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statistical techniques in business

Statistical Methods 3rd Edition Donna L. Mohr - Solutions

Draw a stem and leaf plot of half-life for each drug in Exercise LO.1
In Exercise 13 of Chapter 1, the half-life of aminoglycosides from a sample of 43 patients was recorded. The data are reproduced in Table 5.19. Use these data to see whether there is a significant difference in the mean half-life of Amikacin and Gentamicin. (Use α = 0.10.)Table 5.19 Half-Life of
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 different amounts of sand in the concretemix and each support tested for compression resistance. The
Chlorinated hydrocarbons (mg/kg) found in samples of two species of fish in a lake are as follows:Species 1: 34 1 167 20 Species 2: 45 86 82 70 160 170 Performa hypothesis test to determinewhether there is a difference in themean level of hydrocarbons between the two species. Check
The manager of a large office building needs to buy a large shipment of light bulbs. After reviewing specifications and prices from a number of suppliers, the choice is narrowed to two brandswhose specificationswith respect to price and quality appear identical. He purchases 40 bulbs of each brand
A new method of teaching children to read promises more consistent improvement in reading ability across students. The new method is implemented in one randomly chosen class, while another class is randomly chosen to represent the standard method. Improvement in reading ability using a standardized
In a test of the effectiveness of a device that is supposed to increase gasoline mileage in automobiles, 12 cars were run, in random order, over a prescribed course both with and without the device in random order. The mileages (mpg)are given in Table 5.15. Is there evidence that the device is
In a test of the reliability of products produced by two machines, machine A produced 7 defective parts in a run of 140, while machine B produced 10 defective parts in a run of 200. Do these results imply a difference in the reliability of these two machines? LO.1
Assume that in Exercise 5 the new diet costs more than the old one. The cost is approximately equal to the value of 25 lb. of additional weight. Does this affect the results obtained in Exercise 5? Redo the problem if necessary. LO.1
To assess the effectiveness of a new diet formulation, a sample of 8 steers is fed a regular diet and another sample of 10 steers is fed a new diet. The weights of the steers at 1 year are given in Table 5.14. Do these results imply that the new diet results in higher weights? (Use α = 0.05.)Table
An ANOVA table for a one-way experiment gives the following:Source df SS Between factors 2 810 Within (error) 8 720 Answer true or false for the following six statements:The null hypothesis is that all four means are equal.The calculated value of F is 1.125.The critical value for F for 5%
A closer examination of the records of the air samples in Exercise 3 reveals that each line of the data actually represents readings on the same day: 2.92 and 1.84 are from day 1, and so forth. Does this affect the validity of the results obtained in Exercise 3? If so, reanalyze. LO.1
Table 5.13 shows the observed pollution indexes of air samples in two areas of a city. Test the hypothesis that the mean pollution indexes are the same for the two areas. (Use α = 0.05.)Table 5.13 Data for Exercise 3 Area A Area B 2.92 1.84 1.88 0.95 5.35 4.26 3.81 3.18 4.69 3.44 4.86 3.69 5.81
Construct a 95% confidence interval on the mean difference in the scores for the two classes in Exercise 1. LO.1
Two sections of a class in statistics were taught by two different methods. Students’scores on a standardized test are shown in Table 5.12. Do the results present evidence of a difference in the effectiveness of the two methods? (Useα = 0.05.)Table 5.12 Data for Exercise 1 Class A Class B 74 76
In a test of a newmedication, 65 out of 98males and 45 out of 85 females responded positively. At the 0.05 level of significance, can we say that the drug is more effective for males?Exercises LO.1
The following weights in ounces resulted from a sample of laboratory rats on a particular diet. Use α = 0.05 and test whether the diet was effective in reducing weight.Rat 1 2 3 4 5 6 7 8 9 10 Before 14 27 19 17 19 12 15 15 21 19 After 16 18 17 16 16 11 15 12 21 18 LO.1
Using the data in Exercise 2, compute the 0.90 confidence interval on the difference between the two population means, μ1 − μ2. LO.1
A “statistically significant F” in an ANOVA indicates that you have identified which levels of factors are different from the others. LO.1
The results of two independent samples from two populations are listed below:Sample 1: 17, 19, 10, 29, 27, 21, 17, 17, 14, 20 Sample 2: 26, 24, 26, 29, 15, 29, 31, 25, 18, 26 Use the 0.05 level of significance and test the hypothesis that the two populations have equal means. Assume the two samples
An engineer was comparing the output from two different processes by independently sampling each one. From process A she took a sample of n1 = 64, which yielded a sample mean of y¯1 = 12.5. Process A has a known standard deviation,σ = 2.1. From process B she took a sample of n2 = 100, which
If the calculated value of the t statistic is negative, then there is strong evidence that the null hypothesis is false. LO.1
It is not necessary to have equal sample sizes for the paired t test. LO.1
Using the results of Exercise 13, determine what degree of polynomial curve is required to relate fitness to time with the department. Illustrate the results with a graph. LO.1
The pooled variance estimate is used when comparing means of two populations using independent samples. LO.1
The F distribution is skewed and its mean is close to 1. LO.1
The F distribution is symmetric and has a mean of 0. LO.1
The standard normal (z ) score may be used for inferences concerning population proportions. LO.1
A study of firefighters in a large urban area centered on the physical fitness of the engineers employed by the fire department. To measure the fitness, a physical therapist sampled five engineers each with 5, 10, 15, and 20 years’ experience with the department. She then recorded the number of
The F distribution is used for testing differences betweenmeans of paired samples. LO.1
The χ2 distribution is used for making inferences about two population variances. LO.1
The use of paired samples allows for the control of variation because each pair is subject to the same common sources of variability. LO.1
When the means of two independent samples are used to compare two population means, we are dealing with dependent (paired) samples. LO.1
If every observation is multiplied by 2, then the t statistic is multiplied by 2. LO.1
A two-sample test is twice as powerful as a one-sample test. LO.1
In the two-sample t test, the number of degrees of freedom for the test statistic increases as sample sizes increase. LO.1
One of the assumptions underlying the use of the (pooled) twosample test is that the samples are drawn from populations having equal means. LO.1
Each year, the Florida Department of Education grades K–12 schools on a scale of A to F. In spring 2009, 71 schools in Duval changed their grade compared to the previous year, 46 improving, and 25 declining. In the nearby county of Putnam, which is much more rural, 9 schools changed their grade,
McCluskey et al. (2008) conducted a survey of citizens’ attitudes toward police in San Antonio, Texas. Before proceeding with their main analysis, they first compare the ethnic distribution in their sample to that of San Antonio as a whole.According to the 2000 Census, 59% of San Antonio
In an experiment to determine the effectiveness of sleep-inducing drugs, 18 insomniacs were randomly assigned to three treatments: LO.1
In Example 4.3, the paper mill had to demonstrate that its effluent had mean DO greater than 6 mg/L. But to ensure against occasional very low DO, keeping the mean high is not enough, the mill must also keep the standard deviation low.(a) Using the data in Table 4.3, is there evidence that the
When sample sizes are smaller, then methods based directly on the binomial distribution can be used. Suppose a vendor claims that at most 5%of parts are defective. In a random sample of 20 parts shipped by this vendor, you find four that are defective.(a) State the null and alternative
The methods for proportions discussed in Section 4.3 assume that np0 ≥ 5 and n(1 − p0) ≥ LO.1
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 6.38 are from a completely randomized design with four samples for each of seven media. The response is the diameters of the colonies of
In Exercise 24, suppose that we interpret the standard as meaning that there should be only a small probability (no more than 10%) that the time-weighted sound level at a site will exceed 90 dBA. In 70 independent measurements of the sound level, you find 10 instances where the noise exceeds 90
Federalworkplace safety standards for noise levels state that personal protective equipment is required if the time-weighted sound level at awork site exceeds 90 dBA. Suppose that this is interpreted as saying that themean sound level at a site should not significantly exceed 90 dBA. At one
Warren and McFadyen (2010) interviewed 44 residents of Kintyre, Scotland. This rural area in southwest Scotland is home to a growing number of wind farms.Twenty-two of the interviewees rated the visual impact of the wind farms as Positive or Very Positive. Assuming this was a random sample, give a
The following data gives the average pH in rain/sleet/snow for the two-year period 2004–2005 at 20 rural sites on the U.S. West Coast. (Source: National Atmospheric Deposition Program)(a) Box plot this data and identify any anomalous observations.(b) Would the sample mean or the sample median be
This experiment concerns the precision of four types of collecting tubes used for air sampling of hydrofluoric acid. Each type is tested three times at five different concentrations. The data shown in Table 4.7 give the differences between the three observed and true concentrations for each level
Draw a power curve for the test constructed in Exercise 19. (Refer to the discussion on power curves in Section 3.2 and plot 1 − β versus p = proportion of customers drinking another brand.) LO.1
A certain soft drink bottler claims that less than 10% of its customers drink another brand of soft drink on a regular basis.A random sample of 100 customers yielded 18 who did in fact drink another brand of soft drink on a regular basis.Do these sample results support the bottler’s claim? (Use a
Using the data from Exercise 17, construct a 90% confidence interval on the variance of the half-life of Amikacin. LO.1
In Exercise 13 of Chapter 1 the half-lives of aminoglycosides were listed for a sample of 43 patients, 22 of which were given the drug Amikacin. The data for the drug Amikacin are reproduced in Table 4.6. Use these data to determine a 95% confidence interval on the true mean half-life of this
Using the data from Exercise 11, construct a stem and leaf plot and a box plot. Do these graphs indicate that the assumptions discussed in Section 4.5 are valid?Discuss possible alternatives. LO.1
Serious environmental problems arise from absorption into soil of metals that escape into the air from different industrial operations. To ascertain if absorption rates differ among soil types, six soil sampleswere randomly selected from fields having five different soil types (A, B, C, D, and E)
Using the data from Exercise 4, construct a stem and leaf plot and a box plot (Section 1.6). Do these graphs indicate that the assumptions discussed in Section 4.5 are valid? Discuss possible alternatives. LO.1
Suppose that a sample of size 25 from Exercise 13 yielded s = 0.0037. Should the machine be adjusted? LO.1
Construct a 0.95 confidence interval on the variance of weights given in Exercise 11. LO.1
A truth in labeling regulation states that no more than 1% of units may vary by more than 2% from the weight stated on the label. The label of a product states that units weigh 10 oz. each. A sample of 20 units yielded the following:10.01 9.92 9.82 10.04 10.04 10.06 9.97 9.94 9.97 9.86 10.02 10.14
Construct a 0.99 confidence interval on the meanweight of 12-hour-old babies in Exercise 9. LO.1
It is said that the average weight of healthy 12-hour-old infants is supposed to be 7.5 lb. A sample of newborn babies from a low-income neighborhood yielded the following weights (in pounds) at 12 hours after birth:6.0 8.2 6.4 4.8 8.6 8.0 6.0 7.5 8.1 7.2 At the 0.01 significance level, can we
Construct a 0.95 interval on the true proportion of voters preferring candidate X in Exercise 7. LO.1
A public opinion poll shows that in a sample of 150 voters, 79 preferred candidate X. If X can be confident of winning, she can save campaign funds by reducing TV commercials. Given the results of the survey should X conclude that she has a majority of the votes? (Use α = 0.05.) LO.1
Average systolic blood pressure of a normal male is supposed to be about 129.Measurements of systolic blood pressure on a sample of 12 adult males from a community whose dietary habits are suspected of causing high blood pressure are listed below:115 134 131 143 130 154 119 137 155 130 110 138 Do
An advertisement for a headache remedy claims that 90% or more of headache sufferers get relief if they use the remedy.A truth in advertisingagency is considering a suit for false advertising and obtains a sample of 100 individuals, which shows that 88 indicate that the remedy gave them relief.(a)
A sample of 20 insurance claims for automobile accidents (in $1000) gives the following values:1.6 2.0 2.7 1.3 2.0 1.3 0.3 0.9 1.2 1.2 0.2 1.3 5.0 0.8 7.4 3.0 0.6 1.8 2.5 0.3 Construct a 0.95 confidence interval on the mean value of claims. Comment on the usefulness of this estimate (Hint: Look at
A manufacturer of watches has established that on the average his watches do not gain or lose. He also would like to claim that at least 95% of the watches are accurate to ±0.2 s per week. A random sample of 15 watches provided the following gains (+) or losses (−) in seconds in one week:+0.17
In Exercise 1, determine whether a mean weight loss of more than 1 lb was achieved. (Use α = 0.01.) LO.1
placebo (no drug) 2. standard drug 3. new experimental drug The response as shown in Table 6.33 is average hours of sleep per night for a week. Performthe appropriate analysis and make any specific recommendations for use of these drugs.Table 6.33 Data for Exercise 7 Treatment 1 2 3 5.6 8.4 10.6
Weight losses of 12 persons in an experimental one-week diet programare given below:3.0 1.4 0.2 −1.2 5.3 1.7 3.7 5.9 0.2 3.6 3.7 2.0 Do these results indicate that a mean weight loss was achieved? (Use α = 0.05). LO.1
In Exercise 4, howmany voters should the aide sample if the congressmanwanted to estimate the true level of support to within 1%? LO.1
A local congressman indicated that he would support the building of a new dam on the Yahoo River if more than 60% of his constituents supported the dam. His legislative aide sampled 225 registeredvoters in his district and found 135 favored the dam. At the level of significance of 0.10 should the
Using the data in Exercise 2, test the following hypotheses:(a) H0: μ = 13, H1: μ = 13.(b) H0: σ 2 = 10, H1: σ 2 = 10. LO.1
The following sample was taken from a normally distributed population:3, 4, 5, 5, 6, 6, 6, 7, 7, 9, 10, 11, 12, 12, 13, 13, 13, 14, 15.(a) Compute the 0.95 confidence interval on the population mean μ.(b) Compute the 0.90 confidence interval on the population standard deviation σ. LO.1
Find the following upper one-tail values:(a) t 0.05(13)(b) t 0.01(26)(c) t 0.10(8)(d) χ2 0.01(20)(e) χ2 0.10(8)(f ) χ2 0.975(40)(g) χ2 0.99(9) LO.1
The degrees of freedom for the t test do not necessarily depend on the sample size used in computing the mean. LO.1
The data in Table 6.36 are wheat yields for experimental plots having received the indicated amounts of nitrogen. Determinewhether a linear or quadratic trend may be used to describe the relationship of yield to amount of nitrogen.Table 6.36 Data for Exercise 10 Nitrogen 40 80 120 160 200 240 42 45
The t test can be applied with absolutely no assumptions about the distribution of the population. LO.1
The sampling distribution of a proportion is approximated by the χ2 distribution. LO.1
The variance of a binomial proportion is npq [or np(1 − p)]. LO.1
The χ2 distribution is skewed and its mean is always 2. LO.1
When the test statistic is t and the number of degrees of freedom is >30, the critical value of t is very close to that of z (the standard normal). LO.1
The data shown in Table 6.35 relate to the effectiveness of several insecticides.One hundred insects of a particular specieswere put into a chamber and exposed to an insecticide for 15 s. The procedure was applied in random order six times 316 CHAPTER 6: Inferences for Two or More Means for each of
The mean of the t distribution is zero. LO.1
The χ2 distribution is used for inferences on the variance. LO.1
In the t test for a mean, the level of significance increases if the population standard deviation increases, holding the sample size constant. LO.1
The quantity(y¯ − μ)σ 2/n has the t distribution with (n − 1) degrees of freedom. LO.1
The mean of the t distribution is affected by the degrees of freedom. LO.1
The χ2 distributionis used for inferenceson themeanwhen the variance is unknown. LO.1
The t distribution is more dispersed than the normal. LO.1
The data shown in Table 6.34 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 on which paint to use? This problem is an example of a relatively rare situationwhere only themeans
A hospital has observed that the number of nosocomial (hospital-acquired) pneumonias(NP) in its intensive care unit follows a Poisson distribution with a rate of 1.8 per month. The hospital’s infection-control officer monitors the number of NP each month, and calls for an expensive additional
An insurancecompany randomly selects 100 claims froma chain of dialysis clinics and conducts an audit. Themean overpayment per claimin this sample is $21.32.The company is interested in extrapolating this information to the population of all claims from this chain. They want to make a statement of
Refer to the information in Problem 18.(a) Give a 95% confidence interval for the mean consumption among teenage boys in your county.(b) The confidence interval in (b) has a wide margin of error.What sample size would you suggest if you wanted a margin of error of only 75 kcal? LO.1
A large national survey of American dietary habits showed a mean calorie consumption of 2700 kcal and a standard deviation of 450 kcal among teenage boys. You are studying dietary habits of children in your county to see if they differ from the national norm.(a) In a sample of 36 teenage boys, you
The public health official monitoring the community in exercise 16 uses the following rejection rule: decide there has been an increase in the probability of birth defects if there are four or more birth defects among 40 independent births.(a) What α is the official using?(b) What will β be, if
In the United States, the probability a child will be born with a birth defect is thought to be 3%. In a certain community, there were 40 independent births during the last year, and three of those had birth defects. Using α = 0.05, would this constitute evidence that this community had an
If the bank wanted to examine a program similar to that of Exercise 14 and wanted a maximum error of estimation of 0.01 with a level of confidence of 95%, how large a sample should be taken? (Assume that the standard deviation of the number of errors remains the same.) LO.1
Another bank is experimenting with programs to direct bill companies for commercial loans. They are particularly interested in the number of errors of a billing program. To examine a particular program, a simulation of 1000 typical loans is run through the program. The simulation yielded a mean of
Do Exercise 3 in Chapter 5 as an analysis of variance problem. You should verify that t2 = F for the two-sample case. LO.1

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