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statistical techniques in business
Statistical Methods 3rd Edition Donna L. Mohr - Solutions
Find:(a) P(Y > 12 and X > 4)(b) P(Y > 12 or X > 4)(c) P(Y > 10 and X < 5) LO.1
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 = LO.1
Using the distribution in Exercise 2, suppose that the lens can be sold as is if there are no defects for $20. If there is one defect, it can be reworked at a cost of $5 and then sold. If there are two defects, it can be reworked at a cost of $10 and then sold. If there aremore than two defects, it
Using the distribution in Exercise 2, let the random variable Y be the number of defects on a contact lens randomly selected from lenses produced during the shift.(a) Find the mean and variance of Y for the shift.(b) Assume that the lenses are produced independently.What is the probability that
The following is a probability distribution of the number of defects on a given contact lens produced in one shift on a production line:Number of Defects 0 1 2 3 4 Probability 0.50 0.20 0.15 0.10 0.05 Let A be the event that one defect occurred, and B be the event that 2, 3, or 4 defects occurred.
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 rain on neither day?(c) What is the chance of rain on at least one day? LO.1
The limits that bracket the desired mean on a control chart are chosen so that Y will never go outside those limits when the process is in control. LO.1
As α increases, the value of zα will decrease. LO.1
The standard error of the mean increases as the sample size increases. LO.1
The t distribution is used as the sampling distribution of the mean if the sample is small and the population variance is known. LO.1
The standard normal distribution has mean zero and varianceσ 2. LO.1
A normal distribution is characterized by its mean and its degrees of freedom. LO.1
The variance of the number of successes in a binomial experiment of n trials is σ 2 = np(p − 1). LO.1
The probability that a continuous random variable lies in the interval 4 to 7, inclusively, is the sum of P(4) + P(5) + P(6) + P(7). LO.1
The probability distribution function of a continuous random variable can take on any value, even negative ones. LO.1
The probability distribution function of a discrete random variable cannot have a value greater than 1. LO.1
If A andB are two events, then P(A and B) = P(A)P(B), nomatter what the relation between A and B. LO.1
If two events are mutually exclusive, then P(A or B) = P(A) +P(B). LO.1
The distribution is bell shaped and symmetric about the mean. This is apparent in the graph of a normal distribution with μ = 0 and σ = 1, given in Fig. 2.4, and has resulted in the normal distribution being referred to often as the “bell curve.” LO.1
The distribution has only two parameters μ and σ2 (or σ). These are, in fact, the mean and variance (or standard deviation) of the distribution. Thus, knowing the values of these two parameters completely determines the distribution. The fact that these parameters are also the two most
The random variable Y can take on any value from −∞ to +∞. LO.1
The yield of corn per acre in response to fertilizer application at a test site. The statistic is the mean yield at the test site. The parameter is the mean yield of corn per acre in response to given amounts of the fertilizer when used by farmers under similar conditions. LO.1
Testing light bulbs for longevity. Since such testing destroys the product, only a small sample of a manufacturer’s total output of light bulbs can be tested for longevity. The statistic is the mean lifetime as computed from the sample. The parameter is the actual mean lifetime of all light bulbs
The results of a public opinion poll taken from a sample of registered voters. The statistic is the sample proportion of voters favoring a candidate or issue. The parameter to be estimated is the proportion of all registered voters favoring that candidate or issue. LO.1
In Exercise 8 a test of durability of various brands of paint was conducted. The results are given in Table 6.34, which lists the summary statistics only. Perform an analysis of means (Section 6.8) on these data. Do the results agreewith those of Exercise 8? Explain. LO.1
Useful prediction intervals for y can be obtained from a regression analysis. LO.1
In a regression analysis, the estimatedmean of the distribution of y is the sample mean ( ¯ y). LO.1
All data points will fit the regression line exactly if the sample correlation is either +1 or −1. LO.1
The prediction interval for y is widest when x is at its mean. LO.1
The standard error of the estimated slope of a regressionmodel becomes larger as the dispersion of x increases. LO.1
When there is no linear relationship between two variables, a horizontal regression line best describes the relationship. LO.1
If r > 0, then as x increases, y tends to increase. LO.1
If a regression line is computed for data where x ranges from 0 to 30, you may safely predict y for x = 40. LO.1
The correlation coefficient can be used to detect any relationship between two variables. LO.1
If r is very close to either +1 or −1, then there is a cause and effect relationship between x and y. LO.1
Given that SSR = 50 and SSE = 100, calculate R2. LO.1
The multiple correlation coefficient can be calculated as the simple correlation between and . LO.1
The term ˆμy|x serves as the point estimate for estimating both the mean and individual prediction of y for a given x. LO.1
The error or residual sum of squares is the numerator portion of the formula for the variance of y about the regression line. LO.1
The x values must be randomly selected in order to use a regression analysis. LO.1
A manufacturing company uses five identical assembly lines to construct one model of an electric toaster.All the toasters produced go to the same retail outlet.A recent complaint from this outlet indicates that there has been an increase in defective toasters in the past month. To determine the
Tartz et al. (2007) performed two-sample z-tests for proportions comparing men and women on 28 different indices of dream content. They make the following comment:When making 28 comparisons, an average of one comparison might have been significant at the .05 alpha level by chance alone (i.e., a
Sargent et al. (2007, Experiment 2A) randomly divided 125 students into three groups and gave them different instructions regarding the focus of the Implicit Association Test (IAT). The dependent variable is the score on the IAT. The data is summarized in Table 6.41.320 CHAPTER 6: Inferences for
Florida County Data Set. Examine the Florida County data set, described in Appendix C.4. Divide the counties into four groups according to the quartile of their percentage of adults lacking a high school degree. (This quartile information is already part of the data set.)Do the groups differ
NADP Data Set. The data from the National Atmospheric Deposition Program, described in Appendix C.3, also contains data on energy consumption and on energy consumption per squaremile (ECPSM) in each state. States have been subdivided into five groups based on their quintile for energy consumption
The need for a nonlinear regression can only be determined by a lack of fit test. LO.1
The correlation coefficient indicates the change in y associated with a unit change in x. LO.1
To conduct a valid regression analysis, both x and y must be approximately normally distributed. LO.1
Rejecting the null hypothesis of no linear regression implies that changes in x cause changes in y. LO.1
In linear regressionwe may extrapolatewithout danger. LO.1
If x and y are uncorrelated in the population, the expected value of the estimated linear regression coefficient (slope) is zero. LO.1
If the true regression of y on x is curvilinear, a linear regression still provides a good approximation to that relationship. LO.1
(a) What value of R2 is required so that a regressionwith five independent variables is significant if there are 30 observations? [Hint: Use the 0.05 critical value for F(5,24)].(b) Answer part (a) if there are 500 observations.(c) What do these results tell us about the R2 statistic? LO.1
If x is the number of inches and y is the number of pounds, what is the unit of measure of the regression coefficient? LO.1
Four groups of 20 children each (dyslexic-type I, dyslexic-type II, age-matched control, reading-matched control) are selected. Each child’s parents fill out an ADHD rating scale for the child. Researchers are interested in whether the groups differ in their mean ratings (Boada, 2006). LO.1
Sixty children (20 each in three age groups) participate in an experiment to measure visual memory. Each child is given five tasks, of varied difficulty. The researchers are interested in whether the impact of task difficulty differs by age(Riggs et al., 2006). LO.1
Thirty children are randomly assigned to one of two contexts and one of three item lists, with five children in each combination. Each child is read the words in his/her item list and asked to say whether it is being mispronounced. Children in the picture context are shown pictures of the items as
Twenty-eight children in second grade each are given word-training in every combination of two different contexts and four different levels of repetition. The researchers are interested in whether the level of repetition, averaged over the two contexts, impacts the number of words learned
In Example 12.6, it was found that the occupations did not all have the same distribution of cancer type. You want to know which occupations differ. How could you carry out the pairwise comparisons while controlling the experimentwise error rate? LO.1
In Section 5.6, we describe the test for the null hypothesis that the medians in two groups are the same. How could you adapt the χ2 test to the null hypothesis that the medians in k ≥ 2 groups are all the same? LO.1
Under what circumstances might the X 2 value be large but the contingency coefficient be low? How would you interpret that result? LO.1
The probability of an event is a value between __ and __, the odds of the event are between __ and __, and the ln(odds) are between __ and __. LO.1
In one situation, Poisson regression and logistic regression can substitute for each other. Describe that situation. LO.1
Your professor comments, “what appears as an interaction when a profile plot is made for the probabilitiesmay not appear as an interactionwhen the ln(odds) are plotted.” Use an example with some probabilities you make up to illustrate the professor’s meaning. LO.1
Neither logistic regressionnor Poisson regression produce an estimate of the error variance.Why? LO.1
Sixty participants each watched scenes of people holding conversations. The scenes were of three types, and each participant gave a rating of the perceived closeness of the actors for each of these types. The researchers are interested in whether there are differences in the mean ratings by type
The steel bar datawas analyzed once in Example 9.6 as a three-way ANOVA, and revisited in Section 10.4 as a randomized block design with an embedded twoway factorial design. What consideration would determine which method is the correct analysis?Each of the scenarios described in Questions 2
Explain why this hypothesis would rarely be of interest. LO.1
What is the common feature of most “influence” statistics? LO.1
Under what conditions is least squares not the best method for estimating regression coefficients? LO.1
What is the interpretation of the regression coefficient when using logarithms of all variables? LO.1
What is the basic principle underlying inferences on partial regression coefficients? LO.1
Why is multicollinearity a problem? LO.1
List some reasons why variable selection is not always an appropriate remedial method when multicollinearity exists. LO.1
________ (True/False) When all VIF are less than 10, then multicollinearity is not a problem. LO.1
________ (True/False) The adjusted R-square attempts to balance good fit against model complexity. LO.1
________ (True/False) The t statistic for an individual coefficient measures the contribution of the corresponding independent variable, after controlling for the other variables in the model. LO.1
________ (True/False) Because polynomials are smooth functions, it is permissible to extrapolate slightly beyond the range of the independent variablewhen fitting quadratic models. LO.1
You fit a full regressionmodel with five independent variables, obtaining an SSE with 40 df. Then you fit a reduced model that has only three of the independent variables, but now you obtain an SSE with 46 df. Does this make sense?What is the most likely explanation?What should you do? LO.1
The null hypothesis for the test for the model (Section 8.3) does not include the intercept term β0. Give the interpretation of a null hypothesis that did includeβ0, H0 : β0 = β1 = . . . = βm = LO.1
Suppose that in Example 13.4 the number of workers had been expressed in millions, that is, 2.850803 rather than 2,850,803. Howwould the estimated regression coefficients change? LO.1
In Exercise 4 an experimentwas conducted to determine the effect of the percent of sand in concrete bridge supports on the strength of these supports. A set of orthogonal polynomial contrasts was used to determine the nature of this relationship.The ANOVA results indicated a cubic polynomial would
If the treatments in a CRD consist of numeric levels of input to a process, the LSD multiple comparison procedure is the most appropriate test. LO.1
If every observation is multiplied by 2, then the value of the F statistic in an ANOVA is multiplied by 4. LO.1
To use the F statistic to test for the equality of two variances, the sample sizes must be equal. LO.1
The logarithmic transformation is used when the variance is proportional to the mean. LO.1
With the usual ANOVA assumptions, the ratio of two mean squares whose expected values are the same has an F distribution. LO.1
One purpose of randomization is to remove experimental error from the estimates. LO.1
To apply the F test in ANOVA, the sample size for each factor level (population) must be the same. LO.1
To apply the F test for ANOVA, the sample standard deviations for all factor levels must be the same. LO.1
To apply the F test for ANOVA, the population standard deviations for all factor levels must be the same. LO.1
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. LO.1
If for two samples the conclusions from an ANOVA and t test disagree, you should trust the t test. LO.1
Lake Data Set. The Florida Lakewatch data set is described in Appendix C.1. It contains water quality information on a sample of lakes in North Central Florida taken during 2005. For most of the lakes, total phosphorus level is reported for a summer month and also for a winter month. Does the
Martinussen et al. (2007) compared “burnout” among a sample of Norwegian police officers to a comparison group of air traffic controllers, journalists, and building constructors. Burnout was measured on three scales: exhaustion, cynicism, and efficacy. The data is summarized in Table 5.22. The
In an experiment in which infants interacted with objects, Sommerville, et al.(2005) randomly divided 30 infants into a reach-first versuswatch-first condition.The authors’ state, Whereas 11 of 15 infants in the reach-first condition looked longer at the new goal events than the new path events,
Researchers atWolfson Children’s Hospital, Jacksonville, FL tested new technologymeant to reduce the number of attempts needed to draw blood from children.They collected data on the number of successes on the first attempt using the new technology and on a historicalcomparison group using
Elevated levels of blood urea nitrogen (BUN) denote poor kidney function. Ten elderly cats showing early signs of renal failure are randomly divided into two groups.Group 1 (controlgroup) is placed on a standard high-protein diet. Group 2(intervention group) is placed on a low-phosphorus
In Exercise 12 of Chapter 1 a study of characteristics of successful salespersons indicated that 44 of 120 sales managers rated reliability as the most important characteristic in salespersons. A study of a different industry showed that 60 of 150 sales managers rated reliability as the most
Do the assumptions necessary for the test in Exercise 13 seem to be satisfied by the data?Explain. LO.1
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