Animal Sciences Final word questions

The population of paired differences is normally distributed. The paired observations in the sample are randomly selected from the target population of paired observations.

required for small-sample estimation of (μ1 - μ2) when using matched pairs of observations

= 0.034 Use TABLE 2 n = 15; p = 0.60 k = 5

Assume X is a binomial random variable. If n = 15 and p = 0.60, find P (r ≤ 5 successes).

False

A 2 x 4 factorial experiment is conducted in which we use 2 different training programs in 3 breeds of horses that are being trained for a particular event. An Analysis of Variance shows that there is a significant training program by breed interaction. We should next test the hypotheses involving differences in mean levels of performance of the horses for the main effects of training program and breed.

We are 99% confident that the TRUE POPULATION PROPORTION (p) falls within the interval that we derived.

A Gallop poll is conducted to estimate the proportion of voters who plan to vote in favor of a certain issue on the ballet. 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. Construct a 99% confidence interval for the TRUE POPULATION PROPORTION of people who plan to vote in favor of the issue. What is the meaning of this confidence interval?

We are 99% confident that the true population proportion (p) falls within the interval that we derived.

A Gallop poll is conducted to estimate the proportion of voters who plan to vote in favor of a school levy in a certain school district. A random sample of 400 people of voting age is selected. Results of the poll show that 240 of the 400 people polled plan to vote in favor of the school levy. Construct a 99% confidence interval for the true population proportion of people who plan to vote in favor of the school levy. What is the meaning of this confidence interval?

random sample

A ______________ of n experimental units is one selected in such a way that every different sample of size n has an equal probability of being selected.

a statistic

A _______________ is a quantity computed from the observations in a sample

reject

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. Using a level of significance of α = 0.05 and a one-tailed hypothesis test, the bottling company should ____________ the Ho.

Ho: μ = 156 grams Ha: μ < 156 grams

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: μ1 = μ2 = μ3 Ha: at least 2 of the means differ

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..

the grocery item

A local consumer reporter wants to compare the average costs of grocery items purchased at three different supermarkets - Kroger, Giant Eagle, and Meier. Prices (in dollars) were recorded for a sample of 60 randomly selected grocery items at each of the three supermarkets. In order to reduce item-to-item variation, the prices were recorded for each item on the same day at each supermarket. Item Kroger Giant Eagle Meier 1) Big Thirst Towel $1.21 $1.49 $1.59 2) Post Golden Crisp 2.78 2.99 3.35 3) Tylenol Tablets 5.98 5.29 5.98 . . . . . . . . 59) Colgate Shave 0.94 1.10 1.19 60) Kidney Beans 0.45 0.56 0.38 Identify the experimental units for this experiment.

A statistic

A plant scientist wants to determine the average yield (in bushels per acre) of brand X corn in Ohio. Five thousand Ohio corn fields are planted using brand X. The plant scientist is able to obtain data for the yields of 500 of these 5,000 fields. The average yield of these 500 fields planted to brand X is 175 bushels per acre. What does the value of 175 bushels per acre represent?

15 lbs

A population of cats has a mean weight of 15 lb and a standard deviation of the weights equal to 4 lb. A cat breeder selects a large number of samples of 64 cats each, calculates the mean weight of the cats in each of these samples, and then graphs the sample means. The mean of these sample means is expected to be equal to

This rabbit weighs more than 75% of the rabbits.

A rabbit falls at the 75th percentile for weight. This means that:

The sale price of $46,000 is not a suspect or highly suspect outlier, because it falls inside the inner fences.

A random sample of sale prices of homes in Columbus, Ohio yielded the following summary information: Median = $125,000 Lower quartile = $82,000 Upper quartile = $168,000 Lowest price = $46,000 Highest price = $276,000 Construct a box plot for these data. Based on this box plot, is the lowest selling price of $46,000 a suspect or highly suspect outlier?

Since -2.0 < -1.28, the boss should reject Ho: p = 0.80.

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.

We are 99% confident that the TRUE POPULATION PROPORTION (p) lies within the interval that was derived.

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. She constructs a 99% confidence interval for the true population proportion of mares that conceived when bred by AI. What is the meaning of the confidence interval that she derived?

A υ C

A state energy agency mailed questionnaires on energy conservation to 1,000 homeowners in Columbus. Suppose an experiment consists of randomly selecting one of the returned questionnaires. Consider the events: Event A: the home is constructed of brick Event B: the home is more than 30 years old Event C: the home is heated with oil A home that is constructed of brick or is heated with oil would be represented by which one of the following?

Because the calculated F value is less than the critical value of F from the table, we do not reject the null hypothesis, which states that there is no interaction between line and breed.

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 What is the correct conclusion regarding the line x breed interaction? Use a significance level of 0.05.

B U C P (A ᴜ B) = A union B = union of events A and B (either A or B or both occur)

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.

95%

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

We are 99% confident that the TRUE POPULATION PROPORTION lies within the interval that we derived.

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. Explain the meaning of the confidence interval that you derived.

a statistical inference

An estimate, or prediction, or some other generalization about a population based on information contained in a sample is called

False

For a fixed confidence coefficient, the width of the confidence interval increases as the sample size increase

the individual calves

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: Angus Simmental 5 7 6 7 7 8 5 6 7 7 6 What are the experimental units?

The population of paired differences has an approximate normal distribution.

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?

proportion of dogs of each breed

If we were to construct a relative frequency bar graph for the breeds of dogs in a kennel, the heights of the bars would represent the

We are 97% confident that the AVERAGE TOTAL COMPENSATION of all CEO's in the service industry falls in the interval $2,181,260 to $5,836,180.

It is desired to estimate the AVERAGE TOTAL COMPENSATION of CEO's in the service industry. Data were collected from 18 CEO's and a 97% confidence interval was calculated to be ($2,181,260, $5,836,180). Which one of the following interpretations is correct?

the 250 students on whom the data were collected

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 sample in this study of parking times.

proportion of observations falling in each class

Pie charts normally show the

*How to make a box plot* Observations that fall between the inner and outer fences are called SUSPECT OUTLIERS. Observations that fall outside the outer fences are called HIGHLY SUSPECT OUTLIERS.

Step 1: find the interquartile range IQR = QU - QL Step 2: Construct a box with lower and upper quartiles located at the lower corners The base width of the box = IQR Step 3: Find inner fences, which lie a distance of 1.5 (IQR) below the QL and above the QU Step 4: Find outer fences, which lie a distance of 1.5 (IQR) below the lower inner fence and above the upper inner fence

decrease the confidence level from 99% to 95%

Suppose a 99% confidence interval for the population mean for weight of cows of a certain breed turns out to be (800 lb, 1400 lb). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced width of the confidence interval?

only count numbers that start under 50 dogs number 05 07 18 20 14

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? For your convenience, here are rows 8 and 9 of the random number table:

increase the sample size

Suppose that an 85% 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?

p1 - p2

Suppose we want to make an inference about the difference in population proportions (p1 - p2). For sufficiently large sample sizes, n1 and n2, the mean of the sampling distribution of p1-hat minus p2-hat is equal to __________

For a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the distribution of the population.

The Central Limit Theorem is important in statistics, because:

The sample size must be large (i.e., n must be greater than or equal to 30).

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?

Ho: µ = 6.0 hr Ha: µ < 6.0 hr

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 6.0 hours. In order to prove that the time required to fill out the form is reduced, a sample of 49 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 5.3 hours with a standard deviation of 2.1 hours. In order to prove the time to complete the form is reduced, state the appropriate null and alternative hypothesis to test.

null

The ________ hypothesis is the theory that generally represents the status quo, which we accept until it is proven false

complement

The __________ of an event A is the event that A does not occur.

sampling distribution

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.

descriptive statistics

The branch of statistics that uses numerical and graphical methods to look for patterns in a data set, to summarize the information contained in a data set, and to present the information in a convenient form is called

False Does not add up to 1

The following is a valid probability distribution for a discrete random variable, X: X -2 -1 0 P (X) 0.25 0.50 0.20

True

The frequency for a particular class is the number of observations falling in that class.

Approximately 95% use empirical rule since mound shaped and symmetric; within 2 standard deviations of the mean

The mean score on an IQ test is a 100 and the standard deviation of the scores is 15. If the distribution of IQ scores is symmetric and mound-shaped, what percentage of the scores would be expected to fall between 70 and 130?

at least 89%

The mean weight of a sample of pigs is 220 lb and the standard deviation of the weights is 35 lb. If the data set does NOT have a symmetric and mound shaped distribution, and we therefore use Chebyshev's Rule, we would expect what % of the pigs to weigh between 115 and 325 lb?

experimental units

The object upon which the response variable is measured (animals, people, etc.) is called the

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.

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?

significance level

The probability of making a Type I error in hypothesis testing is called the __________________ for a hypothesis test

False

The sample mean and sample standard deviation are examples of parameters

False

The standard deviation of the sampling distribution of the sample mean is equal to σ, the standard deviation of the population

True

The t and z distributions are very similar. Both are symmetric, mound-shaped, and have a mean of zero.

0.333 1/3 options in the national league are in the central or western divisions

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 National League, what is the probability that the winner plays in either the Central or Western Division?

frequency histogram

The total payrolls of all Major League Baseball teams are shown using a graphical technique. The payrolls of the teams are divided into five equal intervals. Bars are drawn above the intervals where the heights of bars represent the number of teams falling within each interval. This type of graphical display is called a

True

The value of a population parameter (e.g., the mean, μ) is a constant; its value does not change; in other words, it does not vary from sample to sample.

True

The value of a sample statistic will vary from sample to sample.

66

The weights of 25 lambs (in pounds) in a flock of sheep are as follows: 68 73 66 76 86 74 61 89 65 90 69 92 76 62 81 63 68 81 70 73 60 87 75 64 82 Construct a stem-and-leaf display using the first digit as the stem and the second digit as the leaf. Based on the stem-and-leaf display, the lower quartile for this set of weights is __________ lb.

50 mpg

Toyota would like to know how many miles per gallon the average person gets when driving the hybrid Toyota Prius. A random sample of 225 drivers yields a mean of 50 mpg and a standard deviation of 7.5 mpg. The point estimate of the population mean for the miles per gallon of the Toyota Prius would be:

The mean of the sampling distribution is equal to the population mean. The sampling distribution is approximately normal whenever the sample size is sufficiently large (n> 30). The sampling distribution is generated by repeatedly taking samples of size n, computing the sample means, and then graphing these sample means.

True about sampling distribution of the mean

True

Two disadvantages of using the "pulling numbers of a hat" method of obtaining a random sample are (1) that it is not feasible for large populations (e.g., 5 million cows) and (2) it is difficult to get a thorough mixing of the pieces of paper.

P (A) = 3/4 HH, HT , TH, TT

Two fair coins are tossed and the events A and B are defined as follows: A: {At least one head appears} B: {Exactly one head appears} Find P (A)

the 60 soccer players who participated in the study

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 experimental units in this study are

The interval (p-hat + 3 standard deviations) for population 1 is (0.5289, 0.8111) and for population 2 is (0.3803, 0.6797). Because both intevals fall between 0 and 1, it is appropriate to use large-sample confidence interval procedures.

We are interested in determining whether men's and women's attitudes concerning the environment are different. Therefore, we sample 100 men and 100 women and ask: "Do you think environmental issues are a major concern"? Of those sampled, 67 women and 53 men responded that they believe environmental issues are a major concern. Perform the calculations needed to determine whther or not it would be appropriate to construct a large-sample confidence interval for (p1 - p2). Is it appropriate? Why or why not?

quantitative data

Weights are recorded for 500 Labrador Retriever dogs. The type of data being collected is ____________ data. Heights of 50 trees in a nursery are an example of a ____________ variable. Starting salary and GPA of students who graduate from OSU are examples of ____________ data.

the level of significance

When we perform hypothesis testing, we specify a value for α (alpha), where α represents:

Standard normal distribution

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.

an inference made about the population based on the sample

Which of the following is NOT an element of descriptive statistical problems?

P(A) = 1/4, P(B) = 1/2, P(C) = 1/4 - have to add up to 1

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?

The sample of paired differences is normally distributed

Which one of the following is NOT an assumption required for small-sample estimation of (μ1 - μ2) when using matched pairs of observations

number of credit hours taken by students during autumn quarter

Which one of the following is NOT an example of a continuous random variable?

The two target populations have a normal distribution.

Which one of the following is not an assumption required for large-sample estimation of (μ1 - μ2)?

The standard deviation of the sampling distribution is equal to the population standard deviation.

Which one of the following statements about the sampling distribution of the sample mean is incorrect

sample

a subset of data selected from a population

Chebyshev's Rule

can be applied to any data set, regardless of the shape of the distribution.

1 - sample space S: {H1H2, H1T2, T1H2, T1T2} 2- sample points Ex) experiment - tossing two coins four simple events or sample points: H1H2, H1T2, T1H2, T1T2

the _____(1)_____ for an experiment is the collection of all of the sample points. mutually exclusive events that represent the most basic outcomes of an experiment are called ____(2)____.

Empirical Rule

the relative frequency distribution for the dataset must be symmetric and mound-shaped

Sample point probability For example, P(H1H2) = ½ x ½ = 1/4

the relative frequency of occurrence of a sample point.