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theory of statistics

Questions and Answers of Theory of Statistics

Refer to the Real Estate data at the back of the text, which report information on homes sold in the Denver, Colorado, area last year.Consider the following variables: selling price, number of
Suppose you recently opened an account with Ameritrade, Inc., an online broker. You have decided to purchase shares of either Johnson & Johnson(a pharmaceutical company) or PepsiCo (the parent
The following chart depicts the amount consumers spent on holiday gifts.Write a brief report summarizing the amounts spent during the holidays. Be sure to include the total amount spent, and the
The table below reports the number of cars and light duty trucks sold by the six largest automakers for the months of January 2006 and January 2007.a. Compare the total sales in the two months. What
The Struthers Wells Corporation employs more than 10,000 white collar workers in its sales offices and manufacturing facilities in the United States, Europe, and Asia. A sample of 300 of these
Using data from such publications as the Statistical Abstract of the United States, The World Almanac, Forbes, or your local newspaper, give examples of the nominal, ordinal, interval, and ratio
Place these variables in the following classification tables. For each table, summarize your observations and evaluate if the results are generally true. For example, salary is reported as a
For the following questions, would you collect information using a sample or a population? Why?a. Statistics 201 is a course taught at a university. Professor A. Verage has taught nearly 1,500
Explain the difference between qualitative and quantitative variables. Give an example of qualitative and quantitative variables not included in the text.
For each of the following, determine whether the group is a sample or a population.a. The participants in a study of a new cholesterol drug.b. The drivers who received a speeding ticket in Kansas
Look in the latest edition of USA Today or your local newspaper and find examples of each level of measurement. Write a brief memo summarizing your findings.
What is the level of measurement for these items related to the newspaper business?a. The number of papers sold each Sunday during 2007.b. The departments, such as editorial, advertising, sports,
What is the level of measurement for each of the following variables?a. Student IQ ratings.b. Distance students travel to class.c. Student scores on the first statistics test.d. A classification of
What is the level of measurement reflected by the following data?(a) The age of each person in a sample of 50 adults who listen to one of the 1,230 talk radio stations in the United States is:(b) In
The Atlanta-based advertising firm Brandon and Associates, asked a sample of 1,960 consumers to try a newly developed chicken dinner by Boston Market. Of the 1,960 sampled, 1,176 said they would
Distinguish among the nominal, ordinal, interval, and ratio levels of measurement.
Describe how a discrete variable is different from a continuous variable.
Distinguish between a qualitative variable and a quantitative variable.
Explain what is meant by descriptive statistics and inferential statistics.
Is this value a statistical outlier? If so, does removing it change the results of the comparison of the two groups?
Data presented in Table 23.9 is collected for comparing two groups of data. The researcher is interested in whether or not there is a difference between the two groups. At the same time she is
An experiment was designed to evaluate different theoretical concentrations of a particular agent. Based on HPLC analysis, the following recoveries were observed.Is the observation at 50% a possible
The analytical laboratory at Acme Chemical assayed a solution that was assumed to be homogeneous, but found the following assay results (in percent). Is 94.673 a possible outlier?89.470, 94.673,
Is the data point 12.9 an outlier from the following set of observations?12.3, 12.0, 12.9, 12.5, 12.4
Production of a certain product in two different countries (A and B) were compared to the manufacturer’s original production site (standard). Dissolution data is presented in Table 22.6 and Figure
In a clinical trial, data comparing Gigantic Drugs’ new generic product was compared with the innovator’s branded antipsychotic; both products contain the exact same chemical entity. One subject
Repeat Problem 3, Chapter 13 (comparison of two analytical methods) using the appropriate nonparametric alternative.
Repeat Problem 3, Chapter 10 (comparison of results from four different laboratories) using an appropriate nonparametric alternative.
Repeat Problem 4, Chapter 9 (comparison of results between two laboratories)using an appropriate nonparametric alternative.
Repeat Problem 2, Chapter 9 (effectiveness of a bronchodilator) using an appropriate nonparametric alternative.
Thirty volunteers for a clinical trial are to be randomly divided into two groups of 15 subjects each. Using a random number table the assignments are presented below. Using the runs test, was the
Six healthy male volunteers are randomly assigned to receive a single dose of an experimental anticoagulant at various dosages. Using Theil’s incomplete method, define the line that best fits these
Two scales are used to measure certain analytical outcome. Method A is an established test instrument, while Method B (which has been developed by the researchers) is quicker and easier to complete.
The absorption of ultraviolet light is compared among three samples. Are there any significant differences among Samples A, B, and C (Table 21.16)?
Following training on content uniformity testing, comparisons were made between the analytical results of the newly trained chemist with those of a senior chemist. Samples of four different drugs
Two groups of physical therapy patients were subjected to two different treatment regimens. At the end of the study period, patients were evaluated on specific criteria to measure percent of desired
Patients are randomly assigned to two different treatments for Stage III prostate cancer. The first is the current gold standard therapy, the second in a combination of products believed to produce
Infection is a common problem associated with a specific surgical procedure. The P&T Committee, based on a review of the literature, wanted to evaluate new Antibiotic B compared to the current
A container manufacturer has developed a new safety closure system for prescription vials. The company tests these closures by asking 30 volunteers to open and close a vial 200 times or until there
Assume that we suspect 15% of the patients with a given risk factor will develop a particular disease. From the literature (or online databases) we see that the test has a sensitivity of 0.75 and
One test for occult blood in the feces has a sensitivity of 52% and a specificity of 91% for colorectal cancer. At the same time the estimated incidence of colorectal cancer in the U.S. for 40-59
Returning to the first example in the problem set for Chapter 2, we employed 150 healthy female volunteers to take part in a multicenter study of a new urine testing kit to determine pregnancy.
During a cholera outbreak in a war-devastated country, records for one hospital were examined for the survival of children contracting the disease. These records also reported the children’s
Modifying Problem 5 in Chapter 16, assume that containers that contained a moisture level
A total of 750 women were followed for a period of ten years following radical mastectomy. A comparison of their survival rates versus whether there was axial node involvement at the time of the
In a retrospective study of 170 randomly selected patients, the researcher is interested in determining if several factors (family history of hyperlipidemia, presence of hypertension, presence of
Using the following information:a) calculate the various measures of association for a 3 × 5 design; andb) indicate which results are best, given the types of variables involved.A survey of
Using the following information:a) calculate the various measures of association for a 3 × 3 design; andb) indicate which results are best, given the types of variables involved.Patients are
Using the following information:a) calculate the various measures of association for a 2 × 2 design; andb) indicate which results are best, given the types of variables involved.Assume an equal
In one of the example problems in Chapter 15, an instrument manufacturer ran a series of disintegration tests to compare the pass/fail rate of a new piece of equipment at two extreme temperatures.
Twenty volunteers were randomly assigned to a randomized three-way crossover clinical trial involving the same topical medication presented in three different formulations (A, B, and C). During each
A manufacturer is experimenting with a new 50-mm diameter screw-type container using various amounts of torque for closure. The tightness of the containers is tested based on moisture permeability.
In preparing to market an approved tablet in a new package design, the manufacturer tests two different blister packs to determine the rates of failure(separation of the adhesive seal) when stored at
Immediately after training on a new analytical method, technicians were asked their preference between the new method and a previously used, “old” method.Six months later, after the technicians
A pharmacist is evaluating the amount of time needed for nurse surveyors to observe drug delivery in 70 long-term care facilities. The median time required by the surveyors is 2.5 hours. The
A medication known to cause severe irritation to stomach mucosa is tested with a series of special tablet coatings to prevent release until after the tablet has passed through the stomach. Three
During preapproval clinical trials with a specific agent, it was found that the incidence of blood dyscrasia was 2.5%. In a later Phase IV study involving 28 patients, two developed blood dyscrasia.
During the development of a final dosage form, the frequency of defects was analyzed to determine the effect of the speed of the tablet press. Samples were collected at 80,000 (lower) and 120,000
During initial Phase I and II studies, the incidence of nausea and vomiting of a new cancer chemotherapeutic agent was 36% for 190 patients, while 75 control patients receiving conventional therapy
During production runs, historically a specific dosage form is expected to have a defect rate of 1.5%. During one specific run, a sample of 100 tablets was found to have a defect rate of 5%. Does
Various dilutions are made of a homogeneous mixture and results analyzed. Is there a linear relationship between the dilution factor and the analytical outcome?
During the formulation of a new product, various percent of a polymeric coating are added and the resultant release of the therapeutic agent is evaluated below. Is there a strong linear relationship
Acme Chemical reassesses the previous results by comparing the data against a reference standard solution at the same concentrations and found the results in the following table. Were the slopes of
Acme Chemical is testing various concentrations of a test solution and the effect the concentration has on the optical density of each concentration.Is there a significant linear relationship between
Samples of a drug product are stored in their original containers under normal conditions and sampled periodically to analyze the content of the medication.Does a linear relationship exist between
A random sample of twelve students graduating from a school of pharmacy was administered an examination to determine retention of information received during classes. The test contained four sections
It is believed that two assay methods will produce identical results for analyzing a specific drug. Various dilutions are assayed using both the currently accepted method (GS) and the proposed
Two drugs (A and B) are commonly used together to stabilize patients after strokes and the dosing for each is individualized. Listed in Table 13.15 are the dosages administered to eight patients
Two different scales are used to measure patient anxiety levels upon admission to a hospital. Method A is an established test instrument, while Method B (which has been developed by the researchers)
In a multicenter study, individuals at seven laboratories trained to perform specific analyses using identical equipment from an instrument manufacturer.Following training, three samples were sent to
An investigator compares three different indexes for measuring the quality of life of patients with a specific disease state. She randomly selects four hospitals and identifies twelve individuals
A preformulation department is experimenting with different fillers and various speeds on a tableting machine (Table 12.10). Are there any significant differences in hardness based on the following
Using Problem 6 in Chapter 10 once again, consider the same results, but use the placebo results as a control. How do the three benzodiazepines compare to the control group?
Problem 6 in Chapter 10, which evaluated various benzodiazepines and responses to a computerized simulated driving test, resulted in the rejection of the null hypothesis μA = μB = μC = μPlacebo.
Consider the results presented in Figure 11.4. Five different dissolution apparatuses (testers) are evaluated to determine if there is significant difference in their results based on testing of a
Problem 3 in Chapter 10 compares the viscosity of a raw material delivered to three different sites.Hypotheses: H0: μA = μB = μC H1: H0 is false Decision rule: With α = 0.05, reject H0 if F >
A prospective study was conducted on 105 patient randomly assigned to one of three HMG-CoA reductase inhibitors for lowering cholesterol levels. After 12 months 94 of the patients were still being
Replicate measures are made on samples from various batches of a specific biological product. The researcher is concerned that the first measure may influence the outcome on the second measure. Using
To evaluate the responsiveness of individuals receiving various commercially available benzodiazepines, volunteers were administered these drugs and subjected to a computer simulated driving test.
Three physicians were selected for a study to evaluate the length of stay for patients undergoing a major surgical procedure. All these procedures occurred in the same hospital and were without
During a clinical trial, Acme Chemical wants to compare two possible generic formulations to the currently available brand product (reference standard). Based on the following results (Table 10.8),
Acme Chemical and Dye received from the same raw material supplier three batches of oil from three different production sites. Samples were drawn from drums at each location and compared to determine
In the previous example, perform a test to determine if there is homogeneity of variance.
In a collaborative trial, four laboratories were sent samples from the same batch of a pharmaceutical product and requested to perform ten assays and report the results based on percentage of a
In a major cooperative of hospitals the average length of stay for kidney transplant patients is 21.6 days. In one particular hospital the average time for 51 patients was only 18.2 days with a
A study was undertaken to determine the cost effectiveness of a new treatment procedure for peritoneal adhesiolysis. Twelve pairs of individuals who did not have complications were used in the study,
An examination evaluating cognitive knowledge in basic pharmacology was mailed to a random sample of all pharmacists in a particular state. Those responding were classified as either hospital or
Following training on content uniformity testing, comparisons are made between the analytical result of the newly trained chemist with those of a senior chemist.Samples of four different drugs
A first-time-in-man clinical trial was conducted to determine the pharmacokinetic parameters for a new calcium channel blocker. The study involved 20 healthy adult males and yielded the following
Samples are taken from a specific batch of drug and randomly divided into two groups of tablets. One group is assayed by the manufacturer’s own quality control laboratories. The second group of
Calculate the mean, standard deviation, relative standard deviation, and 95%confidence interval for each of the time periods presented in the following dissolution profile (percentage of label claim)
Twelve subjects in a clinical trial to evaluate the effectiveness of a new bronchodilator were assessed for changes in their pulmonary function. Forced expiratory volume in one second (FEV1)
Two groups of physical therapy patients are subjected to two different treatment regimens. At the end of the study period, patients are evaluated on specific criteria to measure the percent of
Analyzing a drug substance compared to its reference standard produces the following results.103.5% 99.2% Mean = 99.97 101.2% 100.9% SD = 2.42 96.6% 98.4%If the reference standard has a 2%
In order to calculate the average density of objects it is necessary to calculate the weight and volume of each object and calculate density using the formula:density = mass/volume. Initial data
If power is calculated to be 85%, with a Type I error rate of 5%, what are the percentages associated with the four possible outcomes associated with hypothesis testing? What if the power was only
Write the alternate hypothesis for each of the following null hypotheses:a. μA = μBb. μH ≥ μLc. μ1 = μ2 = μ3 = μ4 = μ5 = μ6d. μA ≤ μBe. μ = 125f. Populations C, D, E, F, and G are
During the production of a specific solid dosage form it is expected that the standard deviation (σ) for the specific strength will be approximately 3.5 mg, based on experience with the product.
Assume that a manufacturer has set the upper and lower specification limits to be within 20% of the target for a given process (USL = 1.20 and LSL = 0.80). A random sample of 100 samples during a
During a production run of an injectable agent, 20 ampules are randomly sampled. Listed below are the volumes contained in each ampule. What are the tolerance limits, by volume, within which we would

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