Essentials of Biostatistics and Public Health Chapter 6 & 7 Test Questions with Verified Solutions
Latest Update 2024 (Already Passed)
Define point estimate, standard error, confidence level, and margin of error. - Answers A point estimate
for a population parameter is a single-valued estimate of that parameter.
A confidence interval (CI) estimate is a range of values for a population parameter
with a level of confidence attached (e.g., 95% confidence that the interval contains the unknown
parameter). The level of confidence is similar to a probability. The CI starts with the point estimate and
builds in what is called a margin of error.
A CI is a range of values that are likely to cover the true population parameter, and its general form is
point estimate ± margin of error.
The point estimate is determined first. The point estimates for the population mean and proportion are
the
sample mean and sample proportion, respectively. These are our best single-valued estimates of the
unknown population parameters. Recall from Chapter 5 that the sample mean is an
unbiased estimator of the population mean. The same holds true for the sample proportion with regard
to estimating the
population proportion. Thus the starting place, or point estimate, for the CI for the population mean is
the sample mean, and the point estimate for the population proportion is the sample proportion.
Next, a level of confidence is selected that reflects the likelihood that the CI contains the true, unknown
parameter. Usually, confidence levels of 90%, 95%, and 99% are chosen, although theoretically any
confidence level between 0% and I 00% can be selected.
Suppose we want to generate a CI estimate for an unknown
population mean. Ag_ain, the form of the CI is point estimate ±
margin of error, or X ± margin of error. Suppose we select a
95% confidence level. This means that there is a 95% probability
,that a CI will contain the true population mean. Thus, P(X -margin of error<μ,< X +margin of error) =
0.95.
The margin of error incorporates the confidence level (e.g.
Compare and contrast standard error and margin of error. - Answers
Compute and interpret confidence intervals for means and
proportions. - Answers
Differentiate independent and matched or paired samples - Answers
Compute confidence intervals for the difference in means and proportions in independent samples and
for the mean
difference in paired samples. - Answers
Identify the appropriate confidence interval formula based on type of outcome variable and number of
samples. - Answers
- Answers Estimation is the process of determining a likely value for
a population parameter (e.g., the true population mean or
population proportion) based on a random sample.
There are two broad areas of statistical inference, estimation and hypothesis testing. Define each. -
Answers In estimation, sample statistics are used to generate estimates about unknown population
parameters.
In hypothesis testing, a specific statement or hypothesis is generated about a population parameter and
sample statistics are used to assess the likelihood that the hypothesis is true.
In practice, how should you determine an unknown parameter? - Answers By selecting a sample from
the target population and using statistics (e.g., the sample mean or the sample proportion) to estimate
the unknown parameter. The sample should be representative of the population, with participants
selected at random from the population. Because different samples can produce different results, it is
necessary to quantify the precision-or lack thereof-that might exist among estimates from different
samples.
The techniques for estimation as well as for other procedures in statistical inference depend on what? -
Answers The appropriate classification of the key study variable (which we also call the outcome or
endpoint) as continuous or dichotomous.
, - Answers In practice, we often do not lmow the value of the population
standard deviation (a-). If the sample size is large (n > 30),
then the sample standard deviation (s) can be used to estimate
the population standard deviation.
- Answers There are instances in which the sample size is not
sufficiently large (e.g., n < 30), and therefore the general result
of the Central Limit Theorem does not apply. In this case, we
cannot use the standard normal distribution (z) in the confidence
interval. Instead we use another probability distribution,
called the t distribution, which is appropriate for small samples.
- Answers The t distribution is another probability model for a
continuous variable. The t distribution is similar to the standard
normal distribution but takes a slightly different shape depending
on the exact sample size. Specifically, the tvalues for Cis are
larger for smaller samples, resulting in larger margins of error
(i.e., there is more imprecision with small samples).
- Answers It is important
to note that appropriate use of the t distribution assumes that
the outcome of interest is approximately normally distributed.
- Answers interpretation
of Cls in general. Suppose we want to estimate a
population mean using a 95% confidence level. If we take 100
different samples (in practice, we take only one) and for each
sample we compute a 95% CI, in theory 95 out of the 100 Cls
will contain the true mean value(μ,). This leaves 5of100 Cis
Latest Update 2024 (Already Passed)
Define point estimate, standard error, confidence level, and margin of error. - Answers A point estimate
for a population parameter is a single-valued estimate of that parameter.
A confidence interval (CI) estimate is a range of values for a population parameter
with a level of confidence attached (e.g., 95% confidence that the interval contains the unknown
parameter). The level of confidence is similar to a probability. The CI starts with the point estimate and
builds in what is called a margin of error.
A CI is a range of values that are likely to cover the true population parameter, and its general form is
point estimate ± margin of error.
The point estimate is determined first. The point estimates for the population mean and proportion are
the
sample mean and sample proportion, respectively. These are our best single-valued estimates of the
unknown population parameters. Recall from Chapter 5 that the sample mean is an
unbiased estimator of the population mean. The same holds true for the sample proportion with regard
to estimating the
population proportion. Thus the starting place, or point estimate, for the CI for the population mean is
the sample mean, and the point estimate for the population proportion is the sample proportion.
Next, a level of confidence is selected that reflects the likelihood that the CI contains the true, unknown
parameter. Usually, confidence levels of 90%, 95%, and 99% are chosen, although theoretically any
confidence level between 0% and I 00% can be selected.
Suppose we want to generate a CI estimate for an unknown
population mean. Ag_ain, the form of the CI is point estimate ±
margin of error, or X ± margin of error. Suppose we select a
95% confidence level. This means that there is a 95% probability
,that a CI will contain the true population mean. Thus, P(X -margin of error<μ,< X +margin of error) =
0.95.
The margin of error incorporates the confidence level (e.g.
Compare and contrast standard error and margin of error. - Answers
Compute and interpret confidence intervals for means and
proportions. - Answers
Differentiate independent and matched or paired samples - Answers
Compute confidence intervals for the difference in means and proportions in independent samples and
for the mean
difference in paired samples. - Answers
Identify the appropriate confidence interval formula based on type of outcome variable and number of
samples. - Answers
- Answers Estimation is the process of determining a likely value for
a population parameter (e.g., the true population mean or
population proportion) based on a random sample.
There are two broad areas of statistical inference, estimation and hypothesis testing. Define each. -
Answers In estimation, sample statistics are used to generate estimates about unknown population
parameters.
In hypothesis testing, a specific statement or hypothesis is generated about a population parameter and
sample statistics are used to assess the likelihood that the hypothesis is true.
In practice, how should you determine an unknown parameter? - Answers By selecting a sample from
the target population and using statistics (e.g., the sample mean or the sample proportion) to estimate
the unknown parameter. The sample should be representative of the population, with participants
selected at random from the population. Because different samples can produce different results, it is
necessary to quantify the precision-or lack thereof-that might exist among estimates from different
samples.
The techniques for estimation as well as for other procedures in statistical inference depend on what? -
Answers The appropriate classification of the key study variable (which we also call the outcome or
endpoint) as continuous or dichotomous.
, - Answers In practice, we often do not lmow the value of the population
standard deviation (a-). If the sample size is large (n > 30),
then the sample standard deviation (s) can be used to estimate
the population standard deviation.
- Answers There are instances in which the sample size is not
sufficiently large (e.g., n < 30), and therefore the general result
of the Central Limit Theorem does not apply. In this case, we
cannot use the standard normal distribution (z) in the confidence
interval. Instead we use another probability distribution,
called the t distribution, which is appropriate for small samples.
- Answers The t distribution is another probability model for a
continuous variable. The t distribution is similar to the standard
normal distribution but takes a slightly different shape depending
on the exact sample size. Specifically, the tvalues for Cis are
larger for smaller samples, resulting in larger margins of error
(i.e., there is more imprecision with small samples).
- Answers It is important
to note that appropriate use of the t distribution assumes that
the outcome of interest is approximately normally distributed.
- Answers interpretation
of Cls in general. Suppose we want to estimate a
population mean using a 95% confidence level. If we take 100
different samples (in practice, we take only one) and for each
sample we compute a 95% CI, in theory 95 out of the 100 Cls
will contain the true mean value(μ,). This leaves 5of100 Cis
