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mathematics
statistics

Questions and Answers of Statistics

Suppose that a 95% confidence interval for (µ1 - µ2) is calculated to be (- 7.4, - 2.3). If we test H0: µ1 = µ2 versus HA: µ1 ≠ µ2 using α = 0.10, will we reject H0? Why or why not?
A dairy researcher has developed a new technique for culturing cheese that is purported to age cheese in substantially less time than traditional methods without affecting other properties of the
A scientist conducted a t test using α = 0.05 and arrived at a P-value of 0.03, which led him to reject H0. µ1 = µ2. However, he made a mistake in his calculations; the correct P-value is 0.23.
In 2005, 5.3% of the deaths in the United States were caused by chronic lower respiratory diseases (e.g., asthma and emphysema). In Arizona, 6.2% of deaths were due to chronic lower respiratory
Suppose an observational study that compares two groups (group 1 and group 2) has sample means 1 = 115 and 2 = 108. Further suppose that we reject H0 in favor of HA when doing a hypothesis test.
Consider the setting of Exercise 7.4.2. (a) What is the explanatory variable? (b) What is the response variable? (c) What are the observational units? Exercise 7.4.2 It has been hypothesized that
In a study of 1,040 subjects, researchers found that the prevalence of coronary heart disease increased as the number of cups of coffee consumed per day increased. (a) What is the explanatory
For an early study of the relationship between diet and heart disease, the investigator obtained data on heart disease mortality in various countries and on national average dietary compositions in
Shortly before Valentine's Day in 1999, a newspaper article was printed with the headline "Marriage makes for healthier, longer life, studies show." The headline was based on studies that showed that
In June 2009, the New York Times published an article entitled "Alcohol's Good for You? Some Scientists Doubt It." The author wrote, "Study after study suggests at alcohol in moderation may promote
In a study of the relationship between birthweight and race, birth records of babies born in Illinois were examined. The researchers found that the percentage of low birthweight babies among babies
Does the release of a Harry Potter book lead children to spend more time reading and thus reduce the number of accidents they have? Doctors in England compared the number of emergency room visits due
For each of the following data sets, use Table 4 to bracket the one-tailed P-value of the data as analyzed by the t test, assuming that the alternative hypothesis isHA: µ1 > µ2.(a)(b)
A pain-killing drug was tested for efficacy in 50 women who were experiencing uterine cramping pain following childbirth. Twenty-five of the women were randomly allocated to receive the drug, and the
Postoperative ileus (POI) is a form of gastrointestinal dysfunction that commonly occurs after abdominal surgery and results in absent or delayed gastrointestinal motility. Does rocking in a chair
An ecologist studied the habitat of a marine reef fish, the six bar wrasse (Thalassoma hardwicke), near an island in French) Polynesia that is surrounded by a barrier reef. He exam-led 48 patch reef
Improvement in quality of life was measured for a group of heart disease patients after 8 weeks in an exercise program. This experimental group was compared to a control group who were not in the
Refer to the data in Exercise 7.5.14. There is one extremely low point in the control group. If that point is deleted, then the summary statistics change, as shown in the following table.(a) What is
A researcher performed a t test of the null hypothesis that two means are equal. He stated that he chose an alternative hypothesis of HA: µ1 > µ2 because he observed 1 > y2. (a) Explain what is
For each of the following data sets, use Table 4 to bracket the one-tailed P-value of the data as analyzed by the t test, assuming that the alternative hypothesis isHA: µ1 > µ2.(a)(b) (c)
For each of the following situations, suppose H0: µ1 = µ2 is being tested against HA: µ1 > µ2. State whether or not there is significant evidence for HA. (a) ts = 3.75 with 19 degrees of freedom,
For each of the following situations, suppose H0: µ1 = µ2 is being tested against HA: µ1 < µ2. State whether or not there is significant evidence for HA. (a) ts = - 1.6 with 23 degrees of
Ecological researchers measured the concentration of red cells in the blood of 27 field-caught lizards (Sceloporus occidetitalis). In addition, they examined each lizard for infection by the malarial
A study was undertaken to compare the respiratory responses of hypnotized and non-hypnotized subjects to certain instructions. The 16 male volunteers were allocated at random to an experimental group
In a study of lettuce growth. 10 seedlings were randomly allocated to be grown in either standard nutrient solution or in a solution containing extra nitrogen. After 22 days of growth, the plants
Research has shown that for mammals giving birth to a son versus a daughter places a greater strain on mothers. Does this affect the health of their next child? A study compared the birth weights of
An entomologist conducted an experiment to see if wounding a tomato plant would induce changes that improve its defense against insect attack. She grew larvae of the tobacco hornworm (Manduca sexto)
A field trial was conducted to evaluate a new seed treatment that was supposed to increase soybean yield. When a statistician analyzed the data, the statistician found that the mean yield from the
Patients with non chronic low back pain were randomly assigned to either a treatment group that received health coaching via telephone plus physiotherapy care or a control group that received only
In a clinical study of treatments for rheumatoid arthritis, patients were randomly allocated to receive either a standard medication or a newly designed medication. After a suitable period of
There is an old folk belief that the sex of a baby can be guessed before birth on the basis of its heart rate. In an investigation to test this theory, fetal heart rates were observed for mothers
Coumaric acid is a compound that may play a role in disease resistance in corn. A botanist measured the concentration of coumaric acid in corn seedlings grown in the dark or in a light/dark
Repeat Exercise 7.6.4, assuming that the means and standard deviations are as given in the table, but that the sample sizes are 10 times as large (that is, n = 40 for "dark" and n = 40 for
As part of a large study of serum chemistry in healthy people, the following data were obtained for the serum concentration of uric acid in men and women ages 18-55 years.Construct a 95% confidence
Repeat Exercise 7.6.7, assuming that the means and standard deviations are as given in the table, but that the sample sizes are only one-tenth as large (i.e., 53 men and 42 women).Exercise 7.6.7As
One measure of the meat quality of pigs is backfat thickness. Suppose two researchers, Jones and Smith, are planning to measure backfat thickness in two groups of pigs raised on different diets. They
Researchers in Norway examined the records of 85,176 children to look for a possible association between use of folic acid during pregnancy and development of autism. The null hypothesis of interest
Refer to the brain NE data of Example 7.2.1. Suppose you are planning a similar experiment; you will study the effect of LSD (rather than toluene) on brain NE. You anticipate using a two-tailed t
Suppose you are planning a greenhouse experiment on growth of pepper plants. You will grow n individually potted seedlings in standard soil and another n seedlings in specially treated soil. After 21
Diastolic blood pressure measurements on American men ages 18-44 years follow approximately a normal curve with µ = 81 mm Hg and σ = 11 mm Hg. The distribution for women ages 18-44 is also
Suppose you are planning an experiment to test the effect of a certain drug treatment on drinking behavior in the rat. You will use a two-tailed t test to compare a treated group of rats against a
Data from a large study indicate that the serum concentration of lactate dehydrogenase (LD) is higher in men than in women. (The data are summarized in Example 7.6.1.) Suppose Dr. Sanchez proposes to
Refer to the painkiller study of Exercise 7.5.10. That study included 25 observations in each treatment group and showed an effect size of about 0.5. If this is the true population effect size, what
Refer to the painkiller study of Exercise 7.5.10. In that study, the evidence favoring the drug was marginally significant (0.025 (a) 80%(b) 90%Exercise 7.5.10A pain-killing drug was tested for
Consider comparing two normally distributed distributions for which the effect size of the difference is (a) 3 (b) 1 In each case, draw a sketch that shows how the distributions overlap.
To determine if the environment can affect sperm quality and production in cattle, a researcher randomly assigned 13 bulls to one of two environments. Six were raised in an open range environment
Refer to the serotonin data of Exercise 7.2.7. On what grounds might an objection be raised to the use of the / test on these data?Exercise 7.2.7Heart disease patients often experience spasms of the
Suppose we have conducted a t test, with α = 0.05 and the P-value is 0.04. For each of the following statements, say whether the statement is true or false and explain why. (a) There is a 4% chance
For each of the following pairs of samples, compute the standard error of 1 - 2).(a)(b) (c)
A developmental biologist removed the oocytes (developing egg cells) from the ovaries of 24 frogs (Xenopus laevis). For each frog the oocyte pH was determined. In addition, each frog was classified
Refer to Exercise 7.S.10. Summary statistics for the pH measurements are given in the following table. We wish to investigate the relationship of oocyte pH to progesterone response using a t test at
A proposed new diet for beef cattle is less expensive than the standard diet. The proponents of the new diet have conducted a comparative study in which one group of cattle was fed the new diet and
Refer to Exercise 7.S.12. Suppose you discover that the study used 25 animals on each of the two diets, and that the coefficient of variation of weight gain under the conditions of the study was
In a study of hearing loss, endolymphatic sac tumors (ELSTs) were discovered in 13 patients. These 13 patients had a total of 15 tumors (i.e., most patients had a single tumor, but two of the
In an investigation of the possible influence of dietary chromium on diabetic symptoms, 14 rats were fed a low-chromium diet and 10 were fed a normal diet. One response variable was activity of the
Refer to Exercise 7.S.15. Use a Wilcoxon-Mann-Whitney test to compare the diets at Î± = 0.05. Use a non directional alternative.Exercise 7.S.15In an investigation of the possible
Refer to Exercise 7.S.15.(a) Construct a 95% confidence interval for the difference in population means.(b) Suppose the investigators believe that the effect of the low-chromium diet is "unimportant"
In a study of the lizard Sceloporus occidentalis, researchers examined field-caught lizards for infection by the malarial parasite Plasmodium. To help assess the ecological impact of malarial
In a study of the effect of amphetamine on water consumption, a pharmacologist injected four rats with amphetamine and four with saline as controls. She measured the amount of water each rat consumed
To investigate the relationship between intracellular calcium and blood pressure, researchers measured the free calcium concentration in the blood platelets of 38 people with normal blood pressure
Researchers studied subjects who had pneumonia and classified them as being in one of two groups: those who were given medical therapy that is consistent with American Thoracic Society (ATS)
A student recorded the number of calories in each of 56 entrees -28 vegetarian and 28 non vegetarian - served at a college dining hall.81 The following table summarizes the data. Graphs of the data
Lianas are woody vines that grow in tropical forests. Researchers measured liana abundance (stems/ha) in several plots in the central Amazon region of Brazil. The plots were classified into two
Androstenedione (andro) is a steroid that is thought by some athletes to increase strength. Researchers investigated this claim by giving andro to one group of men and a placebo to a control group of
The following is a sample of computer output from a study. Describe the problem and the conclusion, based on the computer output. Y = number of drinks in the previous 7 days Two-sample T for
In a controversial study to determine the effectiveness of AZT, a group of HIV-positive pregnant women were randomly assigned to get either AZT or a placebo. Some of the babies born to these women
Patients suffering from acute respiratory failure were randomly assigned to either be placed in a prone (face down) position or a supine (face up) position. In the prone group, 21 out of 152 patients
A study of postmenopausal women on hormone replacement therapy (HRT) reported that they had a reduced heart attack rate, but had even greater reductions in death from homicide and accidents -two
Alice did a two-sample t test of the hypotheses H0:µ1 = µ2 versus HA: µ1 ≠ µ2, using samples sizes of n1 = n2 = 15. The P-value for the test was 0.13, and α was (1.10. It happened that 1 was
Refer to Exercise 7.S.2. Construct a 95% confidence interval for the difference between the population means.Exercise 7.S.2To investigate the relationship between intracellular calcium and blood
Jayden did a two-sample t test of the hypotheses H0:µ1 = µ2 versus HA: µ1 ≠ µ2, using samples sizes of n1 = n2 = 12. The P-value for the test was 0.12, and α was 0.10. Suppose that everything
Omar collects data from two populations. Sahar uses those data to construct a (two-sided) 90% confidence interval for µ1 - µ2 and gets (- 12.5, - 3.7). At the same time, Miguel uses the data to
A group of 477 healthy children, aged 5-11 years, were randomly divided into two groups. Children in the "sugar-free" group were given one can (250 mL) of an artificially sweetened beverage each day
Adults who broke their wrists were randomly divided into two groups. The "intervention" group was given exercises to do under the direction of a physiotherapist. The "control" group did not receive
Parents of newborn babies were divided into three groups as part of an experiment to see if the age at which a baby first walks can be affected by special exercises. For simplicity we will call the
Patients with pleural infection were randomly assigned to be given either an active medical treatment (n = 52) or a placebo (n = 55). One outcome that was measured on each patient was duration of
In a study of methods of producing sheep's milk for use in cheese manufacture, ewes were randomly allocated to either a mechanical or a manual milking method. The investigator suspected that the
A plant physiologist conducted an experiment to determine whether mechanical stress can retard the growth of soybean plants. Young plants were randomly allocated to two groups of 13 plants each.
Refer to Exercise 7.S.6. Construct a 95% confidence interval for the population mean reduction in stem length. Does the confidence interval indicate whether the effect of stress is "horticulturally
Refer to Exercise 7.S.6. The observations (cm), in increasing order, are shown. Compare the treatments using a Wilcoxon-Mann-Whitney test at Î± = 0.01. Let the alternative hypothesis be that stress
Cyclic adenosine monophosphate (cAMP) is a substance that can mediate cellular response to hormones. In a study of maturation of egg cells in the frog Xenopus laevis, oocytes from each of four
In an agronomic field experiment, blocks of land were subdivided into two plots of 346 square feet each. Each block provided two paired observations: one for each of the varieties of wheat. The plot
Consider the data in Exercise 8.2.9. There are two outliers among the 28 differences: the smallest value, which is 2. and the largest value, which is 18. Delete these two observations and construct a
Invent a paired data set, consisting of five pairs of observations, for which 1, and 2 are not equal, and SE1, > 0 and SE2 > 0, but SE = 0.
2 In an experiment to compare two diets for fattening beef steers, nine pairs of animals were chosen from the herd; members of each pair were matched as closely as possible with respect to hereditary
Refer to the cyclic adenosine monophosphate (cAMP) data in Exercise 8.1.1. Use a t test to investigate the effect of progesterone on cAMP. Let HA be non directional and let Î± = 0.10.
4 During a weight loss study, each of nine subjects was given (1) the active drug m-chlorophenylpiperazine (mCPP) for 2 weeks and then a placebo for another 2 weeks, or (2) the placebo for the first
Refer to Exercise 8.2.4. (a) Construct a 99% confidence interval for LLD. (b) Interpret the confidence interval from part (a) in the context of this setting.
Under certain conditions, electrical stimulation of a beef carcass will improve the tenderness of the meat. In one study of this effect, beef carcasses were split in half; one side (half) was
Refer to Exercise 8.2.6. Use a t test to test the null hypothesis of no effect against the alternative hypothesis that the electrical treatment tends to reduce the collagen shrinkage temperature. Let
A scientist conducted a study of how often her pet parakeet chirps. She recorded the number of distinct chirps the parakeet made in a 30-minute period, sometimes when the room was silent and
Construct a scatterplot of the data. Does the appearance of the scatterplot indicate that the pairing was effective?(a) In an agronomic field experiment, blocks of land were subdivided into two plots
Does temperature affect heart rate in humans? One way to address this question is to conduct an experiment. Take 20 test subjects and randomly split them into two groups of size 10 each: 10 to be
Use Table 7 to find the P-value for a sign test (against a non directional alternative), assuming that nD = 9 and (a) Bs = 6 (b) Bs = 7 (c) Bs = 8 (d) Bs = 9
Refer to Exercise 8.4.9. Calculate the exact P-value of the data as analyzed by the sign test. Exercise 8.4.9 The study described in Example 8.1.1, involving the compound mCPP, included a group of
A researcher is planning to conduct an experiment to compare two treatments in which matched pairs of subjects will be given the treatments and a sign test will be used, with a non directional
Use Table 7 to find the P-value for a sign test (against a non directional alternative), assuming that nD = 15 and (a) Bs = 10 (b) Bs = 11 (c) Bs = 12 (d) Bs = 13 (e) Bs = 14 (f) Bs = 15
A group of 30 postmenopausal women were given oral conjugated estrogen for one month. Plasma levels of plasminogen-activator inhibitor type 1 (PAI-1) went down for 22 of the women, but went up for 8
Can mental exercise build "mental muscle"? In one study of this question, 12 littermate pairs of young male rats were used; one member of each pair, chosen at random, was raised in an "enriched"
Twenty institutionalized epileptic patients participated in a study of a new anticonvulsant drug, valproate. Ten of the patients (chosen at random) were started on daily valproate, and the remaining

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