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fundamentals of statistics

Questions and Answers of Fundamentals Of Statistics

30 A random sample of n = 64 observations is drawn from a population with a mean equal to 20 and standard deviation equal to 16.a. Give the mean and standard deviation of the (repeated)sampling
29 Consider the following probability distribution:a. Find m, s2 , and s.b. Find the sampling distribution of x for random samples of n = 2 measurements from this distribution by listing all possible
49 True or False. The sample mean, x, will always be equal to mx.
48 Describe how you could obtain the simulated sampling distribution of a sample statistic.
47 Hand washing versus hand rubbing. The British Medical Journal (August 17, 2002) performed a study comparing the effectiveness of hand washing with soap and hand rubbing with alcohol. Health care
46 Test of Knowledge about Epilepsy. The Test of Knowledge about Epilepsy (KAE), which is designed to measure attitudes toward persons with epilepsy, uses 20 multiple-choice items, all of which are
44 Motivation of drug dealers. Applied Psychology in Criminal Justice (Sept. 2009) conducted an investigation of the personality characteristics of drug dealers. Convicted drug dealers were scored on
42 Cost of unleaded fuel. According to the American Automobile Association (AAA), the average cost of a gallon of regular unleaded fuel at gas stations in August 2010 was$2.78 ( AAA Fuel Gauge Report
41 Critical part failures in NASCAR vehicles. In The Sport Journal (Winter, 2007) analysis of critical part failures at NASCAR races, researchers found that the time x (in hours) until the first
28 Suppose a random sample of n = 25 measurements is selected from a population with mean m and standard deviation s. For each of the following values of m and s, give the values of mx and sx.a. m =
The rolling machine of a steel manufacturer produces sheets of steel of varying thickness. The thickness of a steel sheet follows a uniform distribution with values between 150 and 200 millimeters.
39 Tomato as a taste modifier. Miraculin is a protein naturally produced in a rare tropical fruit that can convert a sour taste into a sweet taste. Plant Science (May 2010) did an investigation of
13 What are the properties of an ideal estimator?
11 What is the difference between a biased and unbiased estimator?
10 What is a point estimator of a population parameter?
6 Refer to Exercise 5 and find E(x) = m. Then use the sampling distribution of x found in Exercise 5 to find the expected value of x. Note that E1x2 = m .
5 Consider the population described by the probability distribution shown here:The random variable x is observed twice. If these observations are independent, verify that the different samples of
2 What is a sampling distribution of a sample statistic?
Consider the popular casino game of craps, in which a player throws two dice and bets on the outcome (the sum total of the dots showing on the upper faces of the two dice). We looked at the possible
12 What is the MVUE for a parameter?
14 Consider the following probability distributiona. Find m and s2 .b. Find the sampling distribution of the sample mean x for a random sample of n = 2 measurements from this distribution.c. Show
27 Suppose a random sample of n measurements is selected from a population with mean m = 100 and variance s2 = 100. For each of the following values of n , give the mean and standard deviation of the
26 Will the sampling distribution of x always be approximately normally distributed? Explain
25 State the Central Limit Theorem.
24 Another name given to the standard deviation of x is the ___________ . (Fill in the blank.)
21 What do the symbols mx and sx represent?
Suppose a population has the uniform probability distribution given in Figure 8 . Then the mean and standard deviation of this probability distribution are, respectively, m = 175 and s = 14.43. Now
20 Refer to Exercise 7, in which we found the sampling distribution of the sample median. Is the median an unbiased estimator of the population mean m?
18 Refer to Exercise 5.a. Show that x is an unbiased estimator of m.b. Find s 2 x .c. Find the probability that x will fall within 2s x of m.
17 Use the computer to generate 500 samples, each containing n = 25 measurements, from a population that contains values of x equal to 1, 2, … , 48, 49, 50. Assume that these values of x are
51 True or False. The standard error of x will always be smaller than s.
38 Assessing the bending strength of a wooden roof. The white wood material used for the roof of an ancient Japanese temple is imported from Northern Europe. The wooden roof must withstand as much as
49 Explain the meaning of the phrase “ pn is an unbiased estimator of p .”
50 If p is near 0 or 1, how large a sample is needed to employ the large-sample confidence interval procedure?
39 Radioactive lichen. In Lichen Radionuclide Baseline Research project at the University of Alaska, researchers collected 9 lichen specimens and measured the amount(in microcuries per milliliter) of
40 Rainfall and desert ants. In the Journal of Biogeography(December 2003) study of ants and their habitat in the desert of Central Asia, botanists randomly selected five sites in the Dry Steppe
41 Pitch memory of amusiacs. Congenital amusia is a disorder that impacts one’s perception of music. A team of psychologists and neuroscientists tested the pitch memory of individuals diagnosed
42 Studies on treating Alzheimer’s disease. Alzheimer’s disease is a progressive disease of the brain. Much research has been conducted on how to treat Alzheimer’s. The journal eCAM (November
44 Minimizing tractor skidding distance. In planning for a new forest road to be used for tree harvesting, planners must select the location that will minimize tractor skidding distance. In the
46 Eating disorders in females. The “fear of negative evaluation”(FNE) scores for 11 bulimic female students and 14 normal female students, saved in the BULIMIA file, are reproduced at the bottom
56 Satellite radio in cars. In the June 2007 survey on satellite radio subscriber service and usage conducted for the National Association of Broadcasters, a random sample of 501 satellite radio
57 National Firearms Survey. The Harvard School of Public Health conducted a survey to determine the size and composition of privately held firearm stock in the United States.In a representative
68 How does the sampling error SE compare with the width of a confidence interval?
69 True or false. For a specified sampling error SE, increasing the confidence level (1 -a) will lead to a larger n in determining the sample size.
70 True or false. For a fixed confidence level (1 - a), increasing the sampling error SE will lead to a smaller n in determining the sample size.
71 If you wish to estimate a population mean to within .2 with a 95% confidence interval and you know from previous sampling that s2 is approximately equal to 5.4, how many observations would you
73 Suppose you wish to estimate a population mean correct to within .15 with a confidence level of .90. You do not know s2, but you know that the observations will range in value between 31 and 39.a.
75 The following is a 90% confidence interval for p : (.26, .54).How large was the sample used to construct this interval?
58 Are you really being served red snapper? Nature (July 15, 2004) conducted a study of fish specimens labeled “red snapper.” Recall that federal law prohibits restaurants from serving a cheaper
61 Teenagers’ use of emoticons in school writing. Due to the popularity of instant messaging and social networking sites among American teenagers, informal elements such as emoticons (e.g., the
62 Characteristics of ice-melt ponds. In a University of Colorado study of ice-melt ponds in the Canadian Arctic, environmental engineers are using data collected by the National Snow and Ice Data
63 Do you believe in the Bible? Data on the approximately 2,800 Americans who participated in the 2004 National Opinion Research Center’s General Social Survey GSS are saved in the BIBLE file. One
66 Studies on treating Alzheimer’s disease. Refer to the journal eCAM (November 2006) assessment of the quality of the methodology used in studies of the treatment for Alzheimer’s disease,
77 Suppose you wish to estimate the mean of a normal population with a 95% confidence interval and you know from prior information that s2 1.a. To see the effect of the sample size on the width of
37 Duration of daylight in western Pennsylvania. What area of the United States has the least amount of daylight, on average?Having grown up in western Pennsylvania, co-author Sincich wonders if it
10 A random sample of 90 observations produced a mean x = 25.9 and a standard deviation s = 2.7.a. Find a 95% confidence interval for the population mean m.b. Find a 90% confidence interval for m.c.
13 Latex allergy in health care workers. Health care workers who use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy.Symptoms of a latex
14 Lipid profiles of hypertensive patients. Hypertension is diagnosed if a patient’s systolic blood pressure exceeds 140 mmHg and diastolic blood pressure exceeds 90 mmHg A study of the lipid
15 Motivation of drug dealers. In the Applied Psychology in Criminal Justice (Sept. 2009) study of the personality characteristics of drug dealers, each in a sample of 100 convicted drug dealers was
16 Laptop use in middle school. The American Secondary Education (Fall 2009) did a study of middle school students’usage of laptop computers. For a sample of 106 students, the researchers reported
Refer to Example 1 and the problem of estimating m , the average length of stay of a hospital’s patients. The lengths of stay (in days) for the n = 100 sampled patients are shown in Table 1 . Use
1 Define the target parameter.
2 What is the confidence coefficient in a 90% confidence interval for m?
3 Explain the difference between an interval estimator and a point estimator for m.
4 Explain what is meant by the statement “We are 95% confident that an interval estimate contains m. ”
7 Find za>2 for each of the following: a. a = .10 c. = b. = .01 .05 d. = .20
17 Albedo of ice melt ponds. The National Snow and Ice Data Center (NSIDC) took a collection of data on the albedo, depth, and physical characteristics of ice-melt ponds in the Canadian Arctic.
18 Extinct New Zealand birds. Evolutionary Ecology Research(July 2003) did a study of the patterns of extinction in the New Zealand bird population. Suppose you are interested in estimating the mean
19 Personality and aggressive behavior. How does personality impact aggressive behavior? A team of university psychologists conducted a review of studies that examined the relationship between
31 Let t0 be a specific value of t . Use Table VI in Appendix:Tables to find t0 values such that the following statements are true:a. P(t Ú t0) = .025, where df = 10b. P(t Ú t0) = .01, where df =
32 Let t0 be a particular value of t . Use Table VI of Appendix:Tables to find t0 values such that the following statements are true:a. P(-t0 6 t 6 t0) = .95, where df = 16b. P(t … -t0 or t Ú t0)
35 Lobster trap placement. Strategic placement of lobster traps is one of the keys for a successful lobster fisherman.An observational study of teams fishing for the red spiny lobster in Baja
28 Compare the shapes of the z - and t -distributions.
27 State the two problems (and corresponding solutions) that arise with using a small sample to estimate m.
20 Shell lengths of sea turtles. The Aquatic Biology (Vol. 9, 2010) performed a study of green sea turtles inhabiting the Grand Cayman South Sound lagoon. The data on curved carapace (shell) length,
22 Speed training in football. A key statistic used by football coaches to evaluate players is a player’s 40-yard sprint time. Can a drill be developed for improving a player’s speed in the
23 Improving SAT scores. Chance (Winter 2001) and National Education Longitudinal Survey (NELS) performed a study of 265 students who paid a private tutor to help them improve their SAT scores. The
24 Attention time given to twins. Psychologists have found that twins, in their early years, tend to have lower IQs and pick up language more slowly than nontwins. ( Wisconsin Twin Research
25 Study of undergraduate problem drinking. In Alcohol &Alcoholism (Jan/Feb. 2007), psychologists at the University of Pennsylvania compared the levels of alcohol consumption of male and female
Some quality control experiments require destructive sampling (i.e., the test to determine whether the item is defective destroys the item) in order to measure a particular characteristic of the
134 Training zoo animals. Teaching of Psychology (May 1998)did a study in which students assisted in the training of zoo animals. A sample of 15 psychology students rated “The Training Game” as a
136 Salmonella in ice cream bars (cont’d). Refer to Exercise 135. Suppose it is now 1 year after the poisoning was traced to ice cream bars. The manufacturer wishes to estimate the proportion who
137 Removing a soil contaminant. A common hazardous compound found in contaminated soil is benzo(a)pyrene[B(a)p]. An experiment was conducted to determine the effectiveness of a method designed to
Choose a population pertinent to your major area of interest—a population that has an unknown mean or, if the population is binomial, that has an unknown probability of success. For example, a
138 Material safety data sheets. For over 20 years, the Occupational Safety & Health Administration has required companies that handle hazardous chemicals to complete material safety data sheets
133 Jail suicide study. Researchers for American Journal of Psychiatry (July 1995) wanted to know what factors increase the risk of suicide by those incarcerated in urban jails. The data on 37
132 Sentence complexity study. Applied Psycholinguistics (June 1998) conducted a study of language skills of low-income children. Each in a sample of 65 low-income children was administered the
123 Al Qaeda attacks on the United States. Studies in Conflict& Terrorism (Vol. 29, 2006) conducted an analysis of incidents involving suicide terrorist attacks. Data on the number of individual
124 Ammonia in car exhaust. Environmental Science &Technology (September 1, 2000) did a study on the ammonia levels near the exit ramp of a San Francisco highway tunnel. The ammonia concentration
125 Oven cooking study. A group of Harvard University School of Public Health researchers studied the impact of cooking on the size of indoor air particles ( Environmental Science & Technology ,
126 Scary-movie study. According to a University of Michigan study, many adults have experienced lingering “fright”effects from a scary movie or TV show they saw as a teenager ( Tampa Tribune ,
128 Research on brain specimens. The postmortem interval(PMI) is the elapsed time between death and the performance of an autopsy on the cadaver. Brain and Language(June 1995) reported on the PMIs of
131 Time to solve a math programming problem. IEEE Transactions presented a hybrid algorithm for solving a polynomial zero–one mathematical programming problem.The algorithm incorporates a mixture
[ Note: This activity is designed for small groups or the entire class.]Consider the length of time a student spends making a cell phone call, sending/retrieving a text message, or accessing e-mail
61 Children’s attitude toward reading. In the journal Knowledge Quest (January/February 2002), education professors at the University of Southern California investigated children’s attitudes
60 Salaries of travel professionals. According to a Natimal Business Travel Association (NBTA) 2008 survey, the average salary of a travel management professional is$97,300. Assume that the standard
59 A random sample of size n is to be drawn from a large population with mean 100 and standard deviation 10, and the sample mean x is to be calculated. To see the effect of different sample sizes on
58 Suppose x equals the number of heads observed when a single coin is tossed; that is, x = 0 or x = 1. The population corresponding to x is the set of 0’s and 1’s generated when the coin is
55 A random sample of n = 68 observations is selected from a population with m = 19.6 and s = 3.2. Approximate each of the following probabilities:a. P(x … 19.6)b. P(x … 19)c. P(x Ú 20.1)d.
54 A random sample of 40 observations is to be drawn from a large population of measurements. It is known that 30%of the measurements in the population are 1’s, 20% are 2’s, 20% are 3’s, and

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