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probability statistics

Statistics For The Behavioral Sciences 4th Edition Gregory J Privitera - Solutions

Construct a 90% confidence interval for σ in Exercise 9.13 on page 303.
Construct a 99% confidence interval for σ in Exercise 9.12 on page 303.
Construct a 99% confidence interval for σ in Exercise 9.11 on page 303.
Construct a 95% confidence interval for σ in Exercise 9.9 on page 303.
The mean heights of 24 undergraduate students studying mechanical engineering in a college is 170 centimeters, with a 12 1 2 1 2 2 2 variance 14 centimeters. Assuming that the heights are normally distributed, construct a 95% confidence interval forσ .
An electronic firm manufacturing wall clocks claims that their product lasts for an average of 36 months, with a variance of 25 months. If six of those wall clocks were observed to last 30, 29, 37, 41, 34, and 40 months, construct a 95% confidence interval for σ and decide if the manufacturer’s
According to a report released by the production department of a company, 5.8% of the items in their 2014 batch were defective. In 2015, though, due to the use of improved technology, this figure went down to 4.2%. The company stores its products according to the batch they belong to. The quality
Among 465 final semester boys of an engineering college, 180 got placed through the campus recruitment drive. Among 324 girls, 142 got placed through the campus recruitment drive.Compute a 90% confidence interval for the difference between the proportion of boys and girls who were placed through
In the study Germination and Emergence of Broccoli, conducted by the Department of Horticulture at Virginia Tech, a researcher found that at 5°C, 10 broccoli seeds out of 20 germinated, while at 15°C, 15 out of 20 germinated. Compute a 95% confidence interval for the difference between the 12 1 2
A clinical trial was conducted to determine if a certain type of inoculation has an effect on the incidence of a certain disease. A sample of 1000 rats was kept in a controlled environment for a period of 1 year, and 500 of the rats were given the inoculation. In the group not inoculated, there
In the authorized service center of an internationally reputed automobile company, 16 of the 100 cars entered for service had mechanical defects. In another sample, 6 of the 120 cars had electrical defects. Compute a 95% confidence interval for the difference between the proportions of cars with
In a socio-economic survey conducted among 1200 randomly selected villagers from a coastal village A, 672 earn their living by fishing. From a nearby village B, 744 out of the 1200 villagers earn their living by fishing. Compute a 90%confidence interval for the difference between the proportions of
An opinion poll is to conduct among the residents and shopkeepers of a metropolitan city on whether they agree with the route proposed by the authorities for a metro rail project.How large a sample is needed if one wishes to be at least 98%confident that the estimate is within 0.05% of the true
A study is conducted to estimate the percentage of college students who are fond of musical instruments. How large a sample is needed if one wishes to be at least 90% confident that the estimate is within 1% of the true percentage.
According to a new bulletin released by the health department, liquor consumption among adolescents of a certain town has increased in recent years. Someone comments: “it is due to the lack of providing awareness on the ill effects of liquor consumption to students from educational
How large a sample is needed in Exercise 9.52 if we wish to be 98% confident that our sample proportion will be within 0.05 of the true proportion defective?
How large a sample is needed if we wish to be 99%confident that our sample proportion in Exercise 9.51 will be within 0.05 of the true proportion of homes in the city that are heated by oil?
How large a sample is needed if we wish to be 96%confident that our sample proportion in Exercise 9.53 will be within 0.02 of the true fraction of the voting population?
In the newspaper article referred to in Exercise 9.57, 32%of the 1600 adults polled said the U.S. space program should emphasize scientific exploration. How large a sample of adults is needed for the poll if one wishes to be 95% confident that the estimated percentage will be within 2% of the true
1. According to a report in the Roanoke Times, approximately 2/3 of 1600 adults polled by telephone said they think the space shuttle program is a good investment for the country.Find a 95% confidence interval for the proportion of American adults who think the space shuttle program is a good
An international logistic company decided to conduct a qualifying test on computer skills for all the job applicants to that company. From a random sample of 120 applicants, 90 qualified.1. Compute a 95% confidence interval for the proportion of qualifying applicants.2. What can we assert with 95%
Records from a city hospital say that the probability (p)that a confirmed dengue patient stays in the hospital for more than 5 days is 0.7. A new type of medicine claims fast recovery from the fever. A sample of 36 patients admitted with dengue fever is administered with the new medicine and 12 of
A home appliances manufacturing firm producing wet grinders decided to conduct a quality check before marketing their product. From a random sample of 400 units, 18 failed to satisfy the quality requirements. Find a 95% confidence interval for the proportion of wet grinders from the population that
1. A random sample of 200 voters in a town is selected, and 114 are found to support an annexation suit. Find the 96%confidence interval for the fraction of the voting population favoring the suit.2. What can we assert with 96% confidence about the possible size of our error if we estimate the
Compute 95% confidence intervals, using both methods on page 317, for the proportion of defective items in a process when it is found that a sample of size 100 yields 8 defectives.
In a random sample of 1000 homes in a certain city, it is found that 228 are heated by oil. Find 99% confidence intervals for the proportion of homes in this city that are heated by oil using both methods presented on page 317.
Two types of medicine, X and Y, are tested on two groups of insomnia patients to help them sleep. The time until they fall asleep after taking the medicine is recorded. The results are as follows:A B A B A B A B B A A B Assuming that the variances are equal, construct a 99%confidence interval for
Two different brands of latex paint are being considered for use. Fifteen specimens of each type of paint were selected, and the drying times, in hours, were as follows:Assume the drying time is normally distributed with σ = σ .Find a 95% confidence interval on μ – μ , where μ and μ are the
A toilet soap manufacturing company produces two varieties of soaps, A and B. The sample information for the units of soap sold within the previous month is collected from 20 supermarkets in a city. The summary of the sales data is as follows: , , s = 23.7, and s = 31.8. Assume that the data of
An asset management company reported its mutual fund investments growth, through various companies, for the years 2014 and 2015. The figures for 8 of the companies are listed below. Find a 95% confidence interval for the mean change in percentage growth of the asset management company.
The following data represent the running times of films produced by two motion-picture companies.Compute a 90% confidence interval for the difference between the average running times of films produced by the two companies. Assume that the running-time differences are approximately normally
Two different varieties of paddy seeds are cultivated in an experiment. The yield, in kilograms, from seeds sown in 9 sample plots for each variety, under similar conditions, is recorded as follows:Find a 95% confidence interval for the mean difference between the yields of the two varieties,
Referring to Exercise 9.43, find a 99% confidence interval for μ – μ if tires of the two brands are assigned at random to A B 1 2 the left and right rear wheels of 8 taxis and the following distances, in kilometers, are recorded:Assume that the differences of the distances are approximately
A taxi company is trying to decide whether to purchase brand A or brand B tires for its fleet of taxis. To estimate the difference in the two brands, an experiment is conducted using 12 of each brand. The tires are run until they wear out. The results are Compute a 95% confidence interval for μ
An experiment reported in Popular Science compared fuel economies for two types of similarly equipped diesel minitrucks.Let us suppose that 12 Volkswagen and 10 Toyota trucks were tested in 90-kilometer-per-hour steady-paced trials. If the 2 1 12 Volkswagen trucks averaged 16 kilometers per liter
The following data represents the total time taken, in days, to deliver books ordered through two online sellers. The sample delivery times are collected and reveal the following information:Find a 98% confidence interval for the difference, μ – μ .
In a study conducted at Virginia Tech on the development of ectomycorrhizal, a symbiotic relationship between the roots of trees and a fungus, in which minerals are transferred from the fungus to the trees and sugars from the trees to the fungus, 20 northern red oak seedlings exposed to the fungus
In a common university examination for communicative English, 16 of the mathematics graduates score an average of 78 marks with a standard deviation of 6, and 22 of the physics graduates score an average of 72 marks with a standard deviation of 8. Construct a 95% confidence interval for the
Two catalysts in a batch chemical process, are being compared for their effect on the output of the process reaction.A sample of 12 batches was prepared using catalyst 1, and a sample of 10 batches was prepared using catalyst 2. The 12 batches for which catalyst 1 was used in the reaction gave an
A study was conducted to determine if a certain treatment has any effect on the amount of metal removed in a pickling operation. A random sample of 100 pieces was immersed in a bath for 24 hours without the treatment, yielding an average of 12.2 millimeters of metal removed and a sample standard
Two kinds of light bulbs are being compared for their longevity. 50 pieces of each type of bulb are tested under similar conditions. Brand A has an average life of 78.3 hours with a standard deviation of 5.6 hours, while brand B has an average life of 87.2 hours with a standard deviation of 6.3
A random sample of size n = 25 is taken from a normal population with a standard deviation of σ = 5 and mean of. A second random sample of size n = 36 is taken from a different normal population with a standard deviation of σ = 3 and mean of . Find a 94% confidence interval for μ – μ .
Consider Exercise 9.33. Use the MSE discussed in Exercise 9.28 to determine which estimator is more efficient. Write out MSE(S) MSE(S)
Compare S and S′ (see Exercise 9.29), the two estimators of σ , to determine which is more efficient. Assume these estimators are found using X , X , …, X , independent random variables from n(x; μ, σ). Which estimator is more efficient considering only the variance of the estimators? [Hint:
Show that the estimator P′ of Exercise 9.31(b) becomes unbiased as n → ∞.
If X is a binomial random variable, show that 2 2 2 2 22 21. is an unbiased estimator of p;2. is a biased estimator of p.
Consider S′ , the estimator of σ , from Exercise 9.29.Analysts often use S′ rather than dividing by n – 1, the degrees of freedom in the sample.1. What is the bias of S′ ?2. Show that the bias of S′ approaches zero as n → ∞.
Let us define . Show that and hence S′ is a biased estimator for σ .
In Section 9.3, we emphasized the notion of “most efficient estimator” by comparing the variance of two unbiased estimators and . However, this does not take into account bias in case one or both estimators are not unbiased. Consider the quantity where MSE denotes mean squared error. The MSE is
Consider the situation of Case Study 9.1 on page 301 with a larger sample of metal pieces. The diameters are as follows:1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 1.01, 1.03, 0.99, 1.00, 1.00, 0.99, 0.98, 1.01, 1.02, 0.99 centimeters. Once again the normality assumption may be made. Do the following and
Consider the data in Exercise 9.13. Suppose the manufacturer of the shearing pins insists that the Rockwell hardness of the product be less than or equal to 44.0 only 5% of the time. What is your reaction? Use a tolerance limit calculation as the basis for your judgment.
Consider the drying time measurements in Exercise 9.14.Suppose the 15 observations in the data set are supplemented by a 16th value of 6.9 hours. In the context of the original 15 observations, is the 16th value an outlier? Show work.
Refer to Exercise 9.22 again. Suppose that specifications by a buyer of the thread are that the tensile strength of the material must be at least 62 kilograms. The manufacturer is satisfied if at most 5% of the manufactured pieces have tensile strength less than 62 kilograms. Is there cause for
Refer to Exercise 9.22. Why are the quantities requested in the exercise likely to be more important to the manufacturer of the thread than, say, a confidence interval on the mean tensile strength?
A type of thread is being studied for its tensile strength properties. Fifty pieces were tested under similar conditions, and the results showed an average tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilograms. Assuming a normal distribution of tensile strengths, give a lower
In a study conducted by the Department of Biological Sciences at Virginia Tech, fifteen samples of water were collected from a certain station in the James River in order to gain some insight regarding the amount of orthophosphorus in the river. The concentration of the chemical is measured in
Consider the situation of Exercise 9.11. Estimation of the mean diameter, while important, is not nearly as important as trying to pin down the location of the majority of the distribution of diameters. Find the 95% tolerance limits that contain 95% of the diameters.
A random sample of 25 tablets of buffered aspirin contains, on average, 325.05 mg of aspirin per tablet, with a standard deviation of 0.5 mg. Find the 95% tolerance limits that will contain 90% of the tablet contents for this brand of buffered aspirin. Assume that the aspirin content is normally
Referring to Exercise 9.13, construct a 95% tolerance interval containing 90% of the measurements.
Consider Exercise 9.9. Compute a 95% prediction interval for the sugar content of the next single serving of Alpha-Bits.
Consider Exercise 9.10. Compute the 95% prediction interval for the next observed number of words per minute typed by a graduate of the secretarial school.
Referring to Exercise 9.5, construct a 95% prediction interval for the kilometers traveled annually by an automobile owner in Virginia.
The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint:Assuming that the measurements represent a random sample from a normal population, find a 95% prediction interval for the drying time for the next trial of the paint.
A random sample of 12 shearing pins is taken in a study of the Rockwell hardness of the pin head. Measurements on the Rockwell hardness are made for each of the 12, yielding an average value of 48.50 with a sample standard deviation of 1.5.Assuming the measurements to be normally distributed,
A random sample of 10 chocolate energy bars of a certain brand has, on average, 230 calories per bar, with a standard deviation of 15 calories. Construct a 99% confidence interval for the true mean calorie content of this brand of energy bar.Assume that the distribution of the calorie content is
A machine produces metal pieces that are cylindrical in shape. A sample of pieces is taken, and the diameters are found to be 1.01, 0.97, 1.03, 1.04, 0.99, 0.98, 0.99, 1.01, and 1.03 centimeters. Find a 99% confidence interval for the mean diameter of pieces from this machine, assuming an
A random sample of 12 graduates of a certain secretarial school typed an average of 79.3 words per minute with a standard deviation of 7.8 words per minute. Assuming a normal distribution for the number of words typed per minute, find a 95% confidence interval for the average number of words typed
Regular consumption of presweetened cereals contributes to tooth decay, heart disease, and other degenerative diseases, according to studies conducted by Dr. W. H. Bowen of the National Institute of Health and Dr. J. Yudben, Professor of Nutrition and Dietetics at the University of London. In a
A marketing agency wishes to determine the average time, in days, that it takes to sell a product in various stores in a city.How large a sample will they need in order to be 98% confident that their sample mean will be within 2 days of the true mean?Assume that σ = 5 days.
How large a sample is needed in Exercise 9.3 if we wish to be 96% confident that our sample mean will be within 0.0005 inch of the true mean?
How large a sample is needed in Exercise 9.2 if we wish to be 95% confident that our sample mean will be within 10 hours of the true mean?
A random sample of 100 automobile owners in the state of Virginia shows that an automobile is driven on average 23,500 kilometers per year with a standard deviation of 3900 kilometers. Assume the distribution of measurements to be approximately normal.1. Construct a 95% confidence interval for the
The prices of a particular variety of rice, per kilogram, collected from 49 local stores in the suburban areas of a district vary with a mean of $3 and a standard deviation of $1.4.1. Construct a 99% confidence interval for the mean price.2. With 99% confidence, what can we assert about the
Many cardiac patients wear an implanted pacemaker to control their heartbeat. A plastic connector module mounts on the top of the pacemaker. Assuming a standard deviation of 0.0015 inch and an approximately normal distribution, find a 99% confidence interval for the mean of the depths of all
An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an average life of 780 hours, find a 90% confidence interval for the population mean of all bulbs produced by this
As part of a research on nutrition, a particular protein diet was tried out on a large group of mice. Researchers claimed that the new diet led to an increase in the weight of the mice.Assuming that it is known from previous studies that σ = 3.0 grams, how many mice should be included in our
An administrator determines that among students at a local school the probability of missing class is p = .16. Assuming that the school has 300 students enrolled, how many students can we expect to miss class on a given day?
Below is the probability distribution for a random variable x. What is the standard deviation of this probability distribution?b. $4.95c. $24.49
If the standard deviation of a probability distribution is 9, then the variance is ____. [Fill in the blank]Answer: __ [enter whole number]
A researcher records the number of successful outcomes per session in an experimental game. They find that the probability that a participant has 0 successful outcomes is p = .27; 1 successful outcome is p = .51; 2 successful outcomes is p = .17; and 3 successful outcomes is p = .05. How many
Suppose you open a new game at the county fair. When patrons win, you pay them $3.00;when patrons lose, they pay you $1.00. If the probability of a patron winning is p = .20 and the probability of a patron losing is p = .80, then how much can you expect to win (or lose) in the long run? [Hint: You
Below is the probability distribution for the number of times students had to take the same exam before passing it. If a student must pass the exam in two tries or less to pass the class, then what is the probability of passing the class?a. .80b. .40c. .20d. .60
Below is the probability distribution for random variable x. Which of the following is most probable?a. a score of at most 9b. a score of at least 9c. a score of 8d. a score of 10 x 8 9 10 plx) .50 .40 .10
A professor records the grades for their class. They find that the probability that a student earns an A is p = .14; earns a B is p = .36; earns a C is p = .32; earns a D is p = .10; and earns an F is p = .08. What is the probability that a student earns a B or better in this class?a. .36b. .14c.
A researcher records the number of mistakes made during a skills assessment. They find that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this
Which of the following probability distributions is accurate?a. 2/20, 8/20, 12/20, 20/20b. 4/20, 2/20, 4/20, 10/20c. -2/20, -4/20, -4/20, -10/20
Based on the table shown, what percentage of outcomes resulted in losing, given that the team played away? [Hint: Th e answer is given directly in the table; no calculations are required]Answer: __% [enter two-digit whole number]
Based on the table shown, what percentage of outcomes resulted in winning, given that the team played at home? [Hint: Th e answer is given directly in the table; no calculations are required]Answer: __% [enter two-digit whole number]
Based on the table shown, what percentage of outcomes resulted in winning? [Hint: Th e answer is given directly in the table; no calculations are required]Answer: __% [enter two-digit whole number]
Bayes’s theorem can be applied when we want to determine the conditional probability of obtaining samples of data, given that a parameter in some population is ____. [Fill in the blank]a. fi xedb. knownc. unknown
Bayes’s theorem is often applied to a variety of ______ probability situations, including those related to statistical inference. [Fill in the blank]a. genericb. absolutec. condit
A researcher wants to identify the conditional probability (p) of a student passing the high-stakes assessment, given that they did not attend the preparatory course. What is the value of the numerator of the formula using Bayes’s theorem to compute this conditional probability?a. .28b. .48c.
A researcher wants to identify the conditional probability (p) of a student passing the high-stakes assessment, given that they did attend the preparatory course. What is the value of the numerator of the formula using Bayes’s theorem to compute this conditional probability?a. .71b. .69c. .48d.
What is the conditional probability (p) of a student passing the high-stakes assessment, given that they did not attend the preparatory course?a. .28b. .29c. .69d. .73
What is the conditional probability (p) of a student failing the high-stakes assessment, given that they did attend the preparatory course?a. .16b. .31c. .34d. .50
Two outcomes (A and B) are independent, where p(A) = .40 and p(B) is .15. What is the probability of A and B?a. 0b. .06c. .55
In a game, the probability of winning money is p = .16, the probability of losing money is p = .54, and the probability of breaking even is p = .30. What is the probability of winning or losing money in this game?a. .16b. .54c. .70d. 1.00
A researcher determines that the probability of winning a new game is p = .32. Assuming winning and losing are complementary events, what is the probability of winning or losing the new game?a. 0b. .32c. .68d. 1.00
Which probability is most likely for a rat subject?a. Receiving reinforcement in the front arm.b. Receiving reinforcement in the back arm.c. Receiving reinforcement in the front or the back arm.d. Receiving reinforcement in the left or the right arm.
Which of the following statements is true?a. A rat is more likely to obtain reinforcement in the right arm or the front arm than in the left arm or the back arm.b. A rat is equally likely to obtain reinforcement in the right arm or the front arm as in the left arm or the back arm.c. A rat is more

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