given another test. Is there sufficient evidence that the scores improved? Use
In a sample of 150 men, 132 said that they had less leisure time today than they had 10 years ago. In a random sample of 250 women, 240 women said that they had less leisure time than they had 10 years ago. At α = 0.10, is there a difference in the proportions? Find the 90% confidence interval for
Find the 90% confidence for the difference of the means in Exercise 1 of this section.Data from 1 Europe 1385 Asia 722 320 722 487 470 614 1137 350 1246 964 830 1312 984 1904 900 345 820
A researcher wanted to compare the pulse rates of identical twins to see whether there was any difference. Eight sets of twins were randomly selected. The rates are given in the table as number of beats per minute. At α = 0.01, is there a significant difference in the average pulse
An educational researcher devised a wooden toy assembly project to test learning in 6-year-olds. The time in seconds to assemble the project was noted, and the toy was disassembled out of the child€™s sight. Then the child was given the task to repeat. The researcher would conclude that
A survey of 60 men found that 36 gamble. Another survey of 50 women found that 28 gamble. At α = 0.01, is there a difference in the proportions?
A researcher wishes to see if there is a difference in the manual dexterity of athletes and that of band members. Two random samples of 30 are selected from each group and are given a manual dexterity test. The mean of the athletes’ test was 87, and the mean of the band members’ test was 92.
A ninth-grade teacher wishes to see if a new spelling program will reduce the spelling errors in his students€™ writing. The number of spelling errors made by the students in a five-page report before the program is shown. Then the number of spelling errors made by students in a five-page
A recent random survey of households found that 14 out of 50 householders had a cat and 21 out of 60 householders had a dog. At α = 0.05, test the claim that fewer household owners have cats than household owners who have dogs as pets.
A random survey of 80 women who were victims of violence found that 24 were attacked by relatives. A random survey of 50 men found that 6 were attacked by relatives. At α = 0.10, can it be shown that the percentage of women who were attacked by relatives is greater than the percentage of men who
Two random samples of 32 individuals were selected. One sample participated in an activity which simulates hard work. The average breath rate of these individuals was 21 breaths per minute. The other sample did some normal walking. The mean breath rate of these individuals was 14. Find the 90%
Find the 95% confidence interval of the difference in the distance that day students travel to school and the distance evening students travel to school. Two random samples of 40 students are taken, and the data are shown. Find the 95% confidence interval of the difference in the means. п 4.7 6.2
A random sample of monthly gasoline prices was taken from 2011 and from 2015. The samples are shown. Using α = 0.01, can it be concluded that gasoline cost more in 2015? Use the P-value method. 2.02 2.47 2.50 2.70 3.13 2.56 2011 2015 2.36 2.46 2.63 2.76 3.00 2.85 2.77
A large group of friends went miniature golfing together at a par 54 course and decided to play on two teams. A random sample of scores from each of the two teams is shown. At α = 0.05, is there a difference in mean scores between the two teams? Use the P-value method. Team 1 Team 2
In a large hospital, a nursing director selected a random sample of 30 registered nurses and found that the mean of their ages was 30.2. The population standard deviation for the ages is 5.6. She selected a random sample of 40 nursing assistants and found the mean of their ages was 31.7. The
Two random samples of professional baseball players were selected and the number of home runs hit were recorded. One sample was obtained from the National League, and the other sample was obtained from the American League. At α = 0.10, is there a difference in the means? National
The average number of hours of television watched per week by women over age 55 is 48 hours. Men over age 55 watch an average of 43 hours of television per week. Random samples of 40 men and 40 women from a large retirement community yielded the following results. At the 0.01 level of significance,
The average age of pet dogs is 4.3 years. Two random samples of pet owners who own dogs are selected. Sample 1 of 13 dog owners was selected from owners who live in Miami. The standard deviation of the ages of the dogs in this sample is 1.3 years. Sample 2 of 8 dog owners was selected from dog
Find the proportions p̂ and q̂ for each.a. n = 52, X = 32b. n = 80, X = 66c. n = 36, X = 12d. n = 42, X = 7e. n = 160, X = 50
When one is computing the F test value, what condition is placed on the variance that is in the numerator?
Classify each as independent or dependent samples.a. Heights of identical twinsb. Test scores of the same students in English and psychologc. The effectiveness of two different brands of aspirin on two different groups of peopled. Effects of a drug on reaction time of two different groups of
Explain the difference between testing a single mean and testing the difference between two means.
Suppose a statistician chose to test a hypothesis at α = 0.01. The critical value for a right-tailed test is +2.33. If the test value were 1.97, what would the decision be? What would happen if, after seeing the test value, she decided to choose α = 0.05? What would the decision be? Explain the
Approximately 70% of the U.S. population recycles. According to a green survey of a random sample of 250 college students, 204 said that they recycled. At α = 0.01, is there sufficient evidence to conclude that the proportion of college students who recycle is greater than 70%?
To see whether people are keeping their car tires inflated to the correct level of 35 pounds per square inch (psi), a tire company manager selects a random sample of 36 tires and checks the pressure. The mean of the sample is 33.5 psi, and the population standard deviation is 3 psi. Are the tires
A medical college dean read that the average number of applications a potential medical school student sends is 7.8. She thinks that the mean is higher. So she selects a random sample of 35 applicants and asks each how many medical schools they applied to. The mean of the sample is 8.7. The
Room and board fees for a random sample of independent religious colleges are shown.Estimate the standard deviation in costs based on s ‰ˆ R/4. Is there sufficient evidence to conclude that the sample standard deviation differs from this estimated amount? Use α = 0.05. 210
The standard deviation of fuel consumption of a manufacturer’s sport utility vehicle is hypothesized to be 3.3 miles per gallon. A random sample of 18 vehicles has a standard deviation of 2.8 miles per gallon. At α = 0.10, is the claim believable?
The director of a medical hospital feels that her surgeons perform fewer operations per year than the national average of 211. She selected a random sample of 15 surgeons and found that the mean number of operations they performed was 208.8. The standard deviation of the sample was 3.8. Is there
A random sample of second-round golf scores from a major tournament is listed below. At α = 0.10, is there sufficient evidence to conclude that the population variance exceeds 9? 75 69 69 72 74 70 67 74 66 71
The average length of prison term in the United States for white collar crime is 34.9 months. A random sample of 40 prison terms indicated a mean stay of 28.5 months with a standard deviation of 8.9 months. At α = 0.04, is there sufficient evidence to conclude that the average stay differs from
The amounts of vitamin C (in milligrams) for 100 g (3.57 ounces) of various randomly selected fruits and vegetables are listed. Is there sufficient evidence to conclude that the standard deviation differs from 12 mg? Use α = 0.10. 7.9 46.4 32.2 25.0 13.0 18.2 28.1 5.2 34.4 12.8 16.3
Of men aged 65 and over 20.5% are still in the U.S. labor force. A random sample of 120 retired male teachers indicated that 38 were still working. Use both a confidence interval and a hypothesis test. Test the claim that the proportion is greater than 20.5% at α = 0.10.
For each conjecture, state the null and alternative hypotheses.a. The average age of first-year medical school students is at least 27 years.b. The average experience (in seasons) for an NBA player is 4.71.c. The average number of monthly visits/sessions on the Internet by a person at home has
A person read that the average number of hours an adult sleeps on Friday night to Saturday morning was 7.2 hours. The researcher feels that college students do not sleep 7.2 hours on average. The researcher randomly selected 15 students and found that on average they slept 8.3 hours. The standard
In a previous study conducted several years ago, a man owned on average 15 dress shirts. The standard deviation of the population is 3. A researcher wishes to see if that average has changed. He selected a random sample of 42 men and found that the average number of dress shirts that they owned was
A manufacturer of cigarettes wishes to test the claim that the variance of the nicotine content of the cigarettes the company manufactures is equal to 0.638 milligram. The variance of a random sample of 25 cigarettes is 0.930 milligram. At α = 0.05, test the claim.
For each conjecture, state the null and alternative hypotheses.a. The average weight of dogs is 15.6 pounds.b. The average distance a person lives away from a toxic waste site is greater than 10.8 miles.c. The average farm size in 1970 was less than 390 acres.d. The average number of miles a
An automobile owner found that 20 years ago, 76% of Americans said that they would prefer to purchase an American automobile. He believes that the number is much less than 76% today. He selected a random sample of 56 Americans and found that 38 said that they would prefer an American automobile.
An obstetrician read that a newborn baby loses on average 7 ounces in the first two days of his or her life. He feels that in the hospital where he works, the average weight loss of a newborn baby is less than 7 ounces. A random sample of 32 newborn babies has a mean weight loss of 6.5 ounces. The
The National Novel Writing Association states that the average novel is at least 50,000 words. A particularly ambitious writing club at a college-preparatory high school had randomly selected members with works of the following lengths. At α = 0.10, is there sufficient evidence to
The average number of miles a person drives per day is 24. A researcher wishes to see if people over age 60 drive less than 24 miles per day. She selects a random sample of 49 drivers over the age of 60 and finds that the mean number of miles driven is 22.8. The population standard deviation is 3.5
In hypothesis testing, why can’t the hypothesis be proved true?
A corrections officer read that 58% of runaways are female. He believes that the percentage is higher than 58. He selected a random sample of 90 runaways and found that 63 were female. At α = 0.05, can you conclude that his belief is correct?
How can the power of a test be increased?
A researcher knew that before cell phones, a person made on average 2.8 calls per day. He believes that the number of calls made per day today is higher. He selects a random sample of 30 individuals who use a cell phone and asks them to keep track of the number of calls that they made on a certain
A random sample of the distances in miles 8 shoppers travel to their nearest supermarkets is shown. Test the claim at α = 0.10 that the standard deviation of the distance shoppers travel is greater than 2 miles. 3.6 5.1 4.2 1.7 2.9 1.3 6.5 9.3
It has been reported that one in four medical doctors received their degrees from foreign schools. A hospital researcher believes that the percentage is less than 25%. A random survey of 100 medical doctors found that 19 received their degrees from a foreign school. At α = 0.05, is there enough
When should a one-tailed test be used? A two-tailed test?
How is the power of a test related to the type II error?
The average cost for teeth straightening with metal braces is approximately $5400. A nationwide franchise thinks that its cost is below that figure. A random sample of 28 patients across the country had an average cost of $5250 with a standard deviation of $629. At α = 0.025, can it be concluded
Explain what is meant by a significant difference.
A magazine article reported that 11% of adults buy takeout food every day. A fast-food restaurant owner surveyed 200 customers and found that 32 said that they purchased takeout food every day. At α = 0.02, is there evidence to believe the article’s claim? Would the claim be rejected at α =
A researcher found that a cigarette smoker smokes on average 31 cigarettes a day. She feels that this average is too high. She selected a random sample of 10 smokers and found that the mean number of cigarettes they smoked per day was 28. The sample standard deviation was 2.7. At α = 0.05 is there
What symbols are used to represent the probabilities of type I and type II errors?
According to the National Association of Home Builders, the average cost of building a home in the Northeast is $117.91 per square foot. A random sample of 36 new homes indicated that the mean cost was $122.57 and the standard deviation was $20. Can it be concluded that the mean cost differs from
A random sample of $1 Trifecta tickets at a local racetrack paid the following amounts (in dollars and cents). Is there sufficient evidence to conclude that the average Trifecta winnings exceed $50? Use α = 0.10. Assume the variable is normally distributed. 141.00 48.60 72.70 32.40
What symbols are used to represent the null hypothesis and the alternative hypothesis?
Forty-six percent of people believe that there is life on other planets in the universe. A scientist does not agree with this finding. He surveyed 120 randomly selected individuals and found 48 believed that there is life on other planets. At α = 0.10, is there sufficient evidence to conclude that
A researcher wishes to see if the average number of sick days a worker takes per year is greater than 5. A random sample of 32 workers at a large department store had a mean of 5.6. The standard deviation of the population is 1.2. Is there enough evidence to support the researcher’s claim at α =
Test the claim that the standard deviation of the ages of psychologists in Pennsylvania is 8.6 at α = 0.05. A random sample of 12 psychologists had a standard deviation of 9.3.
A shopper in a grocery store purchases 22 items on average. A store manager believes that the mean is greater than 22. She surveyed a randomly selected group of 36 customers and found that the mean of the number of items purchased was 23.2. The population standard deviation is 3.7 items. At α =
What are the mean and the standard deviation of a proportion?
According to a public service website, 69.4% of white collar criminals get prison time. A randomly selected sample of 165 white collar criminals revealed that 120 were serving or had served prison time. Using α = 0.05, test the conjecture that the proportion of white collar criminals serving
Find the critical value (or values) for the t test for each.a. n = 15, α = 0.05, right-tailedb. n = 23, α = 0.005, left-tailedc. n = 28, α = 0.01, two-tailedd. n = 17, α = 0.02, two-tailed
What is meant by a statistical test?
When you are testing hypotheses by using proportions, what are the necessary requirements?
Find the critical value (or values) for the t test for each.a. n = 12, α = 0.01, left-tailedb. n = 16, α = 0.05, right-tailedc. n = 7, α = 0.10, two-tailedd. n = 11, α = 0.025, right-tailede. n = 10, α = 0.05, two-tailed
Why is a proportion considered a binomial variable?
What are the degrees of freedom for the t test?
Many people believe that the average number of Facebook friends is 338. The population standard deviation is 43.2. A random sample of 50 high school students in a particular county revealed that the average number of Facebook friends was 350. At α = 0.05, is there sufficient evidence to conclude
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