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biostatistics

Basic Biostatistics Statistics For Public Health Practice 2nd Edition B.Burt Gerstman - Solutions

Select the best response: This is the “wiggle room” placed around the point estimate to derive a confidence interval.(a) standard deviation(b) standard error(c) margin of error
Select the best response: This is the larger of the two numbers listed when reporting a confidence interval.(a) point estimate(b) lower confidence limit(c) upper confidence limit
Select the best response: The confidence interval for the mean seeks to capture the _____________.(a) sample mean(b) population mean(c) population standard deviation
Select the best response: The standard error of the mean is inversely proportional to the _____________.(a) standard deviation(b) sample size(c) square root of the sample size
What percentage of 90% confidence intervals for μ will fail to capture μ?
What percentage of (1 − α)100% confidence intervals for μ will fail to capture μ?
Select the best response: Which of the following reflects the precision of as an estimate of μ?(a) the margin of error m(b) the confidence interval length(c) both (a) and (b)
Select the best response: The margin of error m for the (1 − α)100%confidence interval for μ is equal to z1−α/2 times the _____________.(a) sample mean(b) standard deviation (c) standard error of the mean
Select the best response: To cut the margin of error in half, we must _____________ the sample size.(a) double(b) triple(c) quadruple
Select the best response: For the same set of data, which confidence interval will be the longest?(a) the 90% confidence interval for μ(b) the 95% confidence interval for μ(c) the 99% confidence interval for μ
Select the best response: Which of the following α levels is associated with 95% confidence?(a) 1%(b) 5%(c) 10%
Select the best response: Which of the following z critical values is used to achieve 95% confidence?(a) z0.90(b) z0.95(c) z0.975
Laboratory scale. The manufacturer of a laboratory scale claims their scale is accurate to within 0.0015 g. You read the documentation for the scale and learn that this means that the standard deviation of an individual measurement (σ) is equal to 0.0015 g. Assume measurements vary according to a
Antigen titer. A vaccine manufacturer analyzes a batch of product to check its titer. Immunologic analyses are imperfect, and repeated measurements on the same batch are expected to yield slightly different titers. Assume titer measurements vary according to a Normal distribution with mean μ and
Newborn weight. The 95% confidence interval for the mean weight of infants born to mothers who smoke is 5.7 to 6.5 pounds. The mean weight for all newborns in this region is 7.2 pounds. Is the birth weight of the infants in this sample significantly different from that of the general population at
Reverse engineering the confidence interval. The 95% confidence interval in Exercise
(5.7 to 6.5 pounds) was calculated with the usual formula Confidence intervals constructed in this way are symmetrical around the mean; is the mid-point of the confidence interval.(a) What is the value of the sample mean used to calculate the confidence interval?(b) What is the margin of error of
True or false? Answer “true” or “false” in each instance. Explain each response.(a) 95% of 95% confidence intervals for a mean will fail to capture .(b) 95% of 95% confidence intervals for a mean will fail to capture μ.(c) 95% of 95% confidence intervals for a mean will capture μ.
True or false? A confidence interval for μ is 13 ± 5.(a) The value 5 in this expression is the estimate’s standard error.(b) The value 13 in this expression is the estimate’s margin of error.(c) The value 5 in this expression is the estimate’s margin of error.
True or false?(a) Populations with high variability will produce estimates with large margins of error (all other things being equal).(b) Studies with small sample sizes will tend to have large margins of error.
Lab reagent, 90% confidence interval for true concentration.Exercise 9.20 presented six measurements of a reagent in which the true concentration of the reagent was uncertain. The sample mean based on these six measurements was 4.9883 mg/dL. The distribution of an infinite number of concentration
Lab reagent, 99% confidence interval for true concentration.Calculate a 99% confidence interval for the true concentration of the solution considered in the prior exercise. Interpret the results. How does this confidence interval compare the 90% confidence interval?
Blood pressure. A study of 35 individuals found mean systolic blood pressure with sample standard deviation s = 10.3 mmHg.(a) Calculate the standard error of the mean based on this information.(b) How many individuals would you need to study to decrease the standard error of the mean to 1 mmHg?
Published report. An article published in the American Journal of Public Health that reported the relation between tall stature and cardiovascular disease mortality included a table with the column heading “Mean Height, cm. (SE).” One entry in the table based on n= 1243 individuals was “173.2
Sketch a curve. Use Table C to determine the values on a t22 distribution that captures the middle 95% of the area under the curve.Sketch the curve showing the t-values on the horizontal axis and associated tail areas.
t-percentiles. Use Table C to determine the value of a t-random variable with 19 degrees of freedom and a cumulative probability of 0.95. In addition, determine the value of t19,0.05.
Probabilities not in Table C. There are times you may need to determine a probability for a t-random variable that does not appear in Table C. For example, you may need to determine the probability a t-random variable with 8 degrees of freedom is greater than 2.65.Even though this value is not in
Upper tail. Determine the probability that a t-random variable with 8 df is greater than 2.98.
Software utility programs. The Internet has many free applets that can determine exact probabilities for t-random variables.f You can also use WinPepig WhatIs.exe or Microsoft Excel’s TDIST function for this purpose. Use one of these software applications to find:(a) Pr(T8≥ 2.65)(b) Pr(T8≥
P-value from t stat. A test of H0: μ = 0 based on n = 16 calculates t stat =2.44.(a) Determine the degrees of freedom for the test statistic.(b) Provide the t-values from the Table C that bracket the t stat.(c) What is the approximate one-sided P-value for the problem?(d) What is the two-sided
Critical values for a t-statistic. The term critical value is often used to refer to the value of a test statistic that determines statistical significance at some fixed α level for a test. For example, ±1.96 are the critical values for a two-tailed z-test at α = 0.05. In performing a t-test
BMI. Body mass index . An adult BMI of 24 is considered desirable.i A study of 12 adults that used a onesample t-test to address H0: μ = 24 reported a t stat of 2.16.(a) What is the one-sided P-value for this test?(b) What is the two-sided P-value?
Menstrual cycle length. Menstrual cycle lengths (days) in an SRS of nine women are as follows: {31, 28, 26, 24, 29, 33, 25, 26, 28}. Use this data to test whether mean menstrual cycle length differs significantly from a lunar month. (A lunar month is 29.5 days.)Assume that population values vary
t-values for confidence. What is the value of tn−1,1−α/2 when calculating a 95% confidence interval for μ based on n = 28? What is tn−1,1−α/2 for 90% confidence?
Menstrual cycle length. Exercise
calculated the mean length of menstrual cycles in an SRS of n = 9 women. The data revealed days with standard deviation s = 2.906 days.(a) Calculate a 95% confidence interval for the mean menstrual cycle length.(b) Based on the confidence interval you just calculated, is the mean menstrual cycle
Placebo effect in Parkinson’s disease patients. The placebo effect occurs when a patient experiences a perceived benefit after receiving an inert substance. To help understand the mechanism behind this phenomenon in Parkinson’s disease patients, investigators measured striatal RAC binding at a
units on a placebo in the six subjects (sd = 0.181).l Test this difference for statistical significance.
Water fluoridation. A study looked at the number of cavity-free children per 100 in 16 North American cities BEFORE and AFTER public water fluoridation projects. Table
lists the data.(a) Calculate delta values for each city. Then construct a stemplot of these differences. Interpret your plot.(b) What percentage of cities showed an improvement in their cavity-free rate?(c) Estimate the mean change with 95% confidence.
When do you use a t-procedure instead of a z-procedure to help infer a mean?
Describe the shape, location, and spread of t-distributions.
How many different t-distributions are there?
The mean of a t-distribution is equal to _______.
How do t-distributions differ from Standard Normal z-distributions?
Select the best response: The total area under a t-curve is equal to(a) −1(b) 0(c) 1
Select the best response: In the notation tdf,p, the subscript df represents the(a) degrees of freedom for the t-distribution.(b) probability of t.(c) cumulative probability of t (AUC to the left of the t-value).
Select the best response: In the notation tdf,p, the subscript p represents the(a) degrees of freedom for the t-distribution.(b) probability of t.(c) cumulative probability of t (AUC to the left of the t-value).
Determine the value of t8,0.50 without the aid of a t-table.
t9,0.90= 1.383; therefore, t9,0.10= ? (t-table not required)
A t-distribution with 60 or more degrees of freedom is very nearly a _________ distribution.
The standard error of the mean is equal to the sample standard deviation divided by the square root of _______.
Select the best response: In the statement H0: μ = μ0, μ0 represents the value of the population mean when the null hypothesis is ______.(a) true(b) false(c) either true or false
Select the best response: With matched paired sample, the null hypothesis is most often H0: μ = ______.(a) −1(b) 0(c) 1
A one-sample t-procedure with 35 observations has this many degrees of freedom.
The P-value for a two-sided t-test is equal to(a) the area under the curve to the right of the t-statistic.(b) twice the area under the curve to the right of the t-statistic.(c) twice the area under the curve to the right of the absolute value of the t-statistic.
Select the best response: P-values assume that(a) the null hypothesis is true.(b) the null hypothesis is false.(c) the null hypothesis is neither true nor false.
Select the best response: A t-test derives a P-value of 0.06. The Pvalue represents the probability that(a) the null hypothesis is true.(b) the null hypothesis is false.(c) we would see the data or data that are more extreme assuming the null hypothesis is true.
Select the best response: A 95% confidence for μ is used to infer the value of the(a) sample mean.(b) population mean.(c) population standard deviation.
Select the best response: A 95% confidence interval for a mean is−0.91 to 1.36. From this we can infer with 95% confidence that the(a) population mean is 0.(b) population mean is greater than 0.(c) population mean is greater than −0.91.
Select the best response: A 95% confidence interval for a mean is 0.86 to 1.66. From this we can infer with 95% confidence that the(a) population mean is 1.(b) population mean is greater than 1.(c) neither of the above
Select the best response: A 95% confidence interval for a mean is 0.91 to 1.36. From this we can infer with 95% confidence that the(a) population mean is 0.(b) population mean is greater than 0.(c) population mean is less than 0.
Select the best response: A 95% confidence interval for a mean is 0.91 to 1.36. From this we can infer with 95% confidence that the population mean is(a) not more than 0.91.(b) not less than 0.91.(c) not less than 1.36.
Select the best response. Paired samples can be achieved via(a) pretest/posttest samples.(b) matching closely on extraneous factors when sampling.(c) both “a” and “b.”
Select the best response: Paired t-procedures focus on the data in the(a) first sample in the pair.(b) second sample in the pair(c) differences between the first and second samples in the pair.
Select the best response: These conditions are needed for valid tprocedures:(a) SRS of individual or paired difference (or reasonable approximation thereof)(b) Normality of the sampling distribution of the mean(c) both “a” and “b”
Select the best response: The sampling distribution of a mean will be approximately Normal even when the population is not exactly Normal as long as the sample is(a) representative.(b) large.(c) small.
List the determinants of the sample size requirements for estimatingμ with a margin of error m.
List the determinants of the sample size requirements when testing a mean at a given α level.
List the determinants of the power of a t-test.Exercises 11.16 t-percentiles. Use Table C to determine the following values of tvalues:(a) t24,0.975(b) t674,0.99(Suggestion: Because there is no row for df = 674, use the row with df = 100 to derive a conservative estimate for the t critical
Large t-statistic. A t-test calculates t stat = 6.60. Assuming the study had more than just a few observations, you do not need a t table or software utility to draw a conclusion about the test. What is this conclusion, and why is a look-up table unnecessary?
Sketch and shade. In testing H0: μ = 0, you find and s = 1.497 based on n = 50. Calculate the t stat for the test. Sketch a t-curve as accurately as possible. Then place this t stat on your curve. Without using Table C, do you think these results would be surprising if H0 were true?
Vector control in an African village. A study of vector control in an African village found that the mean sprayable surface area was 249 square feet with standard deviation 39.82 square feet in a simple random sample of n = 100 homes.(a) Calculate a 95% confidence interval for μ.(b) Would it be
Calcium in sound teeth. The calcium content values in a sample n =5 sound teeth (% calcium) are {33.4, 36.2, 34.8, 35.2, 35.5}. Provide a 99% confidence interval for μ. (Assume the data represent an SRS of healthy adult teeth.)
Boy height. An SRS of n = 26 boys between the ages of 13 and 14 has a mean height of 63.8 inches with a standard deviation 3.1 inches. Calculate a 95% confidence interval for the mean height of the population.
Body weight, high school girls. Body weights expressed as a percentage of ideal in an SRS of n = 9 girls selected at random are as follows {114, 100, 104, 94, 114, 105, 103, 105, 96}.(a) Plot the data as a stemplot. (Use an axis multiplier of 10 and split stem values.) Are there any outliers or
Faux pas. Eight junior high school students were taken to a shopping mall. The number of socially inappropriate behaviors (faux pas) by each student was counted. The students were then enrolled in a program designed to promote social skills. After completing the programs, the subjects were again
Power. A researcher fails to find a significant difference in mean blood pressure in 36 matched pairs. The standard deviation of the differences was 5 mmHg. What was the power of the test to find a mean difference of 2.5 mmHg at α = 0.05(two sided)?
Beware α = 0.05. Two trials looked at red wine consumption in lowering cholesterol levels in hypercholesterolemic men. In each trial, 25 men consumed 8 ounces of red wine for 14 days.(a) In trial A, the 25 subjects lowered their cholesterol by an average of 5% (standard deviation = 11.9%). In
Benign prostatic hyperplasia, quality of life. Benign prostatic hyperplasia is a noncancerous enlargement of the prostate gland that adversely affects the quality of life of millions of men. A study of a minimally invasive procedure for the treatment for this condition looked at pretreatment
Benign prostatic hyperplasia, maximum flow. Table 11.4 also contains data for maximum urine flow at baseline (MAXFLO_B) and maximum urine flow after 3 months of treatment (MAXFLO3M). Test the mean difference in this outcome for statistical significance.
NASA experiment. A NASA study compared two methods of determining white blood cell counts in laboratory animals. Table 11.5 lists results for 42 paired observations. Calculate DELTA values for each observation and plot these differences as a stemplot. Based on this plot, do you think the methods
Therapeutic touch.r Proponents of an alternative medical treatment known as therapeutic touch claim that each person has a human energy field (HEF) that can be perceived and manipulated by touch.Therapists trained to recognize HEF-related perceptions are said to be particularly adept at
Therapeutic touch, n = 28. This exercise is an extension of Exercise 11.29. We add 8 observations to the initial 20, bringing the total sample size to 28. Each observation consists of 10 attempts to identify a human energy field, as previously discussed (see Figure 11.7). The number of correct
Sampling designs. Identify whether the studies described here are based on (1) single samples, (2) paired samples, or (3) independent samples.(a) An investigator compares vaccination histories in 30 autistic schoolchildren to an SRS of nonautistic children from the same school district.(b)
Needle-stick injuries. Healthcare workers are at risk of being exposed to blood-borne pathogens through needle-stick and other sharp object injuries. The pathogens of primary concern are the human immunodeficiency virus, hepatitis B virus, and hepatitis C virus. When a needle-stick injury occurs,
Facetious data. Imagine a study of six monkeys that compares two treatments. Group 1 receives Monkey Tonic while group 2 receives Applied Monkey Training (AMT). Table
lists the performance scores BEFORE and AFTER these interventions.(a) Calculate mean performance scores in each group before the intervention. Then calculate the mean difference. Is this mean difference based on paired or independent samples?(b) Within group 1 (individuals 1 through 3), calculate
Histidine excretion. A study measures total histidine excretion(milligrams) in 24-hour urine samples in men and women on proteinrestricted diets. The histidine values (mg) for men are {172, 204, 229, 236, and 256}. The values for women are {115, 135, 138, 174, 197, and 224}. Table 12.8 also lists
“Histidine excretion data” for Exercises 12.4, 12.6, and 12.8. Data are milligrams of histidine in 24-hour urine samples.Source unknown. Data stored online in the file HISTIDINE.SAV.(b) Calculate means and standard deviations for each group. Relate these statistics to the stemplot created in
Air samples. A study of environmental air quality measured suspended particulate matter in air samples at two sites. Data (μg/m3)for site 1 are {68, 22, 36, 32, 42, 24, 28, and 38}. Data for site 2 are{36, 38, 39, 40, 36, 34, 33, and 32}. Table 12.9 also lists the data.TABLE
“Air samples data” for Exercises 12.5 and 12.7. Data are suspended particulate matter in air samples(μg/m3).Data are fictitious and are stored online in the file AIRSAMPLES.SAV.(a) Create back-to-back stemplots of data from these sites. Discuss the results.(b) Calculate group means and
Histidine excretion. Exercise 12.4 introduced data in which 24-hour histidine excretion was compared in men and women on proteinrestricted diets. Data are listed in Table 12.8. Table 12.11 lists means and standard deviations from this data set.TABLE
Means and standard deviations for Exercise 12.6.(a) Calculate the standard error of the mean difference without assuming equal variances.(b) A computer program calculates dfWelch≈ 9 for these data. Based on this df, calculate a 95% confidence interval for μ1− μ2.(c) Calculate the two-sided
Air samples. The air quality data in Exercise 12.5(Table 12.9) are associated with the summary statistics reported in Table 12.12.TABLE 12.12 Means and standard deviations for Exercise 12.7.(a) Calculate the standard error of the mean difference without assuming equal variance.(b) Calculate a 95%
Histidine, equal variance assumed. Redo the histidine excretion analyses (Exercise 12.6) with equal variance t procedures.
Sample size calculation. We wish to detect a mean difference of 0.25 for a variable that has a standard deviation of 0.67. How large a sample is needed to detect the mean differences with 90% power at α= 0.05(two-sided)?
Sample size requirement, cholesterol comparison. A variable has a standard deviation of 40 mg/dL. We want to test a mean difference in two groups with α =
(two-sided) and power = 80%.(a) How many observations are needed to detect a difference of 10 mg/dL?(b) Suppose we can recruit only 150 subjects into group 1. How many individuals do we need in group 2?
Select the best response: We take an SRS from a population and a separate SRS from a population. Which t procedure should we use?(a) a one-sample t procedure(b) a paired t procedure(c) an independent t procedure

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