Questions and Answers of Statistics Informed Decisions Using Data

Garcia and Ybarra (2007) describe an experiment in which 174 undergraduates were randomly divided into a people-accounting condition (describing a numerical imbalance in an award) and a control
A sample of 90 randomly selected married couples are asked about their views on universal background checks for gun permits (Favor/Do Not Favor). The responses are summarized in Table 5.25. Do
____________ When there are only two samples, you should prefer the independent samples t test because it has more statistical power than the ANOVA.
____________ A set of sample means is more likely to result in rejection of the hypothesis of equal population means if the variability within the populations is smaller.
____________ Dunnett’s Procedure is more powerful than Scheffé’s, but it is more limited in the kinds of hypotheses it tests.
For the following true/false statements regarding concepts and uses of the analysis of variance, indicate whether the statement is true or false and specify what will correct a false
____________ To use the F statistic to test for the equality of two variances, the sample sizes must be equal.
____________ The logarithmic transformation is used when the variance is proportional to the mean.
____________ With the usual ANOVA assumptions, the ratio of two mean squares whose expected values are the same has an F distribution.
____________ One purpose of randomization is to remove experimental error from the estimates.
____________ To apply the F test in ANOVA, the sample size for each factor level (population) must be the same.
____________ To apply the F test for ANOVA, the sample standard deviations for all factor levels must be the same.
____________ To apply the F test for ANOVA, the population standard deviations for all factor levels must be the same.
____________ An ANOVA table for a one-way experiment gives the following: Source Between factors Within (error) df SS - 28 810 720
____________ A “statistically significant F” in an ANOVA indicates that you have identified which levels of factors are different from the others.
____________ Random models are appropriate when we are content simply to make statements about the factor levels actually used in the experiment and not about some larger group of factor levels.
____________ A sum of squares is a measure of dispersion.
Forty participants are randomly divided into five groups. Each participant is given a list of words to memorize. The groups differ in the kinds of word lists given to them. A portion of the ANOVA
Sixty older homes are randomly divided into four groups. Homes in each group are retrofitted with a different type of insulation, and then the change in energy consumption is recorded. A portion of
Thirty participants are randomly divided into three groups. Each participant is given a list of words to memorize. The groups differ in the kinds of words given to them, and the response is the
A sample of 24 older homes are randomly divided into four groups and retrofitted with different types of insulation. The response variable is the relative decrease in energy usage. The data is
A study of the effect of different types of anesthesia on the length of postoperative hospital stay yielded the following for cesarean patients: Group A was given an epidural MS. Group B was given
Three sets of five mice were randomly selected to be placed in a standard maze but with different color doors. The response is the time required to complete the maze as seen in Table
A manufacturer of air conditioning ducts is concerned about the variability of the tensile strength of the sheet metal among the many suppliers of this material. Four samples of sheet metal from four
A manufacturer of concrete bridge supports is interested in determining the effect of varying the sand content of concrete on the strength of the supports. Five supports are made for each of five
The data shown in Table 6.30 are times in months before the paint started to peel for four brands of paint applied to a set of test panels. If all paints cost the same, can you make recommendations
The data shown in Table 6.31 relate to the effectiveness of several insecticides. One hundred insects of a particular species were put into a chamber and exposed to an insecticide for 15 s. The
For laboratory studies of an organism, it is important to provide a medium in which the organism flourishes. The data for this exercise shown in Table 6.33 are from a completely randomized design
For the following true/false statements regarding concepts and uses of simple linear regression analysis, indicate whether the statement is true or false and specify what will correct a false
______ In linear regression we may extrapolate without danger.
______ When there is no linear relationship between two variables, a horizontal regression line best describes the relationship.
The scores of eight persons on the Stanford-Binet IQ test were:The median is:(1) 107 (2) 110 (3) 112 (4) 104 (5) none of the above 95 87 96 110 150 104 112 110
The concentration of DDT, in milligrams per liter, is:(1) a nominal variable(2) an ordinal variable(3) an interval variable(4) a ratio variable
If the interquartile range is zero, you can conclude that:(1) the range must also be zero(2) the mean is also zero(3) at least 50% of the observations have the same value(4) all of the observations
The species of each insect found in a plot of cropland is:(1) a nominal variable(2) an ordinal variable(3) an interval variable(4) a ratio variable
The “average” type of grass used in Texas lawns is best described by(1) the mean(2) the median(3) the mode
A sample of 100 IQ scores produced the following statistics:Which statement(s) is (are) correct?(1) Half of the scores are less than 95.(2) The middle 50% of scores are between 100 and 120.(3)
A sample of 100 IQ scores produced the following statistics:Which statement(s) is (are) correct?(1) Half of the scores are less than 100.(2) The middle 50% of scores are between 70 and 120.(3)
Identify which of the following is a measure of dispersion:(1) median(2) 90th percentile(3) interquartile range(4) mean
A sample of pounds lost in a given week by individual members of a weightreducing clinic produced the following statistics: Identify the correct statement:(1) One-fourth of the members lost less
A measurable characteristic of a population is:(1) a parameter(2) a statistic(3) a sample(4) an experiment
What is the primary characteristic of a set of data for which the standard deviation is zero?(1) All values of the variable appear with equal frequency.(2) All values of the variable have the same
Let X be the distance in miles from their present homes to residences when in high school for individuals at a class reunion. Then X is:(1) a categorical (nominal) variable(2) a continuous
A subset of a population is:(1) a parameter(2) a population(3) a statistic(4) a sample(5) none of the above
The median is a better measure of central tendency than the mean if:(1) the variable is discrete(2) the distribution is skewed(3) the variable is continuous(4) the distribution is symmetric(5) none
A small sample of automobile owners at Texas A & M University produced the following number of parking tickets during a particular year: 4, 0, 3, 2, 5, 1, 2, 1, 0. The mean number of tickets (rounded
To judge the extent of damage from Hurricane Ivan, an Escambia County official randomly selects addresses of 30 homes from the county tax assessor’s roll and then inspects these homes for
A physician tells you the largest typical hemoglobin value is 13.5 and the smallest is 9.5 mg/L. A reasonable estimate of the standard deviation is:(1) 11.5(2) 1.0(3) 4.0(4) unknowable with this
A university published the following distribution of students enrolled in the various colleges: Construct a bar chart of these data. College Enrollment College Enrollment Agriculture 1250 Liberal
On ten days, a bank had 18, 15, 13, 12, 8, 3, 7, 14, 16, and 3 bad checks. Find the mean, median, variance, and standard deviation of the number of bad checks.
Calculate the mean and standard deviation of the following sample: -1, 4, 5, 0.
The following is the distribution of ages of students in a graduate course:(a) Construct a bar chart of the data.(b) Calculate the mean and standard deviation of the data. Age (years) Frequency 20-24
The percentage change in the consumer price index (CPI) is widely used as a gauge of inflation. The following numbers show the percentage change in the average CPI for the years 1993 through 2007:(a)
Most of the problems in this and other chapters deal with “real” data for which computations are most efficiently performed with computers. Since a little experience in manual computing is
Because waterfowl are an important economic resource, wildlife scientists study how waterfowl abundance is related to various environmental variables. In such a study, the variables shown in Table
Someone wants to know whether the direction of price movements of the general stock market, as measured by the New York Stock Exchange (NYSE)Composite Index, can be predicted by directional price
The data in Table 1.17 consist of 25 values for four computer-generated variables called Y1, Y2, Y3, and Y4. Each of these is intended to represent a particular distributional shape. Use a stem and
Climatological records provide a rich source of data suitable for description by statistical methods. The data for this example (Table 1.18) are the number of January days in London, England, having
Make scatterplots for all pairwise combinations of the variables from the tree data(Table 1.7). Which pairs of variables have the strongest relationship? Is your conclusion consistent with prior
The data in Table 1.20 show statistics on the age distribution of Chinese victims of COVID-19. (These data, from China CDC Weekly, are dated February 11, 2020, when the pandemic was well underway in
The use of placement exams in elementary statistics courses has been a controversial topic in recent times. Some researchers think that the use of a placement exam can help determine whether a
_______________If two events are mutually exclusive, then P(A or B) = P(A) + P(B).
_______If A and B are two events, then P(A and B) = P(A)P(B), no matter what the relation between A and B.
This section consists of some true/false questions regarding concepts of statistical inference. Indicate if a statement is true or false and, if false, indicate what is required to make the
________ The probability density function of a continuous random variable. can take on any value, even negative ones.
This section consists of some true/false questions regarding concepts of statistical inference. Indicate if a statement is true or false and, if false, indicate what is required to make the
_______ A normal distribution is characterized by its mean and its degrees of freedom.
This section consists of some true/false questions regarding concepts of statistical inference. Indicate if a statement is true or false and, if false, indicate what is required to make the
__________ The t distribution is used as the sampling distribution of the mean if the sample is small and the population variance is known.
__________ The standard error of the mean increases as the sample size increases.
__________ As α increases, the value of zα will decrease.
The weather forecast says there is a 40% chance of rain today and a 30% chance of rain tomorrow. Assume the days are independent.(a) What is the chance of rain on both days?(b) What is the chance of
The following is a probability distribution of the number of defects on a given contact lens produced in one shift on a production line: Let A be the event that one defect occurred, and B be the
Suppose that Y is a normally distributed random variable with μ = 10 and σ = 2, and X is an independent random variable, also normally distributed with μ = 5 and σ = 5. Find: (a) P(Y>12 and X>4)
In a sample of size 5 from a normal distribution, which is more likely: that the sample variance will be less than half the true variance, or that it will be more than twice the true variance?
Suppose Y = home price per square foot has a normal distribution with a mean of 100 and a standard deviation of 20.(a) What value separates the most expensive 25% of homes from the less expensive
A randomly selected home has a 32% chance of having a fireplace. If you randomly select records for 12 homes, what is the probability that:(a) exactly 4 have a fireplace?(b) at least 7 have a
A lottery that sells 150,000 tickets has the following prize structure: (1) first prize of $$50,000$(2) 5 second prizes of $$10,000$(3) 25 third prizes of $$1000$(4) 1000 fourth prizes of
Assume the random variable y has the continuous uniform distribution defined on the interval a to b, that is, For this problem let a = 0 and b = 2. (a) Find P(Y (b) Find μ and σ2 for the
The binomial distribution for p = 0:2 and n = 5 is:(a) Compute μ and σ2 for this distribution.(b) Do these values agree with those obtained as a function of the parameter p and sample size n?
A system requires two components, A and B, to both work before the system will. Because of the sensitivity of the system, an increased reliability is needed. To obtain this reliability, two duplicate
Let Y be a normally distributed random variable with mean 10 and variance 25. Find: (a) P(Y>15) (b) P(8
A teacher finds that the scores of a particularly difficult test were approximately normally distributed with a mean of 76 and standard deviation of 14.(a) If a score below 60 represents a grade of
A random sample of 100 is taken from a population with a mean of 140 and standard deviation of 25. What is the probability that the sample mean lies between 138 and 142?
A manufacturer wants to state a specific guarantee for the life of a product with a replacement for failed products. The distribution of lifetimes of the product is normal and has a mean of 1000 days
A teacher wants to curve her grades such that 10% are below 60 and 10% above 90. Assuming a normal distribution, what values of μ and σ2 will provide such a curve?
Historically, victims of the Ebola virus had a 30% chance of survival.(a) A new treatment is tested on three victims, and at least two of them survive. What is the probability of this happening, if
Suppose the sales price per square foot of homes follows an approximate normal distribution. If you construct a box plot based on a large dataset for this variable, about what percentage of the
To monitor the production of sheet metal screws by a machine in a large manufacturing company, a sample of 100 screws is examined each hour for three shifts of 8 hours each. Each screw is inspected
Based on data from the 2007 National Health Interview Survey, it is estimated that “10% of adults experienced feelings of sadness for all, most, or some of the time” during the 30 days prior to
The Kaufman Assessment Battery for Children is designed to measure achievement and intelligence with a special emphasis on nonverbal intelligence. Its global measures, such as its Sequential
The number of birth defects in a region is commonly modeled as having a binomial distribution, with a rate of three birth defects per 100 births considered a typical rate in the United
Twelve patients undergoing recuperation from cardiothoracic surgery are randomly divided into two groups. Because the treatment that one group is about to receive affects blood glucose levels, the
______ If the test statistic falls in the rejection region, the null hypothesis has been proven to be true.
______ The risk of a type II error is directly controlled in a hypothesis test by establishing a specific significance level.
______ If the null hypothesis is true, increasing only the sample size will increase the probability of rejecting the null hypothesis.
______ If the null hypothesis is false, increasing the level of significance (α) for a specified sample size will increase the probability of rejecting the null hypothesis.
______ If we decrease the confidence coefficient for a fixed n, we decrease the width of the confidence interval.
______ If a 95% confidence interval on μ was from 50.5 to 60.6, we would reject the null hypothesis that μ = 60 at the 0.05 level of significance.
______ If the sample size is increased and the level of confidence is decreased, the width of the confidence interval will increase.

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