ANIMSCI 2260 all quizzes + exams - final study guide
You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years of ownership. Since you are particulary interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 90% confidence interval. You manage to obtain data on 16 recently resold 5-year-old foreign sedans of that model. These 16 cars were resold at an average price of $10,000 with a standard deviation of $1,500. Estimate the true mean resale value of this model of foreign car using a 90% confidence interval.
($9,342.625, $10,657.375)
Investing in the stock market involves a certain amount of risk. Suppose that there is a 20% chance that a risky stock investment will end up in a total loss of your investment. Because the rewards are so great if your investment is successful, you decide to invest in three independent risky stocks, each of which has the same 20% chance of total loss of your investment. Find the probability that all three stocks will result in total loss of your investment.
0.008
A standard deck contains 52 cards, 13 in each of the 4 suits (hearts, diamonds, spades, and clubs). Suppose that you have been dealt 3 cards from a randomly shuffled standard deck. Find the probability that all 3 cards are spades. Assume that, when you are dealt a card, you note the suit of the card and then return it to the deck such that in each case the next card is still dealt from a deck of 52 cards. We call this sampling with replacement.
0.015625
A physical fitness association is including the mile run in its secondary-school fitness test for boys. The time for this event for boys in secondary school is known to have a normal distribution with a mean of 450 seconds and a standard deviation of 50 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 370 seconds.
0.0548
Find the probability of an observation lying more than z = 1.56 standard deviations below the mean.
0.0594
Assume X is a binomial random variable. If n = 5 and p = 0.10, find P (r > 1 success).
0.0815
Assume that 20% of all pigs die between birth and weaning. In a random sample of 300 births, let X be the number of pigs that die between birth and weaning. Using the normal approximation to the binomial, find the approximate probability that the number of pigs in the sample of 300 that die between birth and weaning is less than or equal to 50.
0.0853
A statistician evaluated the winning strategies of teams in the National Football League (NFL). He used actual NFL play-by-play data to approximate the probabilities associated with certain outcomes (e.g., running plays, short pass plays, and long pass plays). The table below shows the probability distribution for the yardage gained, X, on a running play. A negative gain represents a loss of yards on the play. Find the probability of losing yardage on a running play. X, Yards Gained Probability -4 0.020 -2 0.060 -1 0.070 0 0.150 1 0.130 2 0.110 3 0.090 4 0.070 6 0.090 8 0.060 10 0.050 15 0.085 30 0.010 50 0.004 99 0.001
0.15
A population of rabbits has a mean weight of 10 lb and a standard deviation of the weights equal to 2 lb. A rabbit breeder selects a large number of samples of 100 rabbits each, calculates the mean weight of the rabbits in each of these samples, and then graphs the sample means. The standard deviation of these sample means is expected to be equal to _______.
0.20 lb
A human gene carries a certain disease from the mother to the child with a probability rate of 60% (i.e., there is a 60% chance that a given child will have the disease). Suppose a female carrier of the gene has 3 children. Assume that the infections of the 3 children are independent of one another. What is the probability that all 3 children will get the disease from their mother?
0.216
On a particular ranch weaning weights of calves are normally distributed with a mean of 430 lb and a standard deviation of 20 lb. Find the probability that a randomly selected calf will weigh less than 415 lb.
0.2266
An animal scientist is interested in determining the proportion of ewes that give birth to twins. Rather than examine the records for all ewes in the United States, he randomly selects 500 ewes and finds that 220 of them gave birth to twins. The animal scientist knows that the sample size of n = 500 is large enough for large-sample confidence interval procedures to be valid, because:
0.3734 and 0.5066 both fall between 0 and 1.0
If sample points A, B, C, and D are the only possible outcomes of an experiment, find the probability of D using the table shown below: Sample pointABCDProb.0.200.200.20
0.40
Assume that 16% of all pigs die between birth and weaning. In a random sample of 300 births, let X be the number of pigs that die between birth and weaning. Using the normal approximation to the binomial, find the approximate probability that the number of pigs in the sample of 300 that die between birth and weaning is greater than or equal to 50.
0.4052
Suppose that 20% of the Golden Retrievers in the U.S. have a particular genetic defect. We randomly select 4 Golden Retrievers from the population consisting of all Golden Retrievers in the U.S. What is the probability that exactly 1 of the 4 dogs in this sample will have the genetic defect? To find the answer to this question, you will need to use the equation for the binomial distribution.
0.4096
Suppose that 10% of the Labrador Retrievers in the U.S. have a particular genetic defect. We randomly select 6 Labs from the population consisting of all Labs in the U.S. What is the probability that at least 1 (i.e., 1 or more) of the 6 dogs in this sample have the genetic defect?
0.4686
A litter of 5 pigs is produced. What is the probability that at least 3 of the 5 pigs will be females, assuming that the probability of a male pig is 1/2 and the probability of a female pig is 1/2?
0.50
A Gallop poll is conducted to estimate the proportion of voters who plan to vote in favor of a certain issue on the ballot. A random sample of 500 people of voting age is selected. Results of the poll show that 300 of the 500 people polled plan to vote in favor of the issue. What is the point estimate of the true population proportion of people who plan to vote in favor of the issue?
0.60
The table shown below summarizes the 10 winners of the World Series from 1990 to 2000 by division and league. There was no World Series in 1994 due to a strike by the players. One of these 10 World Series winners is to be chosen at random. League National American Eastern 2 6 Division Central 1 1 Western 0 0 Given that the winning team is a member of the American League, what is the probability that the winning team plays in the Eastern Division?
0.857
An experiment results in five possible outcomes with the following probabilities: P(A) = .10, P(B) = .25, P(C) = .20, P(D) = .15, and P(E) = .30. What is the probability that event A does not occur?
0.90
The amount of corn chips dispensed into a 10 ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 10.5 ounces and a standard deviation of 0.2 ounces. What portion of the 10 ounce bags would be expected to contain more than the advertised 10 ounces of corn chips?
0.9938
Suppose we have a population of horses with a mean weight of 1,000 lb and a standard deviation of 50 lb. If we were to take repeated random samples of size n = 100 from the population, the mean and standard deviation, respectively, of the sampling distribution of the sample mean would be:
1,000 lb and 5 lb
Medical research has shown that a certain type of chemotherapy is successful 70% of the time when used to treat skin cancer. Suppose 5 skin cancer patients are treated with this type of chemotherapy. Let X equal the number of patients out of 5 who are cured. The probability distribution for the number of patients out of 5 who are cured is given in the following table: X 0 1 2 3 4 5 P (X) 0.002 0.029 0.132 0.309 0.360 0.168 Find σ2 = E [(X - μ)2].
1.05
In a pizza takeout restaurant, the following probability distribution was obtained. The random variable X represents the number of toppings for a large pizza. x 0 1 2 3 4 P(x) 0.30 0.40 0.20 0.06 0.04 Calculate the mean (µ) of this discrete probability distribution.
1.14
A population of rabbits has a mean weight of 12 lb with a standard deviation of 3 lb. A rabbit breeder selects 1,000 samples of 36 rabbits each from this population, calculates the mean weight of the rabbits in each of these 1,000 samples, and then graphs the 1,000 sample means. The mean of these 1,000 sample means is expected to be equal to:
12 lb
A random sample of 16 Standardbred horses was selected from a population of Standardbreds. The mean time required for these 16 horses to run a mile while pulling a sulky was 130 seconds (i.e., 2 minutes and 10 seconds), The standard deviation of the sample was 10 seconds. What is the point estimate of the true population mean for racing time of Standardbred horses?
130 seconds
The owner of a herd of cows wants to determine the influence of the ages of his cows on the amount of calving difficulty that occurs in his herd. He constructs the following table: Age of Cow (in years) 0-2 3-5 6-10 over 10 Total No difficulty 40 35 20 5 100 Difficult birth 35 45 15 5 100 Total 75 80 35 10 200 What is the probability that a randomly selected cow either has calving difficulty or is less than 3-years-old?
140/200
A population of turkeys has a mean weight of 20 lb and a standard deviation of the weights equal to 4 lb. A turkey breeder selects a large number of samples of 36 turkeys each, calculates the mean weight of the turkeys in each of these samples, and then graphs the sample means. The mean of these sample means is expected to be equal to _______.
20 lb
Weights of 15 pigs are used to construct the following stem-and-leaf display: stem leaf 21 0 22 2 5 5 7 9 23 1 2 8 9 24 1 4 6 25 2 4 Using the stem-and-leaf display, find the upper quartile.
244
For most populations, sample sizes of n > ________ will be adequate for the sampling distribution of the sample means to be normally distributed.
30
The weights in pounds of 23 dogs were used to construct the following stem-and-leaf display using the first digit as the stem and the second digit as the leaf:. Stem Leaves 3 2 4 4 0 3 4 5 7 8 9 5 0 1 2 3 4 5 6 1 2 5 6 7 7 0 1 8 9 8 Use the stem-and-leaf display to find the lower quartile.
45 lb
The computer science department wants to estimate the average length of time it takes students to complete a computer project correct to within 5 hours with probability 0.96. They do not have an estimate of the standard deviation of the times, but they remember that last year the shortest time needed to complete the project was 6 hours and the longest time was 36 hours. Given this information, an appropriate estimate of the standard deviation of the length of time required to complete the computer project would be:
5 hours
The owner of a herd of cows wants to determine the influence of the ages of his cows on the amount of calving difficulty that occurs in his herd. He constructs the following table: Age of Cow (in years) 0-2 3-5 6-10 over 10 Total No difficulty 40 35 20 5 100 Difficult birth 35 45 15 5 100 Total 75 80 35 10 200 Find the probability that a randomly selected cow had difficulty in giving birth to her calf and was over 10 yr old.
5/200
If we roll a single die, the sample points are 1, 2, 3, 4, 5, or 6. Consider the following two events: Event A: toss an even number on the die Event B: toss a number less than or equal to 3 on the die Calculate the probability of the union of events A and B: P( A U B).
5/6
The range of a population is approximately equal to __________. (Hint: remember the Empirical Rule)
6 standard deviations
The weaning weights (in kilograms) of a sample of 6 lambs born and raised on Farmer Jones' farm are as follows: Lamb Weight 1. 30 2. 32 3. 28 4. 42 5. 40 6. 44 Find the standard deviation of the weaning weights of this sample of 6 lambs.
6.81175 kg
A severe drought has affected several western states in recent years. A Christmas tree farmer is worried about the drought's effect on the size of his trees. To determine whether the growth of his trees has been reduced by the drought, the farmer decides to take a sample of the heights of 6 trees and obtains the following results (recorded in inches): TreeHeight160257362469546654 Find the variance of the heights of this sample of 6 trees.
60.4 inches^2
The heights of 9 students (in inches) are as follows: 60 62 66 72 74 64 68 69 67 Find the median.
67
A dataset consisting of 30 observations has the following mean and standard deviation: mean = 3.74 minutesstandard deviation = 2.20 minutes What percentage of the observations would be expected to fall within the interval (1.54, 5.94)if the data have a symmetric and mound-shaped distribution?
68%
Health care issues are receiving a great deal of attention in both the academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid, but who have no private health insurance. The mean age of the 50 uninsured senior citizens in the survey was 74.04 years and the standard deviation of their ages was 9.75 years. If we assume that the distribution of ages is symmetric and mound-shaped, what percentage of the respondents in the survey would be expected to be between 64.29 and 83.79 years old?
68%
The grades of 8 students on an exam were as follows: Student Grade 1. 66 2. 70 3. 64 4. 88 5. 74 6. 72 7. 87 8. 79 Find the median grade of these 8 students.
73
A random sample of the weights of dogs at a local kennel yielded the following summary information: median = 80 lb lower quartile = 70 lb upper quartile = 90 lb lighest dog = 25 lb heaviest dog = 160 lb Use this information to construct a box plot and then use the box plot to determine which one of the following statements is true.
A dog that weighs 100 lb is not a suspect or highly suspect outlier, because 100 lb falls between the upper quartile of 90 lb and the upper inner fence of 120 lb.
A study of binge alcohol drinking by college students was published in the American Journal of Public Health. Suppose an experiment consists of randomly selecting one of the undergraduate students who participated in the study. Consider the following events: A: {The student is a binge drinker} B: {The student is a male} C: {The student lives in a coed dorm} Describe the following event in terms of unions, intersections, or complements: The student is a male and is a binge drinker.
A ∩ B
Which of the following is not one of the properties of the sampling distribution of the sample mean?
All of the above are properties of the sampling distribution of the sample mean.
The Central Limit Theorem is important in statistics, because:
For a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the distribution of the population.
The peak shopping time at Rod's Western Palace is between 8:00 and 11:00 am on Saturday mornings. The store manager randomly selected 50 customers last Saturday morning and observed their shopping habits. The manager recorded the number of items purchased by each customer and the total time each customer spent in the store. Identify the type of variables recorded by the manager.
Number of items purchased is a discrete random variable and total time spent in the store is a continuous random variable.
At the U.S. Open Tennis Championship a statistician keeps track of every serve that a particular player hits during the tournament. The statistician reports that the mean speed of serves by this player was 100 mph and the standard deviation of his serves was 10 mph. Three of the serves were clocked at 65, 110, and 120 mph. Using the z-score approach for detecting outliers, which of these three serves represent outliers in the distribution of the speed of this player's serves?
Only 65 mph is an outlier.
Which of the following probabilities for the sample points A, B, and C could be true if A, B, and C are the only sample points in an experiment?
P(A) = 1/4, P(B) = 1/2, P(C) = 1/4
It is desired to estimate the average total compensation of CEO's in the service industry. Data were collected from 18 CEO's and the 97% confidence interval was calculated to be ($2,181,260, $5,836,180). What assumption is necessary for this confidence interval to be valid?
The population consisting of the total compensations of all CEO's in the service industry is approximately normally distributed.
If we conduct a matched pairs experiment using small samples, what assumptions are needed for the small-sample confidence interval for the mean difference to be valid?
The population of paired differences has an approximate normal distribution.
Each year the National Opinion Research Center conducts the General Social Survey (GSS), eliciting opinions of Americans on a wide variety of social topics. One question in the survey asked about a person's belief in the Bible. A sample of 4,826 respondents selected from one of the following answers: (1) The Bible is the actual word of God, to be taken literally—1,527 respondents; (2) the Bible is the inspired word of God, but not everything is to be taken literally—2,231 respondents; (3) the Bible is an ancient book of fables, legends, history, and moral precepts—996 respondents; and (4) the Bible has some other origin—72 respondents. Find the relative frequencies for each of the 4 possible responses.
The relative frequencies are 0.3164, 0.4623, 0.2064, and 0.0149 for the Bible is the actual word of God, to be taken literally; the Bible is the inspired word of God, but not everything is to be taken literally; the Bible is an ancient book of fables, legends, history, and moral precepts; and the Bible has some other origin, respectively.
"Cola wars" is the popular term for the intense competition between Coca Cola and Pepsi displayed in their marketing campaigns, which have featured movie and television stars, rock videos, athletic endorsements, and claims of consumer preference based on taste tests. Suppose, as part of a Pepsi marketing campaign, 1,000 cola consumers are given a blind taste test (i.e., a taste test in which the two brand names are disguised). Each consumer is asked to state a preference for brand A or brand B. What is the sample in this blind taste test?
The sample consists of the 1,000 cola consumers selected from the population of all cola consumers.
The Central Limit Theorem says that the sampling distribution of the sample mean is approximately normally distributed under certain conditions. Which of the following is a necessary condition for the Central Limit Theorem to be used?
The sample size must be large (i.e., n must be greater than or equal to 30).
Which of the following statements about the sampling distribution of the sample mean is incorrect?
The standard deviation of the sampling distribution is equal to the population standard deviation, σ.
Which one of the following statements about the sampling distribution of the sample mean is incorrect?
The standard deviation of the sampling distribution is equal to the population standard deviation.
Assume that the mean length of time required to complete the Columbus Marathon is 4.5 hours and that the standard deviation of the times required to complete the race is 0.70 hours. Calculate the z-score for a time of 2.3 hours. Based on the z-score, is this time of 2.3 hours an outlier?
The time of 2.3 hours is an outlier, because the z-score is -3.14, which is more than 3 standard deviations below the mean.
The owner of a herd of pigs wants to determine if the weights of any of her pigs are outliers. The average weight of the pigs in her herd is 250 lb and the standard deviation of the weights is 50 lb. The heaviest pig weighs 275 lb. What should the owner of the pigs conclude?
The z-score for this 275 lb pig is 0.50 and the weight is not an outlier.
The following is a valid probability distribution for a discrete random variable, X: X 0 1 2 3 P (X) 0.20 0.30 0.30 0.20
True
A crop scientist would like to know the average yield of soybeans in Ohio (in bushels per acre). A random sample of 225 soybean fields in Ohio yields a mean of 48 bushels per acre and a standard deviation of 7.5 bushels per acre. Estimate the population mean for the yield of soybeans In Ohio using a 95% confidence interval. Interpret the confidence interval that you derived.
We are 95% confident that the population mean falls within the confidence interval.
A standard normal distribution has
a mean of 0 and a standard deviation of 1.
USA Today reported the results of a study that suggests frequently heading the ball in soccer lowers players' IQs. A psychologist tested 60 male soccer players ages 14 to 29 who played soccer up to five times per week. Players who averaged 10 or more headers per game had an average IQ of 103, whereas players who headed the ball one or fewer times per game had an average IQ of 112. The average IQ of 112 represents:
a statistic
Which of the following is not an element of descriptive statistical problems?
an inference made about the population based on the sample
A vet clinic has found that the number of patients per day has an average of 100 and a standard deviation of 10. If nothing is known about the shape of the distribution of number of patients seen per day, what percentage of the days would be expected to have between 70 and 130 patients?
at least 89%
Graphical methods of describing qualitative data include
bar graphs and pie charts
The standard deviation of the sampling distribution of the sample mean is equal to σ, the standard deviation of the population.
false
Suppose that a 94% confidence interval for μ turns out to be (60 inches, 80 inches). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. What action should we take to reduce the width of the confidence interval?
increase the sample size
The American Angus Association wants to determine the proportion of their members who breed their cows using artificial insemination (AI). They randomly sample 200 of their members and ask them whether or not they breed their cows using AI. 120 of the 200 members sampled said "yes". If the American Angus Association constructed a confidence interval to estimate the true population proportion of their members who breed their cows using AI, they would be using the branch of statistics called ____________.
inferential statistics
What are the 3 measures of central tendency?
mean, median, mode
We want to use a confidence interval to estimate the proportion of students in the College of Food, Agricultural, and Environmental Sciences that are female. What sample size would be necessary if we want to estimate the true population proportion of female students correct to within 0.03 with probability 0.95? In an earlier small-scale pilot study we obtained an estimate of the proportion of female students (p) that was equal to 0.48.
n = 1,066 students
Find the sample size needed to estimate the population proportion (p) correct to within 0.06 with probability 0.95. Assume that we have previous information that indicates that p = 0.30.
n = 225
A __________ __________ of a parameter is a statistic, a single value computed from the observations in a sample, that is used to estimate the value of the target parameter. NOTE: I am looking for the general term, not a specific example.
point estimate
Pie charts normally show the
proportion of observations falling in each class
Major and gender of students enrolled at OSU are examples of ____________ data.
qualitative
The types of trees (maple, oak, elm, etc.) in a nursery are an example of a ____________ variable.
qualitative
Starting salary and GPA of students who graduate from OSU are examples of ____________ data.
quantitative
Parking at a large university has become a big problem. University administrators are interested in determining the average parking time (i.e., the average length of time it takes students to find a place to park on campus) of the students. An administrator inconspicuously follows 250 students and carefully records their parking times. Identify the population of interest to the university administration.
the entire set of students who park at the university
A disadvantage of pulling numbers out of a hat as a method of random sampling is that it is not feasible to use this method when the population consists of a large number of observations.
true
For a given sample size, the width of the confidence interval for a parameter increases as the confidence coefficient increases. In other words, a 95% confidence interval is wider than a 90% confidence interval, and a 99% confidence interval is wider than a 95% confidence interval.
true
For small samples (n < 30), the sampling distribution of the sample mean depends on the particular form of the relative frequency distribution of the population being sampled.
true
If an observation is found to be an outlier, it could be because the observation came from a different population (e.g., we are weighing Doberman Pincher dogs and the weight of a Cairn Terrier somehow got mixed in with the weights of the Dobermans).
true
If we identify an outlier in a dataset, it may be that the observation came from a different population (e.g., we are analyzing weights of Great Danes, but somehow the weight of a Dauschand got mixed in with our data).
true
The frequency for a particular class is the number of observations falling in that class.
true
The sample space for an experiment is the collection of all of the sample points.
true
The value of a sample statistic will vary from sample to sample.
true
Health care issues are receiving a greal deal of attention in both the academic and political arenas. A sociologist recently conducted a survey of senior citizens whose net worth is too high to quality for Medicaid, but who have no private health insurance. The ages (in years) of 9 uninsured senior citizens were as follows: Senior Citizen Age 1. 65 2. 70 3. 64 4. 84 5. 74 6. 72 7. 87 8. 79 9. 80 Find the range for the ages of these 9 senior citizens.
23 years
Find the mean of a binomial probability distribution with a sample size of n = 40 and a probability of success of 0.60.
24
The amount of television viewed by today's youth is a concern of Parents Against Watching Television (PAWT). Three-hundred parents of elementary school-aged children were asked to estimate the number of hours per week that their child watched TV. The mean and standard of their responses were 15 hours and 5 hours, respectively. Identify the type of data collected by PAWT.
quantitative data
Measures of variation include
range, variance, and standard deviation
A measure of __________________ is a statement (usually quantified) about the degree of uncertainty associated with a statistical inference.
reliability
The variable measured in an experiment (e.g., weights of cattle, heights of horses, etc.) is called the:
response variable
The _______________ of a sample statistic (based on n observations) is the relative frequency distribution of the values of the statistic theoretically generated by taking repeated random samples of size n and computing the value of the statistic for each sample.
sampling distribution
We randomly select 100,000 samples of size n from a population. We calculate the sample mean (X-bar) for each of the 100,000 random samples and graph the relative frequency distribution for these 100,000 values of X-bar. This relative frequency distribution is called the ____________________ of X-bar.
sampling distribution
If the lower quartile is farther from the median than the upper quartile, the distribution of data is
skewed to the left
Which one of the following is not a measure of central tendency?
standard deviation
Assume that a population of rabbit weights has a uniform distribution, instead of a normal distribution. We calculate the mean of 1,000 random samples from this population, where the number of observations in each sample is equal to 50. Would you expect the 1,000 sample means to be normally distributed?
yes
____________ data are non numerical data that can only be classified into one of a group of categories.
Qualitative
Suppose x has a binomial probability distribution with n = 400 and p = 0.70. Use the normal approximation to the binomial to find P (X > 300).
0.0166
Find the probability of an observation lying more than z = 1.77 standard deviations above the mean.
0.0384
Independent random samples of 40 Yorkshire litters and 50 Landrace litters are obtained. For Yorkshires, the mean litter size is 9.0 pigs and the standard deviation of litter size is 2.0 pigs. For Landrace, the mean litter size is 8.5 pigs and the standard deviation of litter size is 1.8 pigs. Construct an 80% confidence interval for the difference in population mean litter sizes of Yorkshire and Landrace.
(-0.01962, 1.01962)
A study published in The Journal of American Academy of Business examined whether the perception of service quality at five-star hotels in Jamaica differs by gender. In order to compare the means of two populations (i.e., male vs. female guests), independent random samples were selected from each population, with the results shown in the table below. Use these data to construct a 96% confidence interval for the difference in the two population means. MalesFemalesSample size127114Sample mean score39.0838.79Sample standard deviation6.736.94
(-1.51949, 2.09949)
A college professor wants to estimate the difference in mean test scores of students who have taken his statistics and genetics classes in the past 10 years. He selects a random sample of 20 student records from the statistics course and a random sample of 22 student records from the genetics course. These two samples were independent random samples. The study provided the results shown in the table below. Construct a 95% confidence interval for the true difference in population means of these two populations of students.
(-3.92777, 9.92777)
A professor in the Department of Animal Sciences wants to estimate the mean weight of the Suffolk breed of lambs shown at the Ohio State Fair in the past five years. Therefore, he selects a random sample of n = 25 lamb weights and obtains a sample mean of 125 lb and a sample standard deviation of 15 lb. Construct a 95% confidence interval for the true population mean of the weights of Suffolk lambs shown at the Ohio State Fair in the past five years.
(118.808 lb, 131.192 lb)
In order to compare the means of two populations, independent random samples are selected from each population, with the following results: Sample 1 Sample 2 Sample size 500 400 Sample mean 5,280 5,240 Sample standard deviation 150 200 Construct a 95% confidence interval for the difference in the two population means.
(16.398484, 63.601516)
An Animal Scientist wants to estimate the average weaning weight of the Hereford breed of beef cattle. Therefore, he selects a random sample of 100 Hereford calves and weighs them on the day they are weaned from their mothers. The sample mean for these 100 calves is 450 lb and the sample standard deviation is 50 lb. What is the 95% confidence interval for the mean of the entire population of all Hereford calves?
(440.2 lb, 459.8 lb)
The average height of a certain ornamental plant is 15 inches and the standard deviation of the heights is 3 inches. Find the probability that a randomly selected plant will have a height of more than 18.75 inches.
0.1056
Assume that the mean length of time required to complete the Columbus Marathon was 4.5 hours and that the standard deviation of the times was 0.70 hours. Assume that the racing times were approximately normally distributed. What is the probability that a randomly selected runner completed the race in less than 3.8 hours?
0.1587
Suppose x has a binomial probability distribution with n = 200 and p = 0.60. Use the normal approximation to the binomial to find P (X < 115).
0.2578
A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selected 200 students and finds that 118 of them are receiving financial aid. Find the point estimate for estimating the proportion of all students at the university who receive financial aid.
0.59
A population of turkeys has a mean weight of 20 lb and a standard deviation of the weights equal to 4 lb. A turkey breeder selects a large number of samples of 36 turkeys each, calculates the mean weight of the turkeys in each of these samples, and then graphs the sample means. The standard deviation of these sample means is expected to be equal to _______.
0.66667 lb
Assume that we conduct an experiment using a randomized block design to determine the influece of 4 different diets on the weights of bison. We group the blson into 10 blocks, where the bison within each of the 10 blocks have similar weights. The partially completed Analysis of Variance table is shown below. Source df SS MS F Total 39 15,919.2 Diet 3 3.298.7 Block 9 12,073.9 Error 27 546.6 Calculate the mean squares for blocks.
1,341.5
A two-factor factorial experiment is conducted to compare litter sizes of Yorkshire and Landrace sows derived either from a line unselected for litter size or from a line that has gone through 15 years of selection for increased litter size. Two sows of each breed are randomly selected from each line. Their litter sizes are as follows: Yorkshire Landrace Unselected line 8 9 9 10 Selected line 11 11 10 9 The partially completed ANOVA table is as follows: Source df SS MS F Total 7.875 Line 3.125 3.125 3.57 Breed Line x Breed Error 3.500 0.875 Find the F value for the line x breed interaction.
1.28571
A randomized block design is used to compare postweaning average daily gains of 4 breeds of beef cattle, Hereford, Angus, Charolais, and Simmental (we can think of the breeds as the "treatments"). The breeds are divided into 3 weight classes (i.e., 3 blocks). Block 1 contains cattle weighing 450 to 500 lb at the beginning of the experiment, block 2 contains cattle weighing 500 to 550 lb at the beginning of the experiment, and block 3 contains cattle weighing 550 to 600 lb at the beginning of the experiment. The postweaning average daily gains (in pounds per day) are as follows: BlockHerefordAngusCharolaisSimmental13.503.603.703.7523.553.633.713.8033.563.623.803.90 The partially completed ANOVA table for this experiment is as follows: SourcedfSSMSFTotal .160 Breed .139.04646Block .014.007 Error .007.001 What are the correct degrees of freedom for total, breed, block, and error, respectively?
11, 3, 2, 6
A national organization has been working with electric companies throughout the US to find sites for large windmills to generate electric power. Wind speeds must average more than 21 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted tests at a particular site where windmills are under construction. Based on a sample of n = 40 wind speed recordings (taken at random intervals) at the site, the wind speeds averaged 23 mph with a standard deviation of 3.9 mph. To determine whether the site meets the organization's requirements, they want to test: Ho: μ = 21 mph Ha: μ > 21 mph using a significance level (α) = 0.01. Calculate the value of the test statistic needed to test the null hypothesis.
3.24
Suppose that a random sample of 100 measurements is selected from a population with a mean = 200 lb and a variance = 1,600 lb2. What is the standard deviation of the sampling distribution of the sample mean?
4 lbs
A large labor union wishes to estimate the mean number of hours per month that union members are absent from work. The union samples 475 of its members at random and monitors their working time for 1 month. At the end of the month, the total number of hours absent from work is recorded for each employee. The mean and standard deviation of the sample are 9.6 hours and 3.6 hours, respectively. What is the point estimate of the mean (μ) of the entire population of number of hours absent from work per month?
9.6 hours
According to the Empirical Rule, we expect ________ % of the observations to fall within two standard deviations of the mean, if the data have a symmetric and mound shaped distribution.
95
For normal distributions, __________ % of the observations are expected to lie within plus or minus two standard deviations of the mean.
95%
The heights in inches of young growing trees were measured at a nursery and used to construct the following stem-and-leaf display using the first digit as the stem and the second digit as the leaf: Stem Leaves 3 2 4 4 0 3 4 5 7 8 9 5 0 1 2 3 4 5 6 1 2 5 6 7 7 0 1 8 9 8 Construct a box plot for these data. List any suspect or highly suspect outliers for this dataset.
98 inches is a suspect outlier. There are no highly suspect outliers.
We want to test the hypothesis that the mean number of credit hours taken per semester by OSU undergraduates is less than 16 hours. Therefore, we obtain a random sample of credit hours for 49 students. The sample mean is 15 hours and the sample standard deviation is 4 hours. We want to test: Ho: μ = 16 hours Ha: μ < 16 hours using a significance level (α) = 0.01. Should we reject or not reject the null hypothesis? Why?
Because the calculated value of Z (-1.75) does not fall in the rejection region below the critical value of Z (-2.33) from Table IV, we do not reject Ho: μ = 16 hours at α = 0.01.
A professor in the Department of Animal Sciences wants to estimate the mean weight of the Suffolk breed of lambs shown at the Ohio State Fair in the past five years. Therefore, he selects a random sample of n = 25 lamb weights and obtains a sample mean of 125 lb and a sample standard deviation of 15 lb. He constructs a 95% confidence interval for the true population mean of the weights of Suffolk lambs shown at the Ohio State Fair in the past five years. Explain the meaning of the confidence interval that he obtained.
He is 95% confident that the true population mean (μ) falls within the interval that he obtained.
The IRS is under orders to reduce the time small business owners spend filling out pension form IRS-5500. Previously the average time spent on the form was 5.3 hours. In order to prove that the time required to fill out the form is reduced, a sample of 64 small business owners who annually complete the form is randomly chosen and their completion times are recorded. The mean completion time for this sample of owners was 5 hours with a standard deviation of 2.6 hours. In order to prove the time to complete the form is reduced from the previous time of 5.3 hours, state the appropriate null and alternative hypothesis to test.
Ho: µ = 5.3 hr Ha: µ < 5.3 hr
A box of Mr. Phipps Tater Crisps is supposed to contain 156 grams of potato chips. On the side of the box it says "This package is sold by weight, not by volume. Packed as full as practicable by modern automatic equipment, it contains full net weight indicated. If it does not appear full when opened, it is because contents have settled during shipping and handling". Periodically, the Nabisco Company receives complaints that their boxes of Tater Crisps are not full (i.e., that they contain less than 156 grams of potato chips). To test this claim, the Nabisco Company randomly samples 10 boxes and finds the average amount of potato chips held by the 10 boxes is 154 grams and the standard deviation is 30 grams. State the null and alternative hypotheses the Nabisco Company wishes to test.
Ho: μ = 156 grams Ha: μ < 156 grams
A swine producer reads a report stating that the average litter size in the US is 7.8 pigs per litter. However, he feels that the average litter size on his farm is not 7.8 pigs/litter (he wants to detect departure in either direction from the hypothesized mean of 7.8 pigs/litter). To test his hypothesis, he reviews his records for the past year and randomly selects 16 litters, which averaged 8.0 pigs/litter. The standard deviation is 1 pig/litter. State the null and alternative hypothesis.
Ho: μ = 7.8 pigs per litter Ha: μ ≠ 7.8 pigs per litter
A local consumer reporter wants to compare the average cost of grocery items purchased at 3 different supermarkets: Kroger, Giant Eagle, and Sam's Club. Prices (in dollars) were recorded for a sample of 10 randomly selected grocery items at each of the 3 supermarkets (i.e., a total of 10 x 3 = 30 prices were recorded). We will consider this to be a one-way analysis of variance (i.e., a completely randomized design). The partially completed Analysis of Variance table is shown below: Source df SS MS F Total 120 Supermarkets 20 Error 100 State the null and alternative hypothesis being tested by the consumer reporter..
Ho: μ1 = μ2 = μ3 Ha: at least 2 of the means differ
A sales representative for a seedcorn company tells his boss that within the past year he has contacted 80% of the farmers in his sales district. However, his boss makes random phone calls to 36 farmers in the sales district and finds that the sales rep only contacted 24 of them in the past year. Based on the hypothesis test, what should the boss conclude? Explain.
Since -2.0 < -1.28, the boss should reject Ho: p = 0.80.
Frame score in beef cattle is based on height at the hips and is used as a measure of skeletal size. Frame scores range from 1 to 10 with a higher number indicating a taller animal. Independent random samples of frame scores were selected from the Angus and Simmental breeds of beef cattle with the following results: AngusSimmental57677856776 Using the appropriate table, find the critical F value needed to test the null hypothesis that the breed means for frame score are equal (use α = 0.05). Should we reject or not reject the null hypothesis that the mean frame scores of these two breeds are equal?
Since 4.09 is not greater than 5.12, we do not reject Ho: μ1 = μ2 at α = 0.05.
The person in charge of genetic evaluation of beef cattle wants to know if birth weights of calves are influenced by breed and if they are influenced by the region of the U.S. (i.e., Northern U.S. vs Southern U.S.) in which the calf is born. She has heard that calves born in the South are usually lighter at birth than are calves born in the North. In order to answer these questions, she sets up a 2 x 3 factorial experiment with 3 replications and obtains the birth weights (in pounds) shown in the following table: Angus Charolais Simmental North 85 93 91 85 92 92 83 94 92 South 85 84 82 76 85 83 74 83 83 The partially completed ANOVA table is as follows: Source df SS MS F Total 548.00 Location Breed 174.33 87.165 13.643 Location x breed 9.00 4.500 Error State the null and alternative hypothesis for location. Using a significance level of α = 0.05, do you reject or not reject the Ho?
Since the calculated F value (45.0775) is greater than the F value from the table (4.75), we reject the Ho at α = 0.05.
Independent random samples of litter sizes were selected from the Yorkshire and Landrace breeds of swine, with the following results: YorkshireLandrace8798109889710 We want to analyze these data using Analysis of Variance with a Completely Randomized Design. Which one of the following statements is true?
Since the calculated F value of 5.19787 is greater than the critical F value of 5.12, we reject the null hypothesis that the mean litter sizes of the 2 breeds are equal.
A randomized block design is used to compare postweaning average daily gains of 4 breeds of beef cattle, Hereford, Angus, Charolais, and Simmental (we can think of the breeds as the "treatments"). The breeds are divided into 3 weight classes (i.e., 3 blocks). Block 1 contains cattle weighing 450 to 500 lb at the beginning of the experiment, block 2 contains cattle weighing 500 to 550 lb at the beginning of the experiment, and block 3 contains cattle weighing 550 to 600 lb at the beginning of the experiment. The postweaning average daily gains (in pounds per day) are as follows: BlockHerefordAngusCharolaisSimmental13.503.603.703.7523.553.633.713.8033.563.623.803.90 The partially completed ANOVA table for this experiment is as follows: SourcedfSSMSFTotal .160 Breed .139.04646Block .014.007 Error .007.001 Calculate the F statistic for blocks. Do the block means differ (i.e., was blocking effective in removing variation in average daily gain)? Use a significance level of α = 0.05.
Since the calculated F value of 7 is greater than the critical F value from the table of 5.14, we reject the null hypothesis that the 3 block means were equal and conclude that blocking was effective in removing variation in average daily gain.
When we use z-scores and areas under the normal curve, we are using a _______________, which has a mean of 0 and a standard deviation of 1.
Standard normal distribution
Which one of the following is not an assumption required for small-sample estimation of (μ1 - μ2)?
The samples selected from the two populations are normally distributed.
Which one of the following statements concerning the sampling distribution of the sample mean is incorrect?
The standard deviation of the sampling distribution is equal to the standard deviation of the population from which the samples were taken.
The owner of Get-A-Way Travel has recently surveyed a random sample of 385 customers of the agency. He would like to determine if the mean age of the agency's customers is over 31 years. If so, he plans to alter the destination of their special cruises and tours. If not, no changes will be made. He therefore wants to test: Ho: μ = 31 years Ha: μ > 31 years If he concludes that the mean age is not over 31 years when in fact it is over 31 years, he makes a ________ error.
Type II
Assuming that the two sample sizes are the same, find the sample sizes needed to estimate the difference in population proportions correct to within 0.03 with a 90% level of confidence. From prior experience we have an estimate of p1 that it is equal to 0.70 and an estimate of p2 that is equal to 0.60.
We need a sample of 1,354 observations from population 1 and a sample of 1,354 observations from population 2
A scientist conducts an experiment to determine if the mean alkalinity level of water specimens from the Olentangy River is greater than 50 milligrams per liter (mpl). She selects a random sample of 100 water specimens from the river and finds a sample mean of 67.8 mpl and a sample standard deviation of 14.4 mpl. She decides to test the hypothesis using a significance level of 0.01. Using this information concerning the alkalinity level of water from the Olentangy River, which one of the following statements is correct?
We reject the null hypothesis that the population mean equals 50 mpl, because the calculated value of z = 12.36 is greater than the critical value of z = 2.33 at α = 0.01.
A randomized block design was used to compare the mean responses for three treatments. Four blocks of three homogeneous experimental units were selected, and each treatment was randomly assigned to one experimental unit within each block. The partially completed ANOVA table for this experiment is as follows: Source df SS MS F Total 11 84.489 Treatments 2 12.032 6.016 Blocks 3 71.749 23.916 Error 6 0.708 0.118 Do the data provide sufficient evidence to indicate that the treatment means differ? Use α = 0.05.
Yes, because the calculated F value of 50.98 is greater than the critical F value of 5.14 from the F tables.
We want to test the following null and alternative hypotheses about a population proportion: Ho: p = 0.20 Ha: p ≠ 0.20 We observe 300 successes in a sample of 1,000 observations. Assume that it is valid to use large-sample procedures in this problem. Calculate the test statistic needed to test the null hypothesis.
Z = 7.906
Which one of the following confidence intervals would be the widest?
a 99% confidence interval
The object upon which the response variable is measured (animals, people, etc.) is called the __________.
experimental unit
If the variation within sample means is large relative to the variation between the samples, it indicates that there is a real difference between the population means.
false
The population mean and population variance are examples of statistics.
false
Assume that we have a herd of 50 horses and that we want to select a random sample of 5 of the horses for an experiment. We use row 8 of a random number table and go from left to right across the row of random numbers: 96301 91977 05463 07972 18876 20922 94595 56869 69014 60045 18425 84903 42508 32307 Which 5 horses do we include in our random sample ?
horses number: 05 07 18 20 42
In seeking a free agent NFL running back, a general manager is looking for a player with a high mean for yards gained per carry and a small standard deviation. Suppose the GM wishes to compare the mean yards gained per carry for two free agents based on independent random samples of their yards gained per carry. Data from last year's pro football season indicate that σ1 and σ2 are both equal to approximately 5 yards. If the GM wants to estimate the difference in means for yards gained per carry by the two running backs correct to within 1 yard with a confidence level of 0.90, how many carries would have to be observed for each of the two players? Assume equal sample sizes.
n1 = n2 = 136 carries for each of the two running backs
Assuming that n1 = n2, find the sample sizes needed to estimate (μ1 - μ2) correct to within 2.5 with probability 0.90. From prior experience we know that σ1 = 18 and σ2 = 16.
n1 = n2 = 252
Suppose we want to make an inference about the difference in population proportions (p1 - p2). For sufficiently large sample sizes, n1 and n2, the sampling distribution of p1-hat minus p2-hat has approximately a __________ distribution.
normal
The ____________ in an experiment are the factor level combinations that are utilized.
treatments
Null and alternative hypotheses must be stated in terms of population parameters, and not in terms of sample statistics.
true
The t and z distributions are very similar. Both are symmetric, mound-shaped, and have a mean of zero.
true
