ANIMSCI 2260 Final
Find the probability of an observation lying more than z = 2.25 standard deviations below the mean.
0.0122
We have three independent events (A, B, and C) where P(A) = 0.20 P(B) = 0.30 P(C) = 0.40 Find the probability of all three events occurring at the same time
0.024
The American Journal of Public Health published a study of the relationship between passive smoking and nasal allergies in Japanese female students. The study revealed that 80% (i.e., p = 0.80) of the students from heavy-smoking families showed signs of nasal allergies on physical examinations. Consider a sample of 10 Japanese female students exposed daily to heavy smoking in their families. What is the probability that exactly 8 of the 10 students will have nasal allergies?
0.30199
The fleece weights of 8 sheep (in pounds) are as follows: 5 6 7 8 9 10 10 12 The mode for this sample of fleece weights is
10
Consider the probability distribution shown below for the random variable X: X 10 20 30 40 50 60 P (X) 0.05 0.20 0.30 0.25 0.10 0.10 Find the variance of this discrete probability distribution
174.75
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 Based on the stem-and-leaf display, the median for this set of tree heights is __________ inches.
52 in
The mean weight of a herd of cows is 1,100 lb and the standard deviation of the weights is 170 lb. According to the Empirical Rule, we would expect 95% of the cows to weigh between what two numbers?
760 and 1,440 lb
________________ can be applied to any data set, regardless of the shape of the distribution
Chebyshev's Rule
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
Given that P (A) = 0.30, P (B) = 0.60, and P (A ∩ B) = 0.15, find P (A|B). Correct Answer
P (A|B) = 0.25
A standard normal distribution has
a mean of 0 and a standard deviation of 1
The ∑ symbol in a statistical equation indicates that we are to perform which arithmetic operation?
addition
An estimate that shows no consistent tendency to be above or below the true population parameter that we are trying to estimate is called
an unbiased estimate
Suppose that a veterinarian has received permission from the owners of 50 dogs to use their dogs in an experiment involving a new drug for cancer treatment. The vet decides to use 5 of the 50 available dogs for a small preliminary experiment before conducting a larger study. The vet arbitrarily begins at row 8 column 1 of the random number table and goes from left to right across the row. Which one of the following is the correct random sample of 5 dogs? Column Row . 1 2 . 3 . 4 . 5 . 6 8 96301 91977 05463 07972 18876 20922 9 89579 14342 63661 10281 17453 18103
dogs number 05 07 18 20 14
Suppose that a 95% confidence interval for μ turns out to be (100 lb, 500 lb). 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 25th percentile is also called the
lower quartile
Can the variance of a data set ever be negative?
no
Which one of the following is not an example of a continuous random variable?
number of credit hours taken by students during autumn quarter
A ____________ is a collection or set of data that describes a phenomenon of interest to us
population
Major and gender of students enrolled at OSU are examples of ____________ data.
qualitative data
A ____________ is a subset of data selected from a population
sample
If we identify an outlier in a dataset, it may be that the measurement is correct, but represents a rare or chance event
true
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 List the sample points that would be included in the intersection of events A and B (i.e., A ∩ B)
{2}
A survey of 200 public universities indicated that the 25th percentile of the yearly tuition cost was $4,000, the 50th percentile was $5,700, and 75th percentile was $7,400. Use this information to construct a box plot for the yearly tuition rates and then use the box plot to determine whether yearly tuition rates of $8,000, $14,000, and $20,000 are or are not outliers.
$8,000 is not a suspect or highly suspect outlier, $14,000 is a suspect outlier, and $20,000 is a highly suspect outlier.
An experiment is conducted to compare the starting salaries of male and female college graduates who find jobs. Pairs are formed by choosing a male and a female with the same major and similar grade point averages. Suppose a random sample of 10 pairs is formed in this manner and the starting annual salary of each person is recorded. The differences within the pairs are obtained by subtracting the female salary from the male salary. The following results are obtained: Mean difference in starting salaries = $400 Standard deviation of the difference in starting salaries = $435 Construct a 95% confidence interval for the true mean difference in starting salaries of the male and female graduates.
($88.841365, $711.15863)
Scientists want to estimate the difference in twinning rate of two lines of beef cattle that have been selected for increased frequency of twin births. Last spring, 40 of the 100 cows in Line 1 gave birth to twins. In Line 2, 30 of the 100 cows gave birth to twins. Construct a 90% confidence interval for the true difference in population proportions of cows giving birth to twins in Lines 1 and 2. In the interest of time, you can assume that the sample sizes are large enough that it is appropriate to use a large-sample confidence interval.
(-0.01035, 0.21035)
A study published in The Journal of American Academy of Businessexamined 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. Males . Females . Sample size130 . 115 Sample mean score 39.10 38.70 Sample standard deviation6.70 6.95
(-1.393404, 2.193404)
The American Journal of Orthopsychiatry published an article on the prevalence of homelessness in the United States. A sample of 500 adults was asked to respond to the question: "Was there ever a time in your life when you did not have a place to live"? A total of 30 adults in the sample answered yes to this question. Construct a 95% confidence interval to estimate the true population proportion of U.S. adults who have been homeless at some time in their life.
(0.03918, 0.08082)
An animal scientist conducts a study to estimate the proportion of cows of the Charolais breed that require assistance during calving. A random sample of 500 Charolais cows is selected. Results of the study show that 100 of the 500 cows in the sample required assistance in giving birth. Construct a 99% confidence interval for the true population proportion (p) of Charolais cows that require assistance during calving.
(0.153937, 0.246063)
A scientist wants to estimate the true population proportion of mares who conceive when bred by AI. She randomly selects 500 mares and finds that 300 of them became pregnant when bred by AI. Which one of the following is the correct 99% confidence interval for the true population proportion of mares that conceived when bred by AI?
(0.5436, 0.6564)
n a controlled laboratory environment, independent random samples of 10 adults and 10 children were tested by a psychologist to determine the room temperature that each person finds most comfortable. The study provided the following results: Adults . Children Sample size 10 10 Sample mean (in degrees) 77.5 74.5 Sample variance 4.5 . 2.5 Which one of the following is the correct 99% confidence interval for the true difference in population mean temperatures that adults and children find most comfortable?
(0.5921 degrees, 5.4079 degrees)
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?
(440.2lb, 459.8 lb)
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.
(47.02 bushels/acre, 48.98 bushels/acre)
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
Suppose that 80% of the Holstein cows in the U.S. give birth to their calves with no calving difficulty. We randomly select 4 Holstein cows from the population consisting of all Holstein cows in the U.S. What is the probability that exactly 3 of the 4 cows in this sample will give birth to their calves with no calving difficulty? To find the answer to this question, you will need to use the equation for the binomial distribution.
0.4096
An experiment results in one of two possible outcomes, A or B. We know that P(A) = 0.40, P(B) = 0.60, and P(A ∩ B) = 0.20. Find the P(A U B).
0.80
The average height of a herd of cows is 50 inches and the standard deviation of the heights is 5 inches. Find the probability that a randomly selected cow will have a height between 44 and 58 inches
0.8301
Consider the probability distribution shown below for the random variable X: X 10 20 30 40 50 60 P (X) 0.05 0.20 0.30 0.25 0.10 0.10 Graph P (X). Locate μ and μ ± 2 σ on the graph. What is the probability that X will fall within this interval?
1.0
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 variance of this discrete probability distribution
1.0804
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 5,000 samples of 64 rabbits each, calculates the mean weight of the rabbits in each of these 5,000 samples, and then graphs the 5,000 sample means. The mean of these 5,000 sample means is expected to be equal to _______.
10 lb
The mean length of time required to complete a 5K race was 20 minutes. The standard deviation of the times was 4 minutes. The racing times were approximately normally distributed. Only 10% of the runners would be expected to complete the race in less than x minutes. Find the value of x
14.88 minutes
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 mean of the sampling distribution of the sample mean?
200 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 25th percentile.
225
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
The probability distribution for the number X out of 5 randomly selected dentists who use laughing gas is shown below: X 0 1 2 3 4 5 P (X) 0.0102 0.0768 0.2304 0.3456 0.2592 0.0778 Find the mean number of dentists out of 5 who use laughing gas.
3.0002
Find the standard deviation of a binomial probability distribution with a sample size of n = 40 and a probability of success of 0.60.
3.098
The mean length of time required to complete the Columbus Marathon was 4.5 hours and the standard deviation of the times was 0.50 hours. Assume that the racing times were approximately normally distributed. Only 10% of the runners would be expected to complete the race in less than x hours. Find the value of x
3.86 hours
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.
45lb
The weaning weights (in kilograms) of a sample of 6 lambs born and raised on Farmer Jones' farm are as follows LambWeight 1 . 30 2 . 32 3 . 28 4 . 42 5 . 40 6 . 44 Find the variance of the weaning weights of this sample of 6 lambs
46.4 kg2
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 hrs
The grades of 8 students on an exam were as follows: StudentGrade 1 . 66 2 . 70 3 . 64 4 . 88 5 . 74 6 . 72 7 . 87 8 . 79 Find the variance of the grades of these 8 students
80.85714
The mean of the starting salary data that we have been using is 28,475 dollars and the standard deviation is 9,369 dollars. According to the Empirical Rule, we expect 95% of the starting salaries to fall between what two numbers?
9,737 and 47,213 dollars
Find the variance of a binomial probability distribution with a sample size of n = 40 and a probability of success of 0.40
9.6
According to the Empirical Rule, we expect ________ % of the observations to fall within three standard deviations of the mean, if the data have a symmetric and mound shaped distribution
99%
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 female and is not a binge drinker.
Ac ∩ Bc
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 or lives in a coed dorm.
B U C
A bottling company needs to produce bottles that will hold 12 ounces of liquid for a local beer maker. Periodically, the company receives complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 15 bottles and finds the average amount of liquid held by the 15 bottles is 11.90 ounces and the standard deviation is 0.20 ounces. Which one of the following is the set of hypotheses the company wishes to test?
Ho: μ = 12 Ha: μ < 12
In the 1970's it was generally assumed that the mean birth weight of Angus beef cattle was 75 lb. A researcher believes that, due to selection for increased size and growth rate in Angus, the average birth weight is now greater than 75 lb. He obtains a random sample of n = 144 birth weights of Angus calves and calculates a sample mean of 85 lb and a sample standard deviation of 10 lb. State the null and alternative hypothesis that the researcher wants to test.
Ho: μ = 75 Ha: μ > 75
Given that P (A) = 0.30, P (B) = 0.60, and P (A ∩ B) = 0.15, find P (B|A).
P (B|A) = 0.50
The breeds of dogs in a kennel are an example of what type of variable
Qualitative veriable
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. Does the sample obtained by the producer provide sufficient evidence to reject the null hypothesis? Explain.
Since the calculated value of the test statistic (t = 0.80) is less than the critical value of t = 2.947 from Table VI, we do not reject Ho: μ = 7.8 pigs/litter.
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
In the lectures we worked an example that involved constructing a 95% confidence interval for the mean of the population of starting salaries of students who graduated from a particular university. The 95% confidence interval that we derived was ($25,964, $29,636). Which one of the following interpretations is correct?
We are 95% confident that the average starting salary of all students graduating from this university falls in the interval $25,964 to $29,636.
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 correct interpretation of a 95% confidence interval that can be used to estimate the mean (μ) of the entire population of number of hours absent from work per month?
We are 95% confident that the true population mean (μ) falls in the interval that we derived.
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 5,000 samples of 64 rabbits each, calculates the mean weight of the rabbits in each of these 5,000 samples, and then graphs the 5,000 sample means. If the population of rabbit weights does not have a normal distribution, would we expect the 5,000 sample means to have a normal distribution
Yes, according to the Central Limit Theorem
In the 1970's it was generally assumed that the mean birth weight of Angus beef cattle was 75 lb. A researcher believes that, due to selection for increased size and growth rate in Angus, the average birth weight is now greater than 75 lb. He obtains a random sample of n = 144 birth weights of Angus calves and calculates a sample mean of 85 lb and a sample standard deviation of 10 lb. Using the appropriate table and a significance level (α) = 0.05, find the critical value of the test statistic.
Z = 1.645
Which one of the following confidence intervals would be the widest?
a 99% condifence interval
An assumption required for small-sample estimation of (μ1 - μ2) is that the variances of the samples selected from the two populations are equal.
false
As the sample size (n) increases, the variation in the sampling distribution of the sample means increases
false
Suppose that a random sample of 100 measurements is selected from a population with a mean µ = 200 lb and a variance σ2 = 1,600 lb2. What is the mean and standard deviation of the sampling distribution of the sample mean?
mean = 200 lb and standard deviation = 4 lb
Suppose that a random sample of 625 measurements is selected from a population with a mean µ = 500 lb and a variance σ2 = 100 lb2. What is the mean and standard deviation of the sampling distribution of the sample mean?
mean = 500 lb and standard deviation = 0.4 lb
The ________ ________ is the set of possible computed values of the test statistic for which the null hypothesis will be rejected. Correct Answer
rejection region
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
A _______________ is a quantity computed from the observations in a sample
statistic
We want to test the hypothesis that the mean yield of a particular variety of corn is less than 150 bushels per acre. Therefore, we obtain the yields of a random sample of 20 corn fields in which this variety was planted. The average yield of the sample of fields was 140 bushels per acre with a standard deviation of 10 bushels per acre. We want to test: Ho: μ = 150 bushels/acre Ha: μ < 150 bushels/acre using a significance level (α) = 0.10. What is the critical value that defines the boundary of the rejection region in this problem?
t = -1.328
A bottling company needs to produce bottles that will hold 12 ounces of liquid for a local beer maker. Periodically, the company receives complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 15 bottles and finds the average amount of liquid held by the 15 bottles is 11.90 ounces and the standard deviation is 0.20 ounces. Calculate the appropriate test statistic to test the null hypothesis.
t = -1.936
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 experimental units in this study of parking times.
the 250 students on whom the data were collected
A researcher wants to determine whether men's and women's attitudes regarding environmental issues differ. Therefore, the researcher samples 100 men and 100 women and asks "Do you think the environment is a major concern"? Of those sampled, 67 women and 53 men responded that they believe that environmental issues are a major concern. What criterion is used to assess whether the Central Limit Theorem can be applied to this problem?
the interval, p-hat + 3 √(p-hat)(q-hat)/n, falls between 0 and 1 for both the men and the women.
When we perform hypothesis testing, we specify a value for α (alpha), where α represents:
the level of significance
A dairy producer in Ohio wants to determine if the average milk production of her Holstein cows is greater than 18,000 lb of milk per lactation. Therefore, she obtains a random sample of n = 100 milk production records from her herd and calculates a sample mean of 18,500 lb and a sample standard deviation of 3,500 lb. Use the appropriate table to find the critical value of the test statistic (use α = 0.05).
z=1.645
