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biostatistics
Basic Biostatistics Statistics For Public Health Practice 2nd Edition B.Burt Gerstman - Solutions
What term refers to the proportion of individuals who have a condition at a particular point in time?
What term refers to the proportion of individuals at risk of developing a disease who develop the condition over a specified period of time?
Fill in the blank: While quantitative data are described with sums and averages, categorical data are described with counts and ______.
What is the complement of p?
What symbol denotes the population proportion. It also denotes one of the binomial parameters?
What symbol denotes the sample proportion?
Patient preference. Exercise 16.2 stated that seven of eight patients expressed a preference for a particular medical procedure. Use an exact procedure to calculate a 95% confidence interval for p.1. What is the sample size needed to estimate p with a given margin of error?2. What is the sample
AIDS-related risk factor, 90% confidence interval. Calculate a 90%confidence interval for the problem presented in Exercise 16.9.
AIDS-related risk factor. Use the plus-four method to calculate a 95% confidence interval for the prevalence of multiple sexual partners in adult heterosexuals using the information in Exercise 16.1. Recall that 170 of the 2673 subjects reported this behavior.
Patient preference, Fisher’s method. Exercises 16.2 and 16.4 considered a problem in which seven of eight patients expressed a preference for medical procedure A compared to medical procedure B. A Normal approximation test was precluded because of the small
AIDS-related risk factor (Continuity-corrected z-statistic).Recalculate the P-value for Exercise 16.5 using the continuitycorrected z-statistic. Is the P-value from the continuity-corrected zstatistic larger or smaller than that from the non-corrected z-statistic?
AIDS-related risk factor. Exercises 16.1 and 16.3 considered a survey in which 170 of 2673 individuals (6.4%) reported having two or more sexual partners in the prior 12 months. This study was completed in the early 1990s. Suppose an earlier study (completed in the 1970s) suggested that the
Patient preference. For the problem about patient preference described in Exercise 16.2, characterize the sampling distribution of the number of patients preferring method A. Do you think a Normal approximation could be used to describe this sampling distribution?
AIDS-related risk factor. Exercise 16.1 introduced a problem in which a random sample of 2673 adult heterosexuals were asked about presence of an HIV risk factor.(a) Describe the sampling distribution of the number of individuals who are positive for this risk factor.(b) Do you think a Normal
Patient preference. An investigation uses two different methods of nonvolitional muscle function testing to study the effects of parenteral nutrition in debilitated patients. As part of the study, subjects were asked if they preferred method A or B muscle testing(in terms of comfort). Of the eight
AIDS-related risk factor. A national study of AIDS risk factors used a random-digit dialing technique to contact study participants.Among the 2673 heterosexual adults in the sample, 170 reported two or more sexual partners in the past 12 months.a (a) Describe the population to which inferences will
Breast cancer survival. A study of 1225 incident breast cancer cases found that survival varied greatly by stage of disease at diagnosis.The median 7-year survival rate for stage I breast cancer was 92%.For stage II breast cancer, the 7-year survival rate was 71%. For stage II breast cancer, the
Pancreatic cancer survival. Whether a value is a parameter or a statistic often depends on how we state the research question. For example, suppose that we review all the pancreatic cancer cases in a specified region and find that in those cases where surgical resection was performed, the median
Parameter or statistic? Say whether each of the boldface numbers is a parameter or a statistic.(a) Insured? A data set based on 168 hospital discharge summaries shows that 20% of patients were uninsured. (The review takes place in a large referral hospital.)(b) Percent African American. Data from
Tiny population. A tiny population consists of the following values:1 3 5 7 9 This population has μ = 5 and σ = 2.8.h The distribution is flat, as seen in this stemplot:A total of 5C2 = 10 unique samples with n = 2 that can be selected from this population. These samples are:Calculate the mean of
Survey of health problems. A survey selects an SRS of n = 500 people from a town of 55,000. The sample shows a mean of 2.30 health problems per person (standard deviation = 1.65). Based on this information, say whether each of the following statements is true or false. Explain your reasoning in
Cholesterol in undergraduate men. Suppose the distribution of serum cholesterol values in undergraduate men is approximately Normally distributed with mean μ = 190 mg/dL and standard deviation σ = 40 mg/dL.(a) What is the probability of selecting someone at random from this population who has a
Repeated lab measurements. A laboratory kit states that the standard deviation of its results can be expected to vary with σ = 1 unit. A lab technician takes four measurements using this kit.(a) What is the value of the standard deviation of the of the four measurements taken with this kit?(b)
Sampling behavior of a mean. Suppose you could take all possible samples of size n = 25 from a Normal population with mean μ = 50 and σ = 5.(a) Sketch or describe in words the sampling distribution of .Identify landmarks on the horizontal axis of this sampling distribution that are ±1 and ±2
What is statistical inference?
What is a statistical population?
What is a sample?
Suppose you take an SRS from a population and find that 28% of the people in the study have BMIs in excess of 30. You redo the study the following day in the same population and find that this time 35%of the people in the survey have this characteristic. What is the most plausible explanation for
Select the best response: Which of these is a parameter?(a)(b) s(c) μ
What symbol is used to represent the population mean?
What symbol is used to represent the sample mean?
Is the population mean a statistic?
Is the sample mean a statistic?
Fill in the cells in this table with these choices: Population, Sample, Not usually, Yes, Constant, Random variable, Greek character, or Roman character sometimes modified with overhead “hats.”Parameters Statistics Source Calculated?Mathematical Notation
What does it mean when we say that is an unbiased estimator of μ?
What is a sampling distribution of a mean?
What is the name of the statistical principle that indicates that sampling distributions of means tend toward Normality even when the population is not normal when the sample size is large?
What is the name of the statistical principle that states “the value of will approach the value of μ as n gets larger and larger”?
What is another name for “the standard deviation of the sample mean”?
The standard error of the mean is inversely proportional to the _____________ ____________ of the sample size. (Two words.)
Select the best response: The “standard error of the mean” is the standard deviation of the(a) sample distribution.(b) population distribution.(c) sampling distribution of the mean.
True or false? The precision of a sample mean as a reflection of μ is partially determined by the study’s sample size.
Select the best response: The standard error of the mean is(a) proportional to the sample size.(b) inversely proportional to the sample size.(c) inversely proportional to the square root of the sample size.
Complete this sentence: The point estimator of population proportion p is _____________________.
The number of “successes” among n independent Bernoulli trials is governed by this pmf.
Select the best response: The binomial distribution can be approximated with a Normal distribution when the sample is(a) small.(b) moderate.(c) large.
When is a sample is large enough to use a Normal approximation to a binomial?(a) when n ≥ 5(b) when npq ≥ 5(c) when npq < 5
Fill in the blanks. A particular random sample of n observations can be used to calculate a sample mean. We can determine the characteristics of the distribution of means derived by other samples of the size n taken from the same populations without taking additional samples. This distribution is
Fill in the blanks. A particular random sample of n observations can be used to calculate a sample proportion. The count of successes in the sample will vary according to a (a) ____________________ probability distribution with parameters n and (b)____________________. When the sample is large, the
Undercoverage? Undercoverage is a problem that occurs in surveys when some groups in the population are underrepresented in the sampling frame used to select the sample. We can check for undercoverage by comparing the sample with known facts about the population.(a) Suppose we take an SRS of n =
Patient preference. Ten people are given a choice of two treatments.Let p represent the proportion of patients in the patient population who prefer treatment A. Among the 10 patients asked, 7 preferred method A. Assuming there is no preference in the patient population(i.e., p = 0.5), calculate
Misconceived hypotheses. What is wrong with each of the following hypothesis statements?(a) H0: μ = 100 vs. Ha: μ ≠ 110(b) H0: = 100 vs. Ha: < 100(c) H0: =
vs. Ha: ≠ 0.50
Hypothesis statements. Set up null and alternative hypotheses for each of these claims. Use two-sided alternative hypotheses in each instance.(a) A counselor claims that a new method of conflict resolution is less prone to interruption than an old method. Prior experience suggests that clients
Patient satisfaction. Scores derived from a patient satisfaction survey are Normally distributed with μ = 50 and σ = 7.5, with high scores indicating high satisfaction. An SRS of n = 36 is taken from this population.(a) What is the SE of for these data?(b) We seek evidence against the hypothesis
Patient satisfaction (cont.). Exercise 9.3 considered an SRS of n =36 in which was 48.8. A different sample derives = 46.5. Mark this result on the horizontal axis of your sketch of the sampling distribution of . Calculate the zstat for this finding, and explain why this result provides good
P from z. What is the one-sided P-value for zstat = −2.45? What is the two-sided P-value? (Suggestion: Sketch the Normal curve and shade the P-value region.)
P from z. What is the one-sided P-value for a zstat of 1.72? What is the two-sided P-value?
Patient satisfaction (sample mean of 48.8). In Exercise 9.3, you tested H0: μ = 50 based on a sample of n = 36 showing = 48.8. The population had standard deviation σ = 7.5.(a) What is the one-sided alternative hypothesis for this test?(b) Calculate the z-statistic for the test.(c) Convert the
Patient satisfaction survey (sample mean of 46.5). Carry out a hypothesis test for the conditions laid out in Exercise 9.7 for an observed of 46.5. Is this result statistically significant at α = 0.05?
LDL and fiber. A cross-over trial compared serum cholesterol in 13 subjects while on moderate-fiber diets and while on high-fiber diets.The study concluded that the high-fiber diet reduced very-lowdensity lipoprotein cholesterol by 12.5% (P = 0.01).d A dietician criticizes the study by saying that
Lithium. Lithium carbonate is a drug used to treat bipolar mental disorders. The average dose in well-maintained patients is 1.3 mEq/L with standard deviation 0.3 mEq/L. A random sample of 25 patients on lithium demonstrates a mean level ( ) of 1.4 mEq/L. Test to see whether this mean is
Gestational length, African American women, hypothesis test.Studies in the general population suggest that the gestational length of uncomplicated pregnancies varies according to a Normal distribution with μ = 39 weeks with σ = 2 weeks.e A sample of 22 middle-class African American women
Gestational length, African American women, power. Suppose the average gestational length in African American women is actually 38.5 weeks. What was the power of the test described in Exercise 9.11 to detect this difference at α = 0.05(two-sided)?
Gestational length, African American women, sample size. Let us return to the conditions specified in the previous exercise. How large a sample would be needed to detect the proposed difference in gestational lengths with 90% power at α = 0.05(two sided)?
Select the better response: This term is used interchangeably with statistical hypothesis test.(a) Significance test(b) Statistical inference
Select the better response: This is “the hypothesis of no difference.”(a) H0(b) Ha
Select the better response: This is the hypothesis that declares a(nonrandom) difference between the observed results and the hypothesized value.(a) H0(b) Ha
Select the better response: This statistical hypothesis contradicts the research hypothesis.(a) H0(b) Ha
Select the better response: This statistical hypothesis parallels the research hypothesis.(a) H0(b) Ha
Select the better response: This hypothesis is presumed to be true until proven otherwise.(a) H0(b) Ha
What is wrong with this sentence? A statistical hypothesis addresses whether a statement about a statistic is true.
What is wrong with this statement? A one-sided alternative hypothesis considers possible outcomes that are either higher or lower than expected.
Select the better response: The value of the population mean under the null hypothesis (μ0) comes from the _____________.(a) data(b) research question
Fill in the blank: A mean from a Normal population has a Normal sampling distribution with mean μ and a standard deviation equal to the population standard deviation σ divided by the square root of _____________.
Select the better response: The P-value refers to the probability of the data or data more extreme assuming the null hypothesis is _____________.(a) false(b) true
Select the better response: The evidence against the null hypothesis mounts as the P-value gets _____________.(a) larger and larger(b) smaller and smaller
This is the risk a researcher is willing to take in mistakenly rejecting a true null hypothesis.(a) α(b) β(c) 1 − β
Define β.
Define power.
Fill in the cells in this hypothesis testing decision table with “correct rejection of H0” “correct retention of H0,” “type I error,” and “type II error.”Retain H0 Decision Reject H0 Decision H0 is actually true H0 is actually false
NHES. A National Center for Health Statistics survey suggested that, in the late 1970s, the mean serum cholesterol level in men was μ =210 mg/dL with standard deviation σ = 90 mg/dL. You sample n = 36 men from the population and are willing to assume that the sampling distribution of is
Female administrators. The average annual salary of 20 female hospital administrators is $80,900. These administrators believe they make less than their male counterparts because of sex bias. Published results suggest that hospital administrators have an average salary ofμ = $85,100 (σ =
Fathers had heart attacks. Suppose the mean fasting cholesterol of teenage boys in the United States is μ = 175 mg/dL with σ = 50 mg/dL. An SRS of 39 boys whose fathers had a heart attack reveals a mean cholesterol = 195 mg/dL. Use a two-sided test to determine if the sample mean is significantly
University men. An SRS of 18 male students at a university has an average height of 70 inches. The average height of men in the general population is 69 inches. Assume that male height is approximately Normally distributed with σ = 2.8 inches. Conduct a two-sided hypothesis test to determine
Diet and bowel cancer. Histologically confirmed cases of colorectal adenoma were randomly assigned to a treatment group (low-fat, high-fiber diet) or to a control group (regular diet). Participants were screened for new occurrences of colon polyps over the next 4 years.The mean number of new polyps
The criminal justice analogy. A jury having heard the evidence in a criminal case is debating whether to render a verdict of guilty or not guilty. Because it is worse to convict an innocent person of a crime they did not commit than let a guilty person go free, each case starts with a presumption
Lab reagent, hypothesis test. A reference solution used as a lab reagent is purported to have a concentration of 5 mg/dL. Six samples are taken from this solution and the following concentrations are recorded: {5.32, 4.88, 5.10, 4.73, 5.15, 4.75} mg/dL. These six measurements are assumed to be an
Lab reagent, power analysis. Exercise 9.20 failed to show a significant difference in the mean concentrations in a lab reagent and the specified concentration of 5 mg/dL. Now let us assume that the true concentration of the reagent is 4.75. What was the power of the test performed in Exercise 9.20
Misinterpreting a confidence interval. A pharmacist reads that a 95% confidence interval for the average price of a particular prescription drug is $30.50 to $35.50. Asked to explain the meaning of this, the pharmacist says “95% of all pharmacies sell the drug for between $30.50 and $35.50.” Is
Newborn weight. A study reports that the mean birth weight of 81 full-term infants is 6.1 pounds. The study also reports “SE = 0.22 pounds.”(a) What is the margin of error of this estimate for 95% confidence?(b) What is the 95% confidence interval for μ?(c) What does it mean when we say that
Newborn weight. A study takes an SRS from a population of fullterm infants. The standard deviation of birth weights in this population is 2 pounds. Calculate 95% confidence intervals for μ for samples in which:(a) n = 81 and = 6.1 pounds(b) n = 36 and = 7.0 pounds(c) n = 9 and = 5.8 pounds
90% confidence intervals. Calculate 90% confidence intervals for μbased on the information reported in Exercise 10.3a–c.
SIDS. A sample of 49 sudden infant death syndrome (SIDS) cases had a mean birth weight of 2998 g. Based on other births in the county, we will assume σ = 800 g. Calculate the 95% confidence interval for the mean birth weight of SIDS cases in the county.Interpret your results.
99% confidence interval. Use the information in Exercise 10.5 to calculate a 99% confidence interval for μ.
Hemoglobin. Hemoglobin levels in 11-year-old boys vary according to a Normal distribution with σ = 1.2 g/dL.(a) How large a sample is needed to estimate mean μ with 95%confidence so the margin of error is no greater than 0.5 g/dL?(b) How large a sample is needed to estimate μ with margin of
Sugar consumption. Based on prior studies, a dental researcher is willing to assume that the standard deviation of the weekly sugar consumption in children in a particular community is 100 g.(a) How large a sample is needed to estimate mean sugar consumption in the community with a margin of error
Fill in the blank: The two forms of estimation are point estimation and _____________ estimation.
While the goal of hypothesis testing is to test a claim, the goal of estimation is to estimate a _____________.
Select the best response: is a(n) _____________ estimator of μbecause as a sample size gets larger and larger, we expect to get closer and closer to the true value of μ.(a) biased(b) reliable(c) unbiased
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