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biostatistics

Applied Biostatistics For The Health Sciences 2nd Edition Richard J. Rossi - Solutions

Why should a confidence interval for the parameter being tested be reported along with the results of the hypothesis test?
What is the difference between the ????-value and the significance level in a hypothesis test?
Why are small ????-values taken as evidence against the null hypothesis?
Explain what it means when the result of a hypothesis test is said to be(a) statistically significant but not scientifically significant.(b) not statistically significant but scientifically significant.(c) both statistically and scientifically significant.
What is the difference between statistical significance and practical/scientific significance?
What does it mean when the results of a hypothesis test are said to be(a) statistically significant? (b) scientifically significant?
What information is needed before the sample is selected in order to have a wellplanned and reliable hypothesis test?
In each of the following hypothesis testing scenarios, determine whether or not failing to reject ????0 is a reliable decision.(a) ???? = 0.45.(b) ???? = 0.11.(c) ???? = 0.75.(d) ???? = 0.04.
In each of the following scenarios determine whether the testing decisions reject ????0 and fail to reject ????0 are reliable decisions.(a) ???? = 0.01, ???? = 0.56(b) ???? = 0.15, ???? = 0.06(c) ???? = 0.05, ???? = 0.06(d) ???? = 0.01, ???? = 0.26(e) ???? = 0.30, ???? = 0.01(f) ???? = 0.05, ???? =
What is the value of the power of the test when(a) ????(????) = 0.30?(b) ????(????) = 0.05?
What happens to the value of(a) ???? when the sample size is increased?(b) ???? when the sample size is increased?(c) the power of a test when the sample size is increased?
In a hypothesis test, what(a) is the relationship between the power of a test and the probability of making a Type II error?(b) does it mean when the power is small at a particular value of the parameter being tested?
In a hypothesis test, what does the power of the test measure?
Under what conditions does the failure to reject ????0 become a reliable decision?
Why is failing to reject ????0 often an unreliable decision?
Why is rejecting ????0 a reliable decision?
Under what conditions would using ???? = 0.01 be preferable to using ???? = 0.05 as the significance level of a hypothesis test?
What are the symbols ???? and ???? used to represent in a hypothesis test? What are the acceptable values of ????? What are the small values for ?????
In each of the following scenarios determine whether or not a testing error was made, and if a testing error was made determine which type of error was made.(a) ????0 was rejected and ????0 is actually false.(b) ????0 was rejected and ????0 is actually true.(c) ????0 was failed to be rejected and
Suppose in testing ????0 ∶ ???? ≤ 10 versus ????A ∶ ???? > 10, the rejection region for a???? = 0.05 level test is “Reject ????0 when ???? > 18.6.”(a) What is the chance of making a Type I error before the sample is actually selected?(b) If the sample yields an estimate of ???? of ???? =
How should the significance level ???? be chosen in a hypothesis test?
In a hypothesis test how is a(a) Type I error made? (b) Type II error made?
In a hypothesis test of ????0 versus ????A what is(a) the test statistic? (b) the rejection region?(c) a Type I error? (d) a Type II error?(e) the significance level? (f) the ????-value?
In a hypothesis test what is the(a) null hypothesis?(b) alternative hypothesis?(c) research hypothesis?
Using the Mammography Experience data set(a) create a 2 × 2 contingency table summarizing mother/sister history (HIST) by self examination training (BSE).(b) estimate the odds ratio of BSE for having mother/sister history of breast cancer.(c) compute a 95% confidence interval for the odds ratio of
Using the ICU data set(a) create a 2 × 2 contingency table summarizing vital status (STA) by infection at admission (INF).(b) estimate the odds ratio of death for having an infection at admission.(c) compute a 95% confidence interval for the odds ratio of death for having an infection at admission.
Using the Birth Weight data set(a) create a 2 × 2 contingency table summarizing the number of low weight babies by mother’s smoking status.(b) estimate the odds ratio of having a low weight baby associated with the risk factor smokes during pregnancy.(c) compute a 95% confidence interval for the
Use the data given in Table 6.13 on smokeless tobacco use and dental caries to(a) Compute an estimate of the odds ratio of developing tooth caries due to the risk factor uses smokeless tobacco.(b) Compute the value of the estimated standard error of ln(ˆ????????).(c) Compute an approximate 95%
What does it mean when the confidence interval for the(a) relative risk contains 1?(b) odds ratio contains 1?
Using the Birth Weight data set(a) create a 2 × 2 contingency table summarizing the number of low weight babies by mother’s smoking status.(b) estimate the relative risk of having a low weight baby associated with the risk factor smokes during pregnancy.(c) compute a 95% confidence interval for
In the article “Smoking and risk of myocardial infarction in women and men: longitudinal population study” published in the British Medical Journal (Prescott et al., 1998), the authors reported the results of a longitudinal study investigating the health problems associated with smoking among
The use of smokeless tobacco is known to be associated with increased risk of gingivitis(gum disease) and dental caries (tooth decay). Suppose the data given in Table 6.13 was collected in a study on smokeless tobacco use and dental caries.(a) Compute an estimate of the relative risk of developing
Why is the confidence interval for the relative risk based on the large sample sampling distribution of ln(ˆRR) rather than the sampling distribution of ˆRR?
After computing a confidence interval for the relative risk why is it important to determine whether or not the value 1 is in the confidence interval?
What are the largest and smallest values that the relative risk can take on?
What is the relative risk of a disease/condition for exposure to a particular risk factor?
Using the Birth Weight data set(a) estimate the proportion of low weight babies for mothers who smoked during pregnancy.(b) estimate the standard error of the estimate of the proportion of low weight babies for mothers who smoked during pregnancy.(c) estimate the proportion of low weight babies for
In the article “Efficacy of antibiotic treatment in patients with chronic low back pain and modic changes (the AIM study): double blind, randomised, placebo controlled, multicentre trial” published in the British Journal of Medicine (Braten, 2019), the authors reported the results of a study on
In the article “Incidence, risk factors, and mortality associated with orofacial cleft among children in Ontario, Canada” published in JAMA Network Open (Malic, 2020), the authors reported the summary statistics in Table 6.11 on the birth weights of children born preterm with and without
Determine the overall sample size required so that a 95% upper bound confidence interval for the difference of two proportions will have a margin of error of ???????? = 0.04 when(a) ????̇ ???? = 0.65 and ????̇ ???? = 0.50.(b) ????̇ ???? = 0.40 and ????̇ ???? = 0.80.(c) ????̇ ???? = 0.10 and
Determine the overall sample size required so that a 95% lower bound confidence interval for the difference of two proportions will have a margin of error of ???????? = 0.035 when(a) ????̇ ???? = 0.50 and ????̇ ???? = 0.75.(b) ????̇ ???? = 0.45 and ????̇ ???? = 0.50.(c) ????̇ ???? = 0.90 and
Determine the overall sample size required so that a 99% confidence interval for the difference of two proportions will have a margin of error of ???????? = 0.04 when(a) ????̇ ???? = 0.25 and ????̇ ???? = 0.20.(b) ????̇ ???? = 0.40 and ????̇ ???? = 0.30.(c) ????̇ ???? = 0.80 and ????̇ ???? =
Determine the overall sample size required so that a 95% confidence interval for the difference of two proportions (i.e., ????????−????????) will have a margin of error of???????? = 0.03 when(a) ????̇ ???? = 0.55 and ????̇ ???? = 0.60.(b) ????̇ ???? = 0.12 and ????̇ ???? = 0.15.(c) ????̇
Using the large sample confidence interval formula for ???????? − ????????, compute a 95%(a) lower bound confidence interval for ???????? − ???????? when ???????? = 60, ???????? = 52, ˆ???????? = 0.37, and ˆ???????? = 0.44.(b) lower bound confidence interval for ???????? − ???????? when
Determine whether or not there is a statistically significant difference in ???????? and ????????suggested by each of the confidence intervals in Exercise 6.63.
Using the large sample confidence interval formula for ???????? − ????????, compute a(a) 95% confidence interval for ???????? − ???????? when ???????? = 50, ???????? = 50, ˆ???????? = 0.32, andˆ???????? = 0.38.(b) 98% confidence interval for ???????? − ???????? when ???????? = 120, ????????
What does it mean when two proportions are said to be statistically significantly different?
After computing a confidence interval for the difference of two proportions, why is it important to determine whether or not 0 falls in the confidence interval?
Determine whether or not it is appropriate to use the large sample confidence interval formula for estimating the difference between two proportions, when(a) ???????? = 30, ???????? = 25, ˆ???????? = 0.03, and ˆ???????? = 0.06.(b) ???????? = 60, ???????? = 75, ˆ???????? = 0.24, and ˆ???????? =
Under what conditions can the large sample confidence interval formula be used for estimating the difference between two proportions?
For the variable chest circumference (Chest) in the Body Fat data set,(a) estimate the standard deviation of Chest.(b) bootstrap the approximate standard error of the standard deviation of Chest.(c) determine the 5th and 95th percentiles of the bootstrap sampling distribution of the sample standard
The summary statistics in Table 6.10 are for the bootstrap sampling distribution of the sample standard deviation of the variable percent body fat (PCTBF) in the Body Fat data set. Use the information in Table 6.10 to determine(a) the approximate standard error of the sample standard deviation of
Explain how bootstrapping can be used to compute a 95%(a) lower bound confidence interval?(b) upper bound confidence interval?
What are the percentiles of the bootstrap sampling distribution of an estimator ????used in computing a(a) 90% bootstrap confidence interval?(b) 95% bootstrap confidence interval?(c) 98% bootstrap confidence interval?
What is the bootstrap algorithm for computing a 95% bootstrap confidence interval for a parameter ???? based on estimator ?????
Determine the sample size required for a 95% upper bound confidence interval for the mean when(a) ????̇ = 10 and the desired margin of error is ???????? = 1.(b) ????̇ = 30 and the desired margin of error is ???????? = 2.(c) ????̇ = 0.2 and the desired margin of error is ???????? = 0.01.
Determine the sample size required for a 95% lower bound confidence interval for the mean when(a) ????̇ = 50 and the desired margin of error is ???????? = 5.(b) ????̇ = 15 and the desired margin of error is ???????? = 2.5.(c) ????̇ = 25 and the desired margin of error is ???????? = 3.5.
Determine the sample size required for a 99% confidence interval for the mean when(a) ????̇ = 30 and the desired margin of error is ???????? = 4.(b) ????̇ = 5 and the desired margin of error is ???????? = 0.5.(c) ????̇ = 25 and the desired margin of error is ???????? = 3.5.(d) ????̇ = 80 and
Determine the sample size required for a 95% confidence interval for the mean when(a) ????̇ = 20 and the desired margin of error is ???????? = 2.5.(b) ????̇ = 50 and the desired margin of error is ???????? = 8.(c) ????̇ = 2 and the desired margin of error is ???????? = 0.1.(d) ????̇ = 200 and
Using the Body Fat data set, compute a 95% confidence interval for(a) the mean percentage of body fat (PCTBF).(b) the mean weight (Weight).(c) the mean body density (Density).
In the article “Ultrasound evaluation of the costophrenic recess as a marker of phrenic nerve function” published in The Internet Journal of Anesthesiology (Martin, 2018), the authors reported that in a pilot study the mean body mass index (BMI) of the???? = 20 individuals in their study was
In the article “Dialyzable free cortisol after stimulation with synacthen” published in the journal Clinical Biochemistry (Vogeser et al., 2002), the authors reported the raw data given in Table 6.9 on the free cortisol in 10 patients at time 0 and 60 min following stimulation with synacthen.
Using the Benign Breast Disease data set and the appropriate confidence interval formula, compute a 95% confidence interval for the mean weight of(a) the case group (???? = 50).(b) the control group (???? = 150).
Assuming the distribution being sampled is approximately normally distributed, use the small sample confidence interval for the mean to compute a(a) 90% upper bound confidence interval for ???? when ???? = 31, ????̄ = 761.4, and ???? =80.9.(b) 95% upper bound confidence interval for ???? when ????
Assuming the distribution being sampled is approximately normally distributed, use the small sample confidence interval for the mean to compute a(a) 90% lower bound confidence interval for ???? when ???? = 70, ????̄ = 88.6, and ???? =10.6.(b) 95% lower bound confidence interval for ???? when ????
Assuming the distribution being sampled is approximately normally distributed, use the small sample confidence interval for the mean to compute a(a) 95%lower bound confidence interval for ???? when ???? = 50, ????̄ = 15.6, and ???? = 2.6.(b) 99% lower bound confidence interval for ???? when ???? =
Assuming the distribution being sampled is approximately normally distributed, use the small sample confidence interval for the mean to compute a 98% confidence interval for ???? when(a) ???? = 36, ????̄ = 75.4, and ???? = 3.8.(b) ???? = 45, ????̄ = 563.7, and ???? = 31.6.(c) ???? = 75, ????̄ =
Assuming the distribution being sampled is approximately normally distributed, use the small sample confidence interval for the mean to compute a 95% confidence interval for ???? when(a) ???? = 22, ????̄ = 41.7, and ???? = 7.8.(b) ???? = 30, ????̄ = 0.08, and ???? = 0.01.(c) ???? = 25, ????̄ =
The normal probability plots given in Figure 6.3 are based on samples of 88 and 75 observations. Determine whether or not the normal probability plot in(a) Figure 6.3a supports the use of the small sample confidence interval procedure for the mean.(b) Figure 6.3b supports the use of the small
Which graphical method is best for checking the validity of the normality assumption required of the small sample ???? confidence interval procedure for estimating a mean?
What is the value of ????crit used in a small sample(a) 90% lower bound confidence interval for the mean when the sample size is ???? =55?(b) 95% lower bound confidence interval for the mean when the sample size is ???? =68?(c) 95% upper bound confidence interval for the mean when the sample size
What is the value of ????crit used in a small sample(a) 90% confidence interval for the mean when the sample size is ???? = 25?(b) 95% confidence interval for the mean when the sample size is ???? = 30?(c) 98% confidence interval for the mean when the sample size is ???? = 15?(d) 99% confidence
Using the large sample confidence interval formula for the mean, compute a 95%upper bound confidence interval for the mean when(a) ???? = 185, ????̄ = 874.2, and ???? = 80.5.(b) ???? = 150, ????̄ = 45.3, and ???? = 11.7.(c) ???? = 260, ????̄ = 134.6, and ???? = 12.9.
Using the large sample confidence interval formula for the mean, compute a 90%lower bound confidence interval for the mean when(a) ???? = 133, ????̄ = 28.5, and ???? = 6.7.(b) ???? = 250, ????̄ = 212.3, and ???? = 21.6.(c) ???? = 500, ????̄ = 98.9, and ???? = 2.7.
Using the large sample confidence interval formula for the mean, compute a 98%confidence interval for the mean when(a) ???? = 173, ????̄ = 33.2, and ???? = 3.4.(b) ???? = 211, ????̄ = 561.7, and ???? = 50.2.(c) ???? = 431, ????̄ = 22.9, and ???? = 3.1.
Using the large sample confidence interval formula for the mean, compute a 99%confidence interval for the mean when(a) ???? = 121, ????̄ = 56.8, and ???? = 5.3.(b) ???? = 198, ????̄ = 1.25, and ???? = 0.23.(c) ???? = 238, ????̄ = 16.9, and ???? = 4.1.
Using the large sample confidence interval formula for the mean, compute a 95%confidence interval for the mean when(a) ???? = 217, ????̄ = 283.9, and ???? = 35.6.(b) ???? = 333, ????̄ = 7.8, and ???? = 1.3.(c) ???? = 156, ????̄ = 764.2, and ???? = 108.1.
What is the value of ????crit in a(a) 90% large sample confidence interval for the mean?(b) 95% large sample confidence interval for the mean?(c) 99% large sample confidence interval for the mean?
What happens to the margin of error in a confidence interval for the mean when the sample size is(a) doubled? (b) quadrupled?
How does the estimated standard error of ????̄ affect the width of a confidence interval for the mean?
For a confidence interval for a mean, what is the formula for the margin of error in a(a) small sample ???? confidence interval?(b) large sample ???? confidence interval?
For estimating a mean, when it is appropriate to use a(a) large sample ???? confidence interval?(b) small sample ???? confidence interval?
In the article “Factors associated with potentially missed diagnosis of appendicitis in the emergency department” published in JAMA Network Open (Mahajan, 2020), the authors reported that 217 of 973 children classified as potentially missed apendicitis diagnosis had a unrinalyis test. Use this
In the article “Comparative effectiveness of different treatment pathways for opioid use disorder” published in JAMA Network Open (Wakeman, 2020), the authors reported that 3078 of the 6455 individuals sampled were diagnosed with depression in the inpatient detoxification group. Use this
Determine the cost of sampling for each of the scenarios in Exercise 6.23 when the initial cost of sampling is ????0 = $1250 and the cost of sampling per unit sampled is???? = $2.50.
Determine the sample size required for a large sample(a) 90% upper bound confidence interval for ???? when ????̇ = 0.25 and the desired margin of error is ???????? = 0.04.(b) 95% upper bound confidence interval for ???? when ????̇ = 0.65 and the desired margin of error is ???????? = 0.03.(c) 99%
Use the large sample confidence interval formula to compute a(a) 95% lower bound confidence interval for ???? when ???? = 350 and ˆ???? = 0.46.(b) 99% lower bound confidence interval for ???? when ???? = 250 and ˆ???? = 0.82.(c) 95% lower bound confidence interval for ???? when ???? = 198 and
What is the value of ????crit used in a one-sided large sample confidence interval for a proportion when the confidence level is(a) 90%? (b) 95%?
How is a one-sided confidence interval different from a two-sided confidence interval?
Determine the cost of sampling for each of the scenarios in Exercise 6.18 when the initial cost of sampling is ????0 = $750 and the cost of sampling per unit sampled is???? = $5.
Determine the sample size required for a large sample 95% confidence interval for a population proportion when(a) ????̇ = 0.35 and the desired margin of error is ???????? = 0.04.(b) ????̇ = 0.75 and the desired margin of error is ???????? = 0.025.(c) ????̇ = 0.5 and the desired margin of error
Use the large sample confidence interval formula to compute a(a) 95% confidence interval for the population proportion when ???? = 120 and ˆ???? =0.78.(b) 98% confidence interval for the population proportion when ???? = 68 and ˆ???? =0.33.(c) 95% confidence interval for the population proportion
What would happen to the margin of error in a large sample 95% confidence interval for a proportion when the sample size is(a) doubled? (b) halved?
What is the value of ????crit used in a two-sided large sample confidence interval for a proportion when the confidence level is(a) 90%? (b) 99%?
What is the form of the large sample confidence interval for estimating a population proportion?
Under what conditions can a large sample confidence interval be used for estimating a population proportion?
Suppose a 95% confidence interval for the mean computed from a random sample of ???? = 65 observations is 48.8 to 50.76. Does this confidence interval provide convincing statistical evidence that(a) ???? < 50? Explain. (b) ???? > 50? Explain.(c) ???? < 55? Explain. (d) ???? > 45? Explain.
Suppose a 90% and a 95% confidence interval for the population median were computed from a random sample resulting in the two intervals 114–134 and 118–129.Determine which of the intervals is the 90% confidence interval? Explain.
For a 95% confidence interval, which sample size, 50 or 100, will produce a wider confidence interval? Explain.
For a random sample of size ????, which confidence level, 90% or 95%, will produce a wider confidence interval? Explain.

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