ANIMSCI 2600 Final, ANIMSCI 2600 Midterm 2, ANIMSCI 2600, Midterm 1
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 8 uninsured senior citizens were as follows: Senior Citizen Age 1 66 2 70 3 64 4 88 5 74 6 72 7 87 8 79 Calculate the mean age of these 8 senior citizens.
75 years
The process of collecting sample data is called ____________.
an experiment
What are the 3 measures of central tendency?
mean, median, mode
Assume that 15% of all pigs die between birth and weaning. In a random sample of 200 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 200 that die between birth and weaning is greater than or equal to 40.
0.0301
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
The mean length of time required to complete the Columbus Marathon was 4.5 hours. The standard deviation of the times was 0.50 hours. Assume that the racing times were approximately normally distributed. What proportion of the runners would be expected to require between 5.0 and 5.5 hours to complete the race?
0.1359
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
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 between 9 and 18 inches.
0.8185
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
Find the area under the normal curve between z = -1.25 and z = 1.75.
0.8543
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
The general rule of thumb is that we need a sample size of n > _________ to use large-sample confidence interval procedures to estimate the population mean.
30
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
How many classes are recommended in a histogram of a data set with more than 50 observations?
15 to 20
The ages (in years) of a sample of 6 students are as follows: Student Age 1 19 2 23 3 20 4 20 5 19 6 19 Calculate the median age of this sample of 6 students
19.5 years
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
The average height of a certain ornamental plant is 14 inches and the standard deviation of the heights is 2 inches. Only 20% of the plants are expected to be less than X inches tall. Find the value of X.
12.32 inches
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
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 8 uninsured senior citizens were as follows: Senior Citizen Age 1 66 2 70 3 64 4 88 5 74 6 72 7 87 8 79 Find the median age of these 8 senior citizens.
73 years
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
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.
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 60 soccer players who participated in the study
The Central Limit Theorem states: Consider a random sample of n observations selected from any population with mean μ and standard deviation σ. If the sample size is sufficiently large, then the sampling distribution of the sample mean (X-bar) will be approximately a normal distribution with mean ________ and standard deviation _______.
mean µ and standard deviation σ/√n
Quantitative data are
Continous
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.
random sample
Measures of variation include
range, variance, and standard deviation
The __________ __________ of a statistic 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
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 dependent (response) variable for this experiment.
the price of a grocery item
Find the probability of an observation lying more than z = 1.77 standard deviations above the mean.
0.0384
As the sample size (n) increases, the variation in the sampling distribution of the sample means increases.
False
Which one of the following is not a measure of variation?
Mean
A consumer taste panel study was conducted to determine how people rate the eating quality of steaks from Brahman cattle. Members of the taste panel were asked to rate the overall quality of the steaks from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown below. Stem Leaves 3 2 4 4 0 3 4 7 8 9 9 9 5 0 1 1 2 3 4 5 6 1 2 5 6 6 7 0 1 8 9 2 What proportion of the taste panel members rated overall eating quality of the Brahman steaks as very good (i.e., a score of 80 or above)?
0.04
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 standard deviation of these 5,000 sample means is expected to be equal to _______.
0.25 lb
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
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 diets (i.e., treatments).
1,099.6
Finnish Landrace ewes are noted for producing "litters" of lambs. The number of lambs in a litter for a sample of 6 Finnish Landrace ewes is as follows: Ewe Number Number of Lambs in Litter 1 3 2 4 3 3 4 2 5 5 6 4 Calculate the standard deviation of litter size.
1.04881 lambs
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 mean squares for the line x breed interaction.
1.125
The ages (in years) of a sample of 6 students are as follows: Student Age 1 19 2 23 3 20 4 20 5 19 6 19 Calculate the standard deviation of this sample of 6 student ages.
1.5492 years
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 average weight of a kennel of dogs is 40 lb and the standard deviation of the weights is 5 lb. Only 14% of the dogs are expected to weigh less than X lb. Find the value of X.
34.6 lb
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 Calculate the mean weaning weight of this sample of 6 lambs.
36 kg
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 median weaning weight of this sample of 6 lambs.
36 kg
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 begin at row 5 column 1 of a random number table and observe the random numbers shown in the table below. Col. 1 2 3 4 5 6 Row 5: 37570 39975 81837 16656 06121 91782 6: 77921 06907 11008 42751 27756 53498 Which one of the following is the correct set of 5 randomly selected horses to include in our experiment, assuming that we go from left to right across the rows of random numbers?
37 39 16 06 11
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 average height cows of a certain breed is 54 inches and the standard deviation of the heights is 8 inches. Fifteen percent of the cows are expected to be less than X inches tall. Find the value of X.
45.68 inches
A Randomized Block Design is used to compare fleece weights of three breeds of sheep - Merino, Suffolk, and Dorset (we can think of the three breeds as being the three treatments). The sheep are divided into two weight classes (i.e., two blocks). Block one contains sheep weighing less than 150 lb and block two contains sheep weighing more than 150 lb. The fleece weights (in pounds) are as follows: Merino Suffolk Dorset Block 1 13 8 9 Block 2 14 9 11 The partially completed ANOVA table for this experiment is as follows: Source df SS MS F Total 29.33333 Breed 26.33333 13.16667 79.00003 Block Error 0.33333 0.16667 The correct degrees of freedom for total, breed, block, and error, respectively are:
5, 2, 1, and 2
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
The ∑ symbol in a statistical equation indicates that we are to perform which arithmetic operation?
Addition
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.
Which one of the following is not an assumption when we perform an Analysis of Variance?
All of the p samples have a normal distribution
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
A 2 x 4 factorial experiment is conducted to compare yields of 4 varieties of soybeans that are planted in rows either 15 inches or 30 inches apart. Two plots of ground are randomly assigned to each combination of soybean variety and row spacing. The yields of soybeans (in bushels per acre) are as follows: Rows 1 2 3 4 15" 45 46 47 46 46 46 48 43 30" 35 41 42 39 32 39 38 41 The partially completed ANOVA table is as follows: Source df SS MS F Total 319.75 Variety 41.25 13.75 5.0 Row spacing 225 225 81.8 Variety x row spacing 31.5 Error 22 2.75 Should we reject or not reject the null hypothesis for the interaction between variety and row spacing? Use a significance level of α = 0.05.
Because the calculated F value (3.818) is not greater than the F value from the table (4.07), we do not reject the null hypothesis.
Since 1917, the Girl Scouts of America have been selling boxes of cookies. Currently, there are 12 varieties for sale. Each of the approximately 150 million boxes of Girl Scout cookies sold each year is classified by variety. The results are summarized in a pie chart. From the graph, we can clearly see that the best-selling variety is Thin Mints (25%), followed by Samoas (19%) and Tagalongs (13%). Because the figure shows the various categories of Girl Scout cookies sold, the graph is an example of ________________ statistics.
Descriptive
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 Calculate the mean square (MS) for Error.
Error MS = 6.38917
A 2 x 4 factorial experiment is conducted to compare yields of 4 varieties of soybeans that are planted in rows either 15 inches or 30 inches apart. Two plots of ground are randomly assigned to each combination of soybean variety and row spacing. The yields of soybeans (in bushels per acre) are as follows: Rows 1 2 3 4 15" 45 46 47 46 46 46 48 43 30" 35 41 42 39 32 39 38 41 The partially completed ANOVA table is as follows: Source df SS MS F Total 319.75 Variety 41.25 13.75 5.0 Row spacing 225 225 81.8 Variety x row spacing 31.5 Error 22 2.75 Calculate the mean squares and then the F value for the variety x row spacing interaction.
F = 3.818
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 Calculate the F value for treatments and for blocks.
F value = 50.9831 for treatments and 202.678 for blocks.
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 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). F = 7.21
F= 5.12
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 Central Limit Theorem guarantees that the population is normally distributed whenever n is sufficiently large (n > 30).
False
The standard deviation of the sampling distribution of the sample mean is equal to σ, the standard deviation of the population.
False
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
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
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 Calculate the mean square (MS) for location.
Location MS = 288
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 factors?
The 2 breeds
The weaning weights of 3 herds of beef cattle are compared across the 4 seasons of the year. Thus, this is a 3 x 4 factorial experiment with 3 herds and 4 seasons. Three calves from each herd are sampled during each season (i.e., there are 3 replications). The resulting data were analyzed using Analysis of Variance and the partially completed ANOVA table is as follows: Source df F Total 35 Herd 2 17.2 Season 3 3.0 Herd x Season 6 1.2 Error 24 Was there a significant difference among the 4 seasons for mean weaning weight? Use a significance level of α = 0.01.
No, there is not a significant difference among the season means for weaning weight, because the calculated F value of 3.0 is less than the critical F value from the table of 4.72 when α = 0.01.
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
Proportion of dogs in each breed.
Pie charts normally show the
Proportion of observations falling in each class.
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". What are the experimental units?
The 200 people whose responses to the question were obtained
The types of trees (maple, oak, elm, etc.) in a nursery are an example of a ____________ variable.
Qualitative
____________ data are non numerical data that can only be classified into one of a group of categories.
Qualitative
The manager of a car dealership records the colors of the automobiles on his used car lot. The type of data being collected is ____________.
Qualitative data
Starting salary and GPA of students who graduate from OSU are examples of ____________ data.
Quantitative data
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
Consider a study of aphasia published in the Journal of Communication Disorders. Aphasia is the "impairment or loss of the faculty of using or understanding spoken or written language." Three types of aphasia have been identified by researchers: Broca's, conduction, and anomic. The researchers wanted to determine whether one type of aphasia occurs more often than the others. Consequently, they measured the type of aphasia found in a sample of 22 adult aphasics. They found that the proportion of people with anomic, Broca's, and conduction aphasia was 0.455, 0.227, and 0.318, respectively. These proportions represent the ____________ for the three classes.
Relative frequencies
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 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.
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: Block Hereford Angus Charolais Simmental 1 3.50 3.60 3.70 3.75 2 3.55 3.63 3.71 3.80 3 3.56 3.62 3.80 3.90 The partially completed ANOVA table for this experiment is as follows: Source df SS MS F Total .160 Breed .139 .046 46 Block .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.
What assumption is required for estimating the population mean (μ) when we have small samples of n < 30?
The population consisting of all of the values is approximately normally distributed.
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.
The weaning weights of two breeds of beef cattle are compared in two different regions of the US (say Florida and Wyoming). When the mean weaning weights of the two breeds in the two different states are graphed, the lines are not parallel, and, in fact, intersect with each other. What do you conclude?
There is a breed x location interaction.
The characteristics of cheek teeth (e.g., molars) can provide anthropologists with information on the dietary habits of extinct mammals. The cheek teeth of an extinct primate species were the subject of research reported in the American Journal of Physical Anthropology (Vol. 142, 2010). A total of 18 cheek teeth extracted from skulls discovered in western Wyoming were analyzed. Each tooth was classified according to degree of wear (unknown, unworn, slight, light-moderate, moderate, moderate-heavy, or heavy). The 18 measurements were as follows: Data on Degree of Wear unknown slight unknown slight unknown heavy moderate unworn slight light-moderate unknown light-moderate moderate-heavy moderate moderate unworn slight unknown Find the relative frequency for each wear category.
The relative frequencies for the unknown, unworn, slight, light-moderate, moderate, moderate-heavy, and heavy categories are 0.2778, 0.1111, 0.2222, 0.1111, 0.1667, 0.0556, and 0.0556, respectively.
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 highest selling price of $276,000 a suspect or highly suspect outlier?
The sale price of $276,000 is not a suspect or highly suspect outlier, because it falls inside the inner fences.
The Central Limit Theorem says that the sampling distribution of the sample mean is approximately normal 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 (at least 30 observations).
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 was 4.5 hours. Further assume that the standard deviation of the times required to complete the race was 0.50 hours. One runner completed the race in 5.0 hours. Calculate the z-score for the runner with the time of 5.0 hours. Based on this z-score, is this time of 5.0 hours an outlier? Why or why not?
The time of 5.0 hours is not an outlier, because the corresponding z-score is 1.0, which is less than 3 standard deviations above the mean.
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
In an Analysis of Variance, the mean squares are calculated by dividing the sums of squares by their corresponding degrees of freedom.
True
The normal approximation to a binomial probability distribution is reasonably good even for small sample sizes (say, n as small as 10) when p = 0.5 and the distribution of X is therefore symmetric about its mean.
True
The normal approximation to a binomial probability distrubtion is reasonably good even for small sample sizes (say, n as small as 10) when p = 0.5 and the distribution of X is therefore symmetric about its mean.
True
The probability of an event A is calculated by summing the probabilities of the sample points in the sample space for A.
True
The t and z distributions are very similar. Both are symmetric, mound-shaped, and have a mean of zero.
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
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.
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
Assume that we are interested in the population consisting of the lactation records of all Holstein cows in the U.S. The milk production records have a normal distribution. We select a large number of random samples of size n = 100 from this population and then plot the sample means. Would the sample means still have a normal distribution if the population of milk production records was not normally distributed (e.g., if the population had an exponential distribution)?
Yes
Which one of the following confidence intervals would be the widest?
a 99% confidence interval
Assume that we have 60 plots of ground and that we want to select a random sample of 6 plots 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 6 plots do we include in our random sample?
plots number: 05 07 18 20 56 60
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 union of events A and B (i.e., A U B).
{1, 2, 3, 4, 6}
