Biostatistics Final
the two-sided 95% CI for the population mean given, x= 0,2,3,5
(-.812, 5.812)
a unimodal distribution is said to be negatively skewed if
(∑z^3 )/n<0
Since the proportion of individuals in a population with a coronary heart disease is .4 What is the probability that in a random sample of size 7 obtained from that population that 1 or fewer individuals will have coronary heart disease?
.159
Assuming that 20% of the people over age 65 in the U.S. have high blood pressure, what is the probability that in a random sample of 5 people over 65 in the US none of them would have high blood pressure?
.33
The sensitivity of a test for a disease is .8, its specificity is .6, and the prevalence of the disease is .20. Which of the following corresponds to the ppv of the test for the disease?
.333
F ratios vary in magnitude from
0 to greater than 0
Suppose we calculate the difference between the observed values of y and those estimated from a simple linear regression and for every value of x this difference is zero. The Pearson product-moment correlation coefficient for this dataset will be
1 or -1
If you were to take 40 sets of random samples from a single population and compare the two random samples for each set using an independent samples t-test, how many times on average would you expect the null hypothesis of no difference in means to be rejected using alpha = .05?
2
A researcher wants to have 90% power to detect an effect size of .5 or larger with an alpha of .05 using a one-tailed, one mean z test. What size sample does he or she need?
35
given the following dataset of PSA in 10 men, what is the percentile rank of a PSA value of 2.4?
45
A researcher obtains the following dataset (x: 6, 16, 5) what is the cumulative relative frequency corresponding to the value 10?
6
As is commonly known, Kiwi birds are native to New Zealand. An investigator goes to New Zealand and finds four birds. The mean height of the four birds is 4, the median is 3, and the mode is 2. What is the height of the tallest of the four birds?
8
McNemar's test could be used to
Compare the effectiveness of a vaccine on the presence or absence of a childhood disease in twins and their partners taken from a sample of identical twins
In a recent study, we enrolled 100 older individuals living in a retirement community in Florida. We suspected because of their affluence and higher education that this group might have a higher average IQ than the U.S. population. The mean IQ of the US population is 100 with a standard deviation of 16. When we tested our sample of 100 participants, their mean IQ was 102. What conclusion should we reach if we use an alpha of .05?
Fail to reject the null hypothesis that the mean IQ of our sample is not different from that of the US population
Suppose the mean under the null hypothesis, . For which of the following two-sided 95% confidence intervals would you fail to reject the null hypothesis using a two-tailed test with alpha=.05 ?
L=-.001, U=2.31
A one way analysis of variance is used to compare systolic blood pressure after administration of a new drug for control of high blood pressure. Two groups are compared. One receives a placebo, the other 10 mg. of the medication. After the initial study, the clinical investigator decides to increase the dose of the 10 mg. group to 20 mg. Suppose this increase results in a further decrease in blood pressure for all members of the treated group of 10 points. Which of the following statements regarding changes resulting from the increase in dosage is true?
MSw will remain unchanged
Suppose one wants to compare the frequencies of 4 types of tuberculosis in 6 regions of India to determine whether the distribution of these types varies by region. To do so, one carries out a single chi square test and finds that the null hypothesis of no association between types of tuberculosis and region can be rejected at alpha =.05. One observes what appears to be significant differences between two regions. Can one conclude on the basis of the one test of the 4 X 6 table already conducted that the differences in distribution of types between the two regions is statistically significantly different with alpha =.05?
No
For the following data, calculate Obtained t and determine what decision should be reached for a paired samples t-test with alpha=.05 and
Obtained t = 1.274, fail to reject the null
A one mean Z test is conducted to test the alternative hypothesis: , against the null hypothesis: , using. A sample of size 64 is drawn and the mean of this sample is 28. The standard deviation of the population is known to be 8. The researcher decides to use the Critical Z vs. Obtained Z method to test the hypothesis.
Obtained z = -2, critical z = +/- 1.96, reject the null hypothesis
we know that A and B are independent if
P(A_B) = P(A_)*P(B)
based on the following joint probability table for events A and B, which of the following statements is true?
P(AuB-bar) = .95 and P(A-bar/B-bar) = .542
Suppose that a researcher wishes to determine whether there is a linear relationship between weight and blood pressure in a sample of older persons in the community. Which of the following statistical methods would most likely be employed to answer this question?
PPMCC
If the frequency of prostate cancer in a population were to double, which characteristic of the PSA test would be most likely to increase?
Positive Predictive Value
simple linear regression provides the following
Prediction of the best estimate for y, for any value of x AND a measure of the amount of variation in y due to variation in x
For which of the following tables is the Odds Ratio a better approximation of the Risk Ratio
Table B
A critical assumption of a paired samples t-test is that of independence. By this assumption, we mean that
The difference scores for each pair are independent of the different scores of all other pairs
the term "expected" value in a chi-square test refers to
The number of observations expected to be present in a given cell of the chi-square table when the null hypothesis is true
with regard to a one mean Z test, critical Z represents
The number of standard errors of the mean that lie between the mean of a sampling distribution and the leading edge of a critical region
the coefficient of Non-determination is
The proportion of variation in the dependent variable y not explained by variation in the independent variable x
Which of the following assumptions apply to a paired samples t-test used to assess the difference in blood glucose following ingestion of a medication to reduce blood glucose
The underlying population distribution of change scores of blood glucose before and after ingestion should be approx normal
the main reason that we fail to reject vs. accept the null hypothesis testing is
We do not know the actual magnitude of the Type II error, because we do not know the sampling distribution of the mean
The one-mean Z test is infrequently used in practice. In which of the following instances would it be most appropriate to use the one-mean Z-test?
You have been studying the levels of mercury in blood samples of iron miners in northern Minnesota and have determined a mean and standard deviation from a large representative sample of miners (over 1,000). You would like to know if a particular group of miners working in one city on the iron range have a higher level of mercury in their blood and obtain blood samples from 30 miners living in this city.
in a recent study, we enrolled 100 older individuals livings in a retirement community in Florida. We suspected.When we tested our sample of 100 participants, their mean IQ was 102. What conclusions should we reach if we use an alpha of .05
You should fail to reject the null. This is because by using obtained Z= -1.25 and this is less than the critical z of 1.65.
A test is used to assess whether a particular Pearson correlation coefficient is significantly different from z. The obtained t is less than critical t. What should one conclude?
a dataset does not demonstrate a significant linear correlation
which of the following is NOT required to conduct a one mean Z test?
a sample size of at least 30
the standard error of the mean is
a standard deviation
which one of the following is an example of a statistical population
all birthdates of students in a given class
the actual probability of obtaining a test statistic like the mean in any specified rename is represented by
an area under the alternative (true) curve
which of the following statements is true?
an interval scale possesses all of the properties of an ordinal scale
if there were no association between an exposure and a disease, the risk or odds ratio would be
approx. 1
the principal difference between bar graphs and histograms is that
bar graphs are used to represent discrete data, whereas histograms are used to represent continuous data
as sample size increases
beta decreases
Equivalence testing is carried out by performing two hypothesis tests, allowing a modified version of the null hypothesis to be accepted. The modified version of the null hypothesis is accepted if:
both of the tests lead to rejection of their null hypotheses
The fact that the sampling distribution of tends to be normally distributed even in situations where x is not normally distributed is attributed to the
central limit theorem
A county health department wants to know whether significant groundwater contamination has occurred due to the use of a specific pesticide on farms in 5 different communities within the county. To do this, they obtain samples from 20 wells in each of these communities and determine the percentage of wells in each community that have significant pollution with this pesticide. To determine whether the communities differ in the frequency of polluted wells, what statistical test should be used?
chi square test
A researcher suspects that a particular gene might be associated with the risk of having a common disease. She studies a small community in which 50 cases of this disease have been identified, genotypes everyone in the community, and divides the community into 3 groups corresponding to the alternative forms of this gene. In order to determine whether different forms of the gene are associated with higher or lower risk of the disease, which of the following statistical methods should she use?
chi-squared test
upper and lower limits are used to plot graphs when the data are
continuous
A researcher is interested in testing the . She decides to conduct a one mean t test (two tailed) with alpha=.05 . Based on the information from the hypothesis test, the researcher rejects the null hypothesis. In reality the null hypothesis is false. Rejecting a false null hypothesis results in a
correct decision
The State of Illinois has been notified that it will receive $5.3 million from the Economic Stimulus Package to conduct an intervention program to reduce the hospitalization rate for flu among those over 65. Last year 1.33 % of this group in Illinois was hospitalized for flu symptoms. In examining the rates from different counties, the highest rate among those over 65 was seen in DuPage County (1.41 %). The number of persons over 65 in DuPage County last year was 46,320. To determine whether more of the new funding should be spent in DuPage County, the state epidemiologist is asked to determine whether the proportion hospitalized in DuPage County is significantly larger than the proportion hospitalized in the entire state. S/he carries out a test with alpha=.05. What decision should s/he make?
decide not to target the intervention to DuPage County because the risk is not statistically significantly higher than that in all of Illinois
A researcher wishes to increase the power to detect a difference between the means of the alternative and null distributions of an observed variable. Which of the following are options to him (her)?
decreasing alpha
a biased sample
does not reflect the underlying population fairly
the sp2 term in the independent samples t test is used to
estimate the variance of the populations from which the samples were taken
Exact and approximate methods can be used to carry out one-sample tests for a proportion. Which of the following is true?
exact and approximate methods yield similar results for large samples
an example of a nominal scale is
eye colors
You conduct a study of heights of children in a third world country by taking a random sample of 100 children of age 10. Your hypothesis is that the mean height of children in this country will be less than the mean height of children of the same age in Hillsborough County, which you obtain from school records (assuming all children in the fourth grade had their heights measured and recorded). The mean height of the sample of 100 children in the third world country turns out to lower than that of the mean height of children in Hillsborough County, but the mean falls outside of the Critical Region (defined by you preset alpha = .05).
fail to reject the Null Hypothesis of no difference in mean height between the sample in the third world country and children of the same age in Hillsborough County.
A sample of n=144 is drawn and its mean is 2.95. The standard deviation of the sample is 3. If the null hypothesis is that the population mean is 2.5 and we use a two-tailed test with alpha=.05, what conclusion should we reach?
fail to reject the nul
A study is performed in which a new method for measuring systolic blood pressure is compared with the traditional method. A sample of 27 subjects is used and a Pearson product-moment correlation (r) of 0.38 is obtained between the systolic blood pressures determined by the two methods. A two-tailed test of the null hypothesis rho=0 is conducted at alpha=.05. What conclusion should be reached?
fail to reject the null hypothesis
A two-tailed independent samples t-test with sample sizes 10 and 14 is being performed with alpha = .05. Observed t is 2.070.
fail to reject the null hypothesis
Consider a 2x3 contingency table. The level of significance selected, alpha= .05. The obtained value of the test statistic Chi-square = 5.2519. Based on the comparison of the test statistic Chi-square with the critical Chi Square, which of the following statements is true? (YOU CAN USE THE TABLES TO ANSWER THIS QUESTION.)
fail to reject the null hypothesis
the power of a statistical test is best defined as the probability that a
false null hypothesis will be rejected
what graphical representations can be used for a set of nominal data
frequency and relative frequency graphs
as alpha increases, the power of a one mean Z test
increases
Other factors remaining unchanged, which of the following will increase the size (the distance from L to U) of a confidence interval?
increasing the level of confidence, 90%->95%
The independent samples t-test has three assumptions. For violations of which one of the following assumptions is the test least robust?
independent of observations
We wish to compare the means of a continuous variable in two samples taken from normally distributed populations. Which statistical tests could we use to do this?
independent samples t test
the family wise type 1 error rate
is the probability that 1 or more true null hypotheses will be rejected in a series of tests
What consequences does adjustment for multiple comparisons using Bonferroni's procedure or a similar technique have?
it reduces the power to find differences between pairs of group means
in order to reject the null hypothesis for a one mean Z test, the p value must be
less than or equal to alpha
A statistical test that produces empirical type 1 error rates significantly above nominal alpha levels is termed
liberal
which of the following would increase our chances of rejecting a false null hypothesis?
lower or reduced beta
which of the following measures is least affected by a few extreme observations in a data set?
median
You are conducting a study of the survival of long-lived mice that have been irradiated using a new technique. You want to present a paper on survival of these mice to...What measure of central tendency would be the most appropriate at the present time for summarizing the findings for the entire group of mice being studied?
median survival duration
what measures of central tendency is appropriate for describing a set of nominal data?
mode
when the degrees of freedom are very large, critical t will have a value
near critical Z
Six brothers and sisters from one family were immunized against the flu in 2003. In 2004, none of the brothers or sisters could obtain the vaccine due to a shortage that year. The table below shows which brothers and sisters got the flu in 2003 and 2004. Using McNemar's Test with alpha = .10, assess whether the lack of vaccine caused a significant increase in flu cases in 2004 with this family as the sample.
no, it did not cause a significant increase (fail to reject the null hypothesis)
For which of the following scales would a cumulative relative frequency distribution not be appropriate
nominal
most non-parametric procedures employ
nominal or ordinal
A researcher finds .85 correlation between the number of hours people slept the night before and their score on a mental status exam. Based on this the researcher can conclude
none of the above
To which of the following assumption violations is the independent samples t test generally most robust?
normality
a one mean z test is said to be robust to violation of which of the following assumptions?
normality of the underlying population
a z score represents the
number of std. dev. between the mean of a distribution and some specified point on the distribution
P(AB) may be read as the probability
of A and B
When the null hypothesis is true, the value of obtained F for a one-way ANOVA will most likely be nearest to:
one
the paired samples t test is carried out by the application of
one mean t test
The prevalence of stroke among individuals over age 65 was found to be higher (3.8%) in a particular country of Georgia compared with the prevalence of stroke in the entire state (3.6%). Given the need to target interventions, the State Health Department wanted to know if this rate was significantly higher than the state rate. The size of the 65+ population in the county is known. Which of the following statistical tests would be most applicable to answering this question?
one sample test for a proportion
Three hundred subjects are randomized to three different drugs and a placebo in a study of medications to lower blood glucose. Levels of blood glucose are obtained after the administration of the medications or placebo. The data are best analyzed using
one way analysis of variance
A study of 30 identical twin pairs of similar age carrying the gene for Huntington's disease is conducted to examine the role of educational attainment in modifying early clinical expression of this genetic illness. In each pair, one twin has higher education and the other lower education. McNemar's Test of Paired Sample Proportions is used to determine whether educational attainment influences the early clinical expression of this illness. The data used in the test come from
only pairs in which only one of the two twins in the pair has expressed the disease
The Moffitt Cancer Center is conducting a study of a new drug that they believe may prolong the lives of individuals with inoperable colon cancer. What measures of central tendency are available to them after two years?
only the median
Confidence intervals of the form are designed to estimate the:
population mean
a relative frequency distribution associates each observation (X) in a data set with the
proportion of observations in the data set that have the value of X
A sample of 100 young adults was studied to determine whether taking at least 500 mg. of Vitamin C supplements daily can prevent the occurrence of common colds. Half of the adults agreed to take the supplements in the first year of the study and not to take them in the second year. The other half agreed to take the supplements in the second year, and not to take them in the first year. When the occurrence of 1 or fewer colds/year was compared between the times when the Vitamin C supplements were taken and not taken, the following results were obtained: Had 1 or fewer colds when taking supplements and 2 or more when not taking them: 37 participants Had 2 or more colds when taking supplements and 1 or fewer when not taking them: 23 participants Had 1 or fewer colds when taking supplements and when not taking them: 20 participants Had 2 or more colds when taking supplements and when not taking them: 20 participants The null hypothesis is that taking Vitamin C and having 1 or fewer colds per year are not related. The alternative hypothesis is that Vitamin C reduces the number of colds per year. Using a one-tailed test and alpha=.05, what conclusion would you reach?
reject the null hypothesis
which of the following is an example of a dichotomous variable?
sex
Consider the following sample: 1,5,5,9. Which is larger? Its standard deviation or mean deviation?
standard deviation
the analyses we conduct in biostats are based on what is observed. Other characteristics that we do not observe are extraneous to our analyses and tests. Therefore, what we are studying is not the people themselves, but rather some observable characteristics of these people. IN that sense, we are studying
statistical populations
statistical and popular populations differ in the following way
statistical populations consist of characteristics of people, whereas popular populations consist of people
which of the following 4 statements is true?
statistics can be used to estimate parameters
the point estimate of the confidence interval for a population mean is
the mean of the sample used to estimate the confidence interval
which of the following statements regarding z scores calculated from observations in any distribution is true?
the mean of the z scores is 0, the standard deviation of the z scores is 1
You are studying the frequency of people with different eye colors among a group living in a particular region of northern Italy. For a sample of 200, you tabulate the number ...what summary measures of central tendency can you use to describe eye color in this sample?
the mode
the n-th percentile is defined as
the point on a scale for which n percent of observed values fall below it. A percentile rank, in contrast is the percentage of observations that fall below a certain value on a scale.
What is the difference between ratio and interval
the presence of a true zero
High systolic blood pressure (>139) is present in 50% of individuals over age 60 living in a particular Florida community. A group of 8 friends over this age living in the same community work out together 3 times a week. They go to Publix and check their blood pressures and find that only 1 of them has high systolic blood pressure. Is the prevalence of high systolic blood pressure in the population represented by their group significantly lower than that of the community as a whole or is this just a chance finding? Use alpha= .05 and a one-tailed exact test to answer this question.
the prevalence of high systolic blood pressures in the population represented by their group is significantly lower than that of the community as a whole
A case-control study is performed and an odds ratio of 0.7 is obtained for the association between college education and stroke. The odds ratio implies that
the risk of stroke is lower among individuals with a college education in comparison to those with less than a college education
The one mean t test is more commonly employed by researchers than is the one mean Z test because
the std. dev. of the population is frequently unknown
The original Bonferonni method is considered to be conservative compared to the step-down Bonferonni method, which method is more likely to provide greater statistical power to detect pairwise differences in means?
the step-down Bonferonni method
the residual Sum of Squares refers to
the sum of squared deviations between y's estimated from the regression equation and observed values of y's for each x,y pair
Which of the following is not a characteristic of the normal distribution?
the total area under the curve depends upon the mean and standard deviation
When plotting a cumulative frequency polygon, the points corresponding to the cumulative frequencies are plotted at
the upper real limits of the intervals
in contrast to descriptive statistics, inferential statistics deal with
the use of statistics to arrive at conclusions regarding parameters
the range of a distribution is best classified as the measure of
variability
if we cannot enumerate a population
we could select a sample to study, and the findings could be used to make inferences about the population
the one mean Z test and one mean t test produce essentially identical results
when the sample size exceeds 120
in what situation is the median a better measure of central tendency than the mean?
when there are one or more outliers or values that are far from the average
Type I and Type II errors are related in the following way:
when type I error increases, type II error decreases
the positive predictive value of a test is defined as the probability that a person
with a positive test will have the disease
The specificity of a test is defined as the probability that a person
without the disease will get a negative test result
If the PPMCC between x and y is 1 or -1, the residual sum of squares in the simple linear regression, y hat = a + bx, will be
zero