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mathematics
statistics

Questions and Answers of Statistics

DS 10.3.5 presents a data set compiled from a series of clinical trials to investigate the effectiveness of a certain medication in healing an infection. (a) Is it appropriate to say that there is a
A beverage company has three formulations of a soft drink product. DS 10.3.6 gives the results of some taste tests where participants are asked to declare which formulation they like best. Is it
DS 10.3.7 gives a data set of the number of arrivals at a hospital emergency room during one-hour periods. Is there any evidence that it is not reasonable that the number of arrivals are modeled with
DS 10.3.8 gives a data set of the number of radioactive particles emitted from a substance and passing through a counter in one-minute periods. Is there any evidence that it is not reasonable to
Oyster pearls are graded A. B. C. and D depending on whether their diameter is 9-10 mm, 7 9 mm. 5-7 mm, or 0-5 mm. respectively. DS 10.3.9 shows how a farmer's pearl crop was categorized. Is it
A computer manufacturer has four suppliers of electrical circuit boards. Random samples of 200 circuit boards are taken from each of the suppliers and they are classified as being either acceptable
An experiment was conducted to compare three types of asphalt. Samples of each type of asphalt were subjected to repeated loads at high temperatures, and the resulting cracking was analyzed. For type
Seedlings are grown without fertilizer or with one of two kinds of fertilizer. After a certain period of time a seedling's growth is classified into one of four categories, as given in DS 10.4.2.
DS 10.4.3 gives the results of a taste test in which a sample of 200 people in each of three age groups are asked which of three formulations of a soft drink they prefer. Test whether the preferences
A factory has five production lines that assemble electric motors. A random sample of ISO motors is taken from each production line and is given a quality examination. The results are given in DS
An air-conditioner supplier employs four technicians who visit customers to install and provide maintenance for their air-conditioner units. In an after-visit questionnaire the customers are asked to
DS 10.4.6 presents a 2 × 2 contingency table that compares two drugs with respect to the speed with which a patient recovers from an ailment. Let ps be the probability that a patient recovers in
In the manufacture of semiconductors, reactive ion etching is a technique whereby the surface of the semiconductor is bombarded with ions to remove unwanted material and to leave the desired
A company's sales records show that an extended warranty was purchased on 38 out of 89 sales of a product of type A, an extended warranty was purchased on 62 out of 150 sales of a product of type B.
Crystallization is an important step in the recovery and purification of biological molecules such as enzymes and proteins. The determination of conditions that produce suitable crystals is of great
A garage sells tires of types A. B. and C. and this year's and last year's sales of the three types are given in DS 10.6.5. Is there evidence of a change in the preferences for the three types of
DS 10.6.6 gives the results of a set of clinical trials involving three different medications. Test whether the three medications are equally effective at treating the infection.
DS 10.6.7 presents the results of an opinion poll conducted on students in the College of Engineering and students in the College of Arts and Sciences. Is there any evidence that opinions differ
The dimensions of 3877 manufactured parts were examined and 445 were found to have a length outside a specified tolerance range. (a) Conduct a hypothesis test to investigate whether there is
In a research report on the effect of moisture on a certain kind of composite material, it is reported that in 80' < of cases the effect is minimal, in 15% of cases the effect is strong, and in the
An experiment is performed to investigate the best way to produce a chemical solution. Three different preparation methods are considered, and various trials are conducted with each method. The
Three types of a metal alloy were investigated to see how much damage they suffered when subjected to a high temperature. A total of 220 samples were obtained for each alloy, and after being
A company's orders are classified as coming from geographical area A, B, C, or D. Over a certain period, there were 119 orders from area A. 54 orders from area B. 367 orders from area C. and 115
An experimenter obtained 84 samples of concrete. When the samples were each subjected to a load of size 115, a total of 17 of the samples broke while the other samples were unharmed. The remaining 67
When a random sample of 64 male students was asked their opinion on a proposal, 28 of them expressed support. Also, when a random sample of 85 female students was asked their opinion on the proposal.
A consumer watchdog organization takes a random sample of 500 bags of flour made by a company, weighs them, and discovers that 18 of them are underweight. Suppose that legal action can be taken if it
Patients were diagnosed as being either condition A or condition B before undergoing a treatment. The treatment was successful for 56 out of 94 patients classified as condition A, and the treatment
Are the following statements true or false? (a) Contingency tables can be used to summarize count frequencies for discrete data. (b) The degrees of freedom used in a chi-square goodness of fit test
In a customer satisfaction survey a random sample of 635 customers were asked their opinion on the service they received. A total of 485 of these customers replied that they were very satisfied. (a)
The records at the emergency rooms of five hospitals over a certain period of time were examined. Each patient was classified as either being "admitted to the hospital" or as "returned home." as
After large Hoods and the consequent large river Hows, there can be a reduction in the level of the riverbed around the piers of bridges that is known as scouring. This can be a serious problem if
A bank releases a new credit card that is to be targeted at a population group of about 1.000.000 customers. In a trial run the bank mails credit card applications to a random sample of 5000
Upon checking hospital records, a hospital administrator notices that over a certain period of time. 443 out of 564 surgical operations performed in the morning turned out to be a "total success."
Householders are polled on whether they support a tax increase to build more schools. The householders are also asked whether their annual household income is above or below $60,000. The results of
DS 10.6.1 contains a data set collected during an amateur archery contest. Calculate a X2 statistic to assess whether it is appropriate to model the probabilities of a bull's-eye and a missed target
DS 10.6.2 gives a data set of the number of car accidents occurring during evening rush-hour traffic in a certain city. Does it look like it's reasonable to model these with a Poisson distribution?
A random-number generator is supposed to provide numbers that are uniformly distributed between 0 and 1. A total of n = 10.000 simulations are obtained, and they are classified as falling into one of
Use Table IV to determine whether these probabilities are greater than 10%, between 5% and 10%, between 1% and 5%, or less than 1%. Then use a computer package to evaluate them exactly. (a) P(X >
Consider the data set given in DS 11.1.1.(a) Calculate the sample averages 1,(b) Calculate the overall average ...(c) Calculate the treatment sum of squares SSTr.(e) Calculate the total sum of
Complete parts (a)-(i) of Problem 11.1.11 for the data set in DS 11.1.2.(a) Calculate the sample averages 1,(b) Calculate the overall average ...(c) Calculate the treatment sum of squares SSTr.(e)
A factory has three production lines producing glass sheets that are all supposed to be of the same thickness. A quality inspector takes a random sample of n = 30 sheets from each production line and
A retail company is interested in examining whether the time taken for it to obtain approval for a credit card number by phone varies from one day of the week to another. The manager collects the
The data set in DS 11.1.3 concerns the infrared radiation readings from an energy source measured by a particular meter with various levels of background radiation levels. The meter's manufacturers
DS 11.1.4 gives the times taken to perform a numerical task using three different kinds of keyboard layouts for the numerical keys. Perform hand calculations to investigate how the different layouts
A chemical engineer is interested in how polymethyl methacrylate (PMMA) particles can be prepared by dispersion polymerization in the presence of a stabilizer polyvinyl pyrrolidone (PVP). DS 11.1.5
A computer manufacturer has production lines that utilize three different assembly methods. These methods differ in the order in which tasks are performed and the consequent layout of the production
Three catalysts were compared to investigate how they affect the strength of a compound. When catalyst A was used 8 samples of the compound were obtained and the strengths of these 8 samples had a
Find the missing values in the analysis of variance table shown in Figure 11.20. What is the p-value?In Figure 11.20
The data set in DS 11.1.7 is a one-way layout to compare the quality scores of a product made from five different treatment methods.(a) Construct the ANOVA table.(b) Construct pairwise comparisons of
In a one-way layout to compare five treatments an experiment gave n1 = 10, 1= 46.09, n2 = 9, 2 = 42.21, n3 = 9, 3= 55.32, n4 = 7, 4 = 54.62. n5 = 10, 5= 38.79, with Construct pairwise comparisons of
An experiment was performed to compare four metal alloys. Various samples were made of each alloy, and their strengths were measured. The following data were obtained:Type A: sample size 8, sample
Thirty patients with a similar medical condition were randomly allocated among six physicians, so that each physician received exactly five patients. The times in minutes taken for the physicians to
Four samples of water were taken at five different locations along a river and measurements were obtained of the amount of E. Coli colonies within the water as given in DS 11.1.9. Investigate whether
In a one-way layout, seven observations are taken from treatment I and their sum is 327.8, eight observations are taken from treatment 2 and their sum is 381.3, seven observations are taken from
Find the missing values in the analysis of variance table shown in Figure 11.21. What is the p-value?In Figure 11.21
A balanced experimental design has a sample size of n = 12 observations at each of k = 7 factor levels. The total sum of squares is SST = 133.18, and the sample averages are 1 = 7.75, 2 = 8.41, 3
An experiment to compare k = 4 factor levels has n1 = 12 and = 1 = 16.09, n2 = 8 and 2 = 21.55, n3 = 13 and 3 = 16.72. and n4 = 11 and 4 = 17.57. The total sum of squares is SST = 485.53. Compute
An experiment to compare k = 3 factor levels has n1 = 17 and n2 = 32.30. n2 = 20 and 2 = 34.06, and n3 = 18 and 3 = 32.02. Also,Compute the analysis of variance table. What is the p-value?
A balanced experimental design has a sample size of n = 14 observations at each of k = 4 factor levels. The averages and variance estimates at each of the four factor levels are 1 = 0.705 and s21 =
A balanced experimental design has a sample size of n = 11 observations at each of k = 3 factor levels. The sample averages are 1 = 48.05, 2 = 44.74, and 3 = 49.11, and MSE = 4.96. (a) Calculate
A balanced experimental design has a sample size of n = 6 observations at each of k = 6 factor levels. The sample averages are 1 = 136.3, 2 = 152.1, 3 = 125.7, 4 = 130.2, 5 = 142.3, and 6 =
Find the missing values in the analysis of variance table shown in Figure 11.37. What are the p-values?In Figure 11.37
A randomized block design is used to compare k = 3 radar systems for detecting airborne objects. A total of b = 8 objects are flown toward the radar stations and the distances at detection by the
A total of b = 9 golfers are each asked to hit a golf ball with each of k = 4 types of driver. DS 11.2.5 gives the straight line distances traveled by the balls. Are some drivers better than others?
A manufacturing company wants to investigate which of three possible assembly methods for an electric motor is the most efficient. Since there is a fair amount of variability in the expertise of the
A Realtor's office has live agents, and the manager wants to determine who is the best agent. A data set, given in DS 11.2.7, is collected that consists of the agents' commissions in each month of
Find the missing values in the analysis of variance table shown in Figure 11.38. What are the p-values?In Figure 11.38
A randomized block design has k = 4 factor levels and b = 10 blocks. The total sum of squares is SST = 3736.64 and the block sum of squares is SSB1 = 2839.97. The factor level sample averages are 1
A randomized block design has k = 5 factor levels and b = 15 blocks. The total sum of squares is SST = 1947.89 and the block sum of squares is SSB1 = 1527.12. The factor level sample averages are 1
A randomized block design has k = 3 factor levels and b = 8 blocks. The block sum of squares is SSBI = 50.19, and the factor level sample averages are 1 = 5.93, 2 = 4.62, and 3 = 4.78. Also,(a)
Consider the data set given in DS 11.2.1.(a) Calculate the factor level sample averages i(b) Calculate the block sample averages j(c) Calculate the overall average ..(d) Calculate the treatment sum
Complete parts (a)-(k) of Problem 1 1.2.7 for the data set in DS 11.2.2. If the experimenter wants conlidence intervals for the pairwise differences of the factor level means with an overall
DS 1 1.2.3 gives a data set of brightness measurements for b = 7 batches of kaolin processed through k = 3 calciners. The calciner operators are interested in whether their calciners are operating at
An experimenter measured the Young's modulus values of silicon carbide-silica biaxial nanowires. These synthesized nanowires are potentially useful for high-strength composites in which mechanical
The data set in DS 11.4.9 is a one-way layout to compare the hardness measurements of three different alloys.(a) Construct the ANOVA table. What conclusion can you draw from the ANOVA table about the
A randomized block design has four factor levels with sample averages 1 = 11.43. 2 = 12.03, 3 = 14.88, and 4 = 11.76. There are 9 blocks and SSBI = 53.28.1 Also. SSE = 14.12. Compute the ANOVA
An investigation was conducted of the radon levels in five different rivers. Six samples of water were obtained from each river and the radon levels given in DS 11.4.10 were obtained. Construct an
A completely randomized design to compare k = 4 factor levels has n1 = 11 and 1 = 213.7, n2 = 8 and 2 = 206.3. n3 = 13 and 3. = 205.7, and n4 = 12 and 4 = 215.8. The mean square error is MSE =
A courier service buys four new cars of the same make and model, and they are driven under similar city and suburban conditions. Each time the cars are filled with gasoline, the car's mileage and
An experiment is conducted to assess the effect of the temperature during curing of a certain kind of cement. Six batches of the cement are prepared, and each batch is separated into five parts that
A comparison of k = 5 fertilizers is made in a randomized block design that incorporates b = 10 fields of com. Each field is partitioned into five equal areas, and the five fertilizers are randomly
A hospital has k = 4 clinics where it can send blood samples for adhesion measurements of sickle red blood cells to endothelium layers. A hospital administrator decides to perform a randomized block
The insertion gain of a hearing aid is defined to be the difference between the sound pressure level at the eardrum with and without the hearing aid in place. These sound pressure measurements can be
The reduction of drag from air resistance for large road vehicles is an important component of attempts to improve fuel efficiency. Wind tunnel tests were performed on models of four different
When leather is used to produce furniture or clothes, its shrinkage is an important consideration. An experiment was conducted to discover the differences between four different preparation methods
Are the following statements true or false? (a) A one-way layout with only k = 2 treatments is equivalent to an independent samples design for comparing two means. (b) In an ANOVA table the sum of
Suppose that a dependent variable y is related to an explanatory variable x through a linear regression model with β0 = 4.2, β1 = 1.7. and with normally distributed error terms with a zero mean and
Suppose that the purity of a chemical solution y is related to the amount of a catalyst x through a linear regression model with β0 = 123.0. β1 = -2.16. and with an error standard deviation σ =
Consider the linear regression model y = 5 + 0.9x, with σ = 1.4, which relates the air content of a concrete sample x to the porosity of the sample y. (a) What is the expected value of the porosity
Suppose that you wish to use simple linear regression to investigate the relationship between two variables. Why does the model you obtain depend on which variable is chosen as the y variable? How
Consider the linear regression model y = 675.30 - 5.87x with σ = 7.32. which relates the viscosity y of a substance to the temperature x. If a sample of the substance is prepared at temperature 80,
DS 12.11.1 gives the times taken by a class of n = 14 students to finish a math test together with the math SAT scores of the students. Perform the following linear regression analysis with time as
A simple linear regression analysis has n = 20 and R2 = 0.853. What can you say about the p-value for the two-sided hypothesis test of H0: β1 =0?
Consider the data set in DS 12.11.9 from the mining industry that shows the amount of ore processed in various locations together with the resulting amount of gold that was obtained. A linear
Are the following statements true or false? (a) In simple linear regression, the choice of which variable should be designated as the dependent variable and which variable should be designated as the
The data set in DS 12.11.10 shows the size of some files and the times that they took to download from a website. A linear regression model is used to analyze the data with size as the input variable
Pressure changes in seawater affect the speed at which sound is transmitted, and the data set in DS 12.11.11 shows how the underwater speed of sound relates to the depth at which it is measured. Use
The data used in Example 43 arc taken from the data set given in DS 12.11.2, which relates the variable % scrap to the number of times that the metal plate is passed through the rollers. It is useful
DS 12.11.3 contains data from a set of automobile engines concerning the diameter of the bearing and the friction power loss that occurs in the bearing of the engine. Perform a linear regression
A double pipe heat exchanger is a device that allows energy to be exchanged between a hot liquid and a cold liquid. It consists of two concentric pipes of different diameter. The hot liquid flows

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