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fundamentals of statistics

Questions and Answers of Fundamentals Of Statistics

43 A fair coin is tossed three times, and the events A and B are defined as follows:A: 5At least one head is observed.6 B: 5The number of heads observed is odd.6a. Identify the sample points in the
42 Suppose P1A2 = .4, P1B2 = .7 and P1A B2 = .3 .Find the following probabilities:a. P1Bc2b. P1Ac2c. P1A B2
41 State the additive rule of probability for mutually exclusive events.
28 Detection of rigged school milk prices. Each year, the state of Kentucky invites bids from dairies to supply half-pint containers of fluid milk products for its school districts.In several school
40 Define in words mutually exclusive events.
39 State the additive rule of probability for any two events.
38 State the rule of complements.
37 Define in words the complement of an event.
36 Define in words the intersection of two events.
35 Define in words the union of two events.
Hospital records show that 12% of all patients are admitted for surgical treatment, 16% are admitted for obstetrics, and 2% receive both obstetrics and surgical treatment. If a new patient is
34 Dominant versus recessive traits. An individual’s genetic makeup is determined by the genes obtained from each parent. For every genetic trait, each parent possesses a gene pair, and each parent
33 Post-op nausea study. Nausea and vomiting after surgery are common side effects of anesthesia and painkillers. Six different drugs, varying in cost, were compared for their effectiveness in
32 Matching socks. Consider the following question posed to Marilyn vos Savant in her weekly newspaper column, “Ask Marilyn”:I have two pairs of argyle socks, and they look nearly identical—one
31 Lead bullets as forensic evidence. Chance (Summer 2004)published an article on the use of lead bullets as forensic evidence in a federal criminal case. Typically, the Federal Bureau of
30 Groundwater contamination in wells. Environmental Science & Technology (Jan. 2005) performed a study of methyl tert -butyl ether (MTBE) contamination in New Hampshire wells . Data collected for a
29 Jai alai Quinella bet. The Quinella bet at the parimutuel game of jai alai consists of picking the jai alai players that will place first and second in a game, irrespective of order .In jai alai,
28 ESL students and plagiarism . The Journal of Education and Human Development (Vol. 3, 2009) investigated the causes of plagiarism among six English-as-a-second language (ESL) students taking a
24 Chance of rain. Answer the following question posed in the Atlanta Journal-Constitution : When a meteorologist says, “The probability of rain this afternoon is .4,” does it mean that it will
22 Health risks to beachgoers. According to a University of Florida veterinary researcher, the longer a beachgoer sits in wet sand or stays in the water, the higher the health risk( University of
20 African rhinos. Two species of rhinoceros native to Africa are black rhinos and white rhinos. The International Rhino Federation estimates that the African rhinoceros population consists of 3,610
19 USDA chicken inspection. The United States Department of Agriculture (USDA) reports that, under its standard inspection system, one in every 100 slaughtered chickens passes inspection for fecal
18 Rare underwater sounds. A study of underwater sounds in a specific region of the Pacific Ocean focused on scarce sounds, such as humpback whale screams, dolphin whistles, and sounds from passing
17 Colors of M&Ms candies. In 1940, Forrest E. Mars, Sr., formed the Mars Corporation in order to produce chocolate candies with a sugar shell that could be sold throughout the year and wouldn’t
Use the applet entitled Simulating the Probability of a Head with a Fair Coin to explore the relationship between the proportion of heads on several flips of a coin and the theoretical probability of
16 Simulate the experiment described in Exercise 15, using any five identically shaped objects, two of which are one color and three another. Mix the objects, draw two, record the results, and then
15 Two marbles are drawn at random and without replacement from a box containing two blue marbles and three red marbles.a. List the sample points.b. Assign probabilities to the sample points.c.
14 T wo fair dice are tossed, and the up face on each die is recorded.a. List the 36 sample points contained in the sample space.b. Assign probabilities to the sample points.c. Find the probability
13 Compute the number of ways you can select n elements from N elements for each of the following:a. n = 2, N = 5b. n = 3, N = 6c. n = 5, N = 20
8 Give a scenario where the combinations rule is appropriate for counting the number of sample points.
7 How do you find the probability of an event made up of several sample points?
6 What is an event?
5 Give two probability rules for sample points.
4 What is a Venn diagram?
25 Mongolian desert ants. In the Journal of Biogeography(Dec. 2003) study of ants in Mongolia (central Asia), botanists placed seed baits at 5 sites in the Dry Steppe region and 6 sites in the Gobi
3 Define the sample space.
2 What are the most basic outcomes of an experiment called?
1 What is an experiment?
Suppose a movie reviewer for a newspaper reviews 5 movies each month. This month, the reviewer has 20 new movies from which to make the selection. How many different samples of 5 movies can be
Consider the task of choosing 2 marines from a platoon of 4 to send on a dangerous mission. Use the combinations counting rule to determine how many different selections can be made.
23 How do you choose to argue? Educators frequently lament weaknesses in students’ oral and written arguments. In Thinking and Reasoning (April 2007), researchers at Columbia University conducted a
22 Patent infringement case. Chance (Fall 2002) described a lawsuit charging Intel Corp. with infringing on a patent for an invention used in the automatic manufacture of computer chips. In response,
21 Drug content assessment. Analytical Chemistry (Dec.15, 2009) conducted a study in which scientists used high-performance liquid chromatography to determine the amount of drug in a tablet.
19 Bulimia study. The “fear of negative evaluation” (FNE)scores for 11 female students known to suffer from the eating disorder bulimia and 14 female students with normal eating habits, first
18 Lobster trap placement. In the Bulletin of Marine Science(April 2010) study of lobster trap placement, the variable of interest was the average distance separating traps—called trap spacing
17 Reading Japanese books. In the Reading in a Foreign Language (Apr. 2004) experiment to improve the Japanese reading comprehension levels of University of Hawaii students, 14 students participated
16 Index of Biotic Integrity. The Ohio Environmental Protection Agency used the Index of Biotic Integrity (IBI)to measure the biological condition, or “health,” of an aquatic region. The IBI is
15 Children’s recall of TV ads. Marketing professors at Robert Morris and Kent State Universities examined children’s recall and recognition of television advertisements( Journal of Advertising,
13 Effectiveness of teaching software. Educational software—ranging from video-game-like programs played on Sony PlayStations to rigorous drilling exercises used on computers—has become very
12 Independent random samples selected from two normal populations produced the following sample means and standard deviations:a. Assuming equal variances, conduct the test H0: (m1 - m2) = 0 against
11 Independent random samples are selected from two populations and are used to test the hypothesis H0: (m1 - m2) = 0 against the alternative Ha: (m1 - m2) 0. An analysis of 233 observations from
10 Two independent random samples have been selected, 100 observations from population 1 and 100 from population 2.Sample means x1 = 70 and x2 = 50 were obtained. From previous experience with these
9 Independent random samples from normal populations produced the following results: (saved in the LM9_9 file).a. Calculate the pooled estimate of s2.b. Do the data provide sufficient evidence to
7 Independent random samples of 100 observations each are chosen from two normal populations with the following means and standard deviations:Let x1 and x2 denote the two sample means.a. Give the
5 A confidence interval for (m1 - m2) is (-10, -4). Which of the following inferences is correct?a. m1 7 m2b. m1 6 m2c. m1 = m2d. no significant difference between means
4 A confidence interval for (m1 - m2) is (-10, 4). Which of the following inferences is correct?a. m1 7 m2b. m1 6 m2c. m1 = m2d. no significant difference between means
3 Two populations are described in each of the cases that follow. In which cases would it be appropriate to apply the small-sample t -test to investigate the difference between the population
1 Describe the sampling distribution of (x1 - x2) when the samples are large.
Suppose you wish to compare a new method of teaching reading to “slow learners” with the current standard method. You decide to base your comparison on the results of a reading test given at the
Find the observed significance level for the test in Example 2 . Interpret the result.
Refer to the study of obese people on a low-fat diet and a regular diet presented in Example 1 . Another way to compare the mean weight losses for the two different diets is to conduct a test of
The effect of drugs and alcohol on the nervous system has been the subject of considerable research.Suppose a research neurologist is testing the effect of a drug on response time by injecting 100
3 What is the level of significance of a test of hypothesis?
8 Consider a test of H0: m = 4 . In each of the following cases, give the rejection region for the test in terms of the z -statistic:a. Ha: m 7 4, a = .05b. Ha: m 7 4, a = .10c. Ha: m 6 4, a = .05d.
11 Play Golf America program. The Professional Golf Association (PGA) and Golf Digest have developed the Play Golf America program, in which teaching professionals at participating golf clubs provide
12 Calories in school lunches. A University of Florida economist conducted a study of Virginia elementary school lunch menus. During the state-mandated testing period, school lunches averaged 863
13 A camera that detects liars. According to New Scientist(January 2, 2002), a new thermal imaging camera that detects small temperature changes is now being used as a polygraph device. The United
14 Effectiveness of online courses. The Sloan Survey of Online Learning, “Making the Grade: Online Education in the United States, 2006,” reported that 60% of college presidents believe that
17 Mercury levels in wading birds. According to a University of Florida wildlife ecology and conservation researcher, the average level of mercury uptake in wading birds in the Everglades has
19 Intrusion detection systems. The Journal of Research of the National Institute of Standards and Technology(November–December 2003) conducted a study of a computer intrusion detection system
Refer to the neurological response-time test set up in Example 3 . The sample of 100 drug-injected rats yielded the results (in seconds) shown in Table 3 . At a = .01, use these data to conduct the
20 Explain the difference between a one-tailed and a twotailed test.
21 What conditions are required for a valid large-sample test for m?
22 For what values of the test statistic do you reject H0? fail to reject H0?
23 A random sample of 100 observations from a population with standard deviation 60 yielded a sample mean of 110.a. Test the null hypothesis that m = 100 against the alternative hypothesis that m 7
24 A random sample of 64 observations produced the following summary statistics: x = .323 and s2 = .034.a. Test the null hypothesis that m = .36 against the alternative hypothesis that m 6 .36, using
25 Suppose you are interested in conducting the statistical test of H0: m = 200 against Ha: m 7 200, and you have decided to use the following decision rule: Reject H0 if the sample mean of a random
26 Speeding and young drivers. Teenage drivers will inevitably be tempted to drive faster, even to exceed the speed limit, by their friends. Did you resist such temptations when you first began to
28 Latex allergy in health care workers. Current Allergy &Clinical Immunology (March 2004) ran a study of n = 46 hospital employees who were diagnosed with a latex allergy from exposure to the powder
32 Identifying type of urban land cover. Geographers use remote-sensing data from satellite pictures to identify urban land cover as either grassland, commercial, or residential.In Geographical
33 Bone fossil study. Humerus bones from the same species of animal tend to have approximately the same lengthto-width ratios. When fossils of humerus bones are discovered, archeologists can often
34 Cooling method for gas turbines. During periods of high demand for electricity—especially in the hot summer months—the power output from a gas turbine engine can drop dramatically. One way to
35 Salaries of postgraduates. The Economics of Education Review (Vol. 21, 2002) published a paper on the relationship between education level and earnings. The data for the research were obtained
36 Dissolved organic compound in lakes. The level of dissolved oxygen in the surface water of a lake is vital to maintaining the lake’s ecosystem. Environmentalists from the University of Wisconsin
Find the observed significance level for the test of the mean response time for drug-injected rats in Examples 3 and 4.
The lengths of stay (in days) for 100 randomly selected hospital patients are reproduced in Table 4 .Suppose we want to test the hypothesis that the true mean length of stay (LOS) at the hospital is
38 How does the observed significance level ( p -value) of a test differ from the value of a?
39 In general, do large p -values or small p -values support the alternative hypothesis Ha ?
40 If a hypothesis test using a = .05 were conducted, for which of the following p -values would the null hypothesis be rejected?a. .06b. .10c. .01d. .001e. .251f. .042
41 For each pair consisting of a and an observed significance level ( p -value), indicate whether the null hypothesis would be rejected.a. a = .05, p@value = .10b. a = .10, p@value = .05c. a = .01,
42 An analyst tested the null hypothesis m Ú 20 against the alternative hypothesis m 6 20. The analyst reported a p -value of .06. What is the smallest value of a for which the null hypothesis would
43 In a test of H0: m = 100 against Ha: m 7 100, the sample data yielded the test statistic z = 2.17. Find the p -value for the test.
44 In a test of H0: m = 100 against Ha: m 100, the sample data yielded the test statistic z = 2.17. Find the p -value for the test.
45 In a test of the hypothesis H0: m = 50 versus Ha: m 7 50, a sample of n = 100 observations possessed mean x = 49.4 and standard deviation s = 4.1. Find and interpret the p -value for this test.
46 In a test of the hypothesis H0: m = 10 versus Ha: m 10, a sample of n = 50 observations possessed mean x = 10.7 and standard deviation s = 3.1. Find and interpret the p -value for this test.
47 Consider a test of H0: m = 75 performed with the computer.SPSS reports a two-tailed p -value of .1032. Make the appropriate conclusion for each of the following situations:a. Ha: m 6 75, z =
48 Speeding and young drivers. Refer to the British Journal of Educational Psychology (Vol. 80, 2010) study of teen age drivers’ temptation to exceed the speed limit, Exercise 26 . Recall that in a
49 Teacher perceptions of child behavior. Refer to the Developmental Psychology (Mar. 2003) study on the aggressive behavior of elementary school children, presented in Exercise 27 . Recall that you
50 Latex allergy in health care workers. Refer to the Current Allergy & Clinical Immunology (March 2004) study of latex allergy in health care workers, presented in Exercise 28. Recall that you
51 Bone fossil study. In Exercise 33 , you tested H0: m = 8.5 versus Ha: m 8.5, where m is the population mean length-to-width ratio of humerus bones of a particular species of animal. A SAS

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