Biostatistics Exam #2 Study Guide
Which is wider, a 95% confidence interval or a 90% confidence interval?
Why? - - A 95% confidence interval is wider than a 90% confidence interval.
If you want to be more confident that the true population value is within
interval, then the interval needs to be wider.
- What effect does sample size have on confidence intervals? - - Increasing
the sample size decreases the width of confidence intervals making the
confidence intervals narrower. This happens visa-versa meaning that
decreasing the sample size would increase the width of confidence intervals
making the confidence intervals less
narrow.
- Why must we use the Student's t-distribution, and not the normal
distribution, to obtain a confidence interval around a population mean? - -
The Student's t-distribution is used because it takes into account error
associated with both the sample mean and the sample standard deviation as
estimates of the true population mean and population standard deviation for
specification of the confidence interval.
- Compare and contrast the standard normal distribution with the student's
t-distribution. How are they similar? How are they different? - - The standard
normal distribution (i.e. the z-distribution) does not have any parameters.
The standard normal distribution has a mean of zero and a standard
deviation of one. Both the standard normal distribution and the student's t-
distribution have symmetric, bell-shaped probability density functions
centered at zero. However, the student's t-distribution is more peaked, has
fatter tails, and depends on the degrees of freedom parameter.
- What happens to a student's t-distribution as the degrees of freedom
increase? - - A student's t-distribution converges to normal distribution as
the degrees of freedom increases.
- What is a null hypothesis? - - The null hypothesis is a statement that says
that there is no significant difference between the paired observations and
any observed difference due to sampling or experimental error.
- In hypothesis testing, what is a Type I error? - - A Type I error occurs when
we reject the null hypothesis (Ho) when, in reality, the null hypothesis is true.
- In hypothesis testing, what is a Type II error? - - A Type II error occurs
when you fail to reject the null hypothesis when, in reality, the alternative
hypothesis is true.
, - In hypothesis testing, what is the statistical power of a test? - - The power
of a test is the probability of rejecting the null hypothesis when the null
hypothesis is false. The power is equal to 1-beta, where beta is the
probability of a Type II error.
- How does decreasing the level of significance for a test of hypothesis
change the probability of a Type II error? - - Decreasing the level of
significance for a test of hypothesis increases the probability of a Type II
error, as it increases the critical value.
- If a scientist asked you how he could reduce the probability of a Type II
error in his experiment, what would you tell him/her? - - There are two ways
to decrease the probability of Type II error. One could increase alpha, which
is the probability of a Type I error, but that is not a desirable thing to do. One
could also increase the sample size which increases the power of the test
and decreases the probability of a Type II error.
- When conducting a test of hypothesis for a binomial proportion with a large
sample size, on what probability distribution do we base our test statistic? - -
When conducting a test of hypothesis for a binomial proportion the
probability distribution we base our test statistic is by observing outcomes
from an independent trial in which the probabilities of two outcomes do not
change from one trial to the next. For example, two possible categories of
binomial probability can be male vs. female. We base our test statistic on the
z-distribution which is also called the standard normal distribution.
- Explain how one can use the "p-value" from a statistical software program
to make a decision of whether or not there is evidence to reject a null
hypothesis. - - Statistical software programs can give the exact p-value. it is
then compared to the alpha which is determined by the level of significance,
which is usually 5% (so alpha would be 0.05). If the p-value is greater than
alpha, there is not enough evidence to reject the null hypothesis. If the p-
value is less than alpha, there is enough evidence to reject the null
hypothesis.
- What type of data are needed to conduct a paired t-test? - - The key is
that two comparable (commensurate) measurements are taken from each
experimental subject. These may be before and after data or any other
paired data.
- What is the null hypothesis for a paired t-test? - - The null hypothesis for a
paired t-test is that the mean difference between paired observation is zero.
- What assumptions must we make in order to use a t-test for two
independent groups? - - When using the t-test for two independent groups,
we assume that the dependent variable being tested follows a normal
Which is wider, a 95% confidence interval or a 90% confidence interval?
Why? - - A 95% confidence interval is wider than a 90% confidence interval.
If you want to be more confident that the true population value is within
interval, then the interval needs to be wider.
- What effect does sample size have on confidence intervals? - - Increasing
the sample size decreases the width of confidence intervals making the
confidence intervals narrower. This happens visa-versa meaning that
decreasing the sample size would increase the width of confidence intervals
making the confidence intervals less
narrow.
- Why must we use the Student's t-distribution, and not the normal
distribution, to obtain a confidence interval around a population mean? - -
The Student's t-distribution is used because it takes into account error
associated with both the sample mean and the sample standard deviation as
estimates of the true population mean and population standard deviation for
specification of the confidence interval.
- Compare and contrast the standard normal distribution with the student's
t-distribution. How are they similar? How are they different? - - The standard
normal distribution (i.e. the z-distribution) does not have any parameters.
The standard normal distribution has a mean of zero and a standard
deviation of one. Both the standard normal distribution and the student's t-
distribution have symmetric, bell-shaped probability density functions
centered at zero. However, the student's t-distribution is more peaked, has
fatter tails, and depends on the degrees of freedom parameter.
- What happens to a student's t-distribution as the degrees of freedom
increase? - - A student's t-distribution converges to normal distribution as
the degrees of freedom increases.
- What is a null hypothesis? - - The null hypothesis is a statement that says
that there is no significant difference between the paired observations and
any observed difference due to sampling or experimental error.
- In hypothesis testing, what is a Type I error? - - A Type I error occurs when
we reject the null hypothesis (Ho) when, in reality, the null hypothesis is true.
- In hypothesis testing, what is a Type II error? - - A Type II error occurs
when you fail to reject the null hypothesis when, in reality, the alternative
hypothesis is true.
, - In hypothesis testing, what is the statistical power of a test? - - The power
of a test is the probability of rejecting the null hypothesis when the null
hypothesis is false. The power is equal to 1-beta, where beta is the
probability of a Type II error.
- How does decreasing the level of significance for a test of hypothesis
change the probability of a Type II error? - - Decreasing the level of
significance for a test of hypothesis increases the probability of a Type II
error, as it increases the critical value.
- If a scientist asked you how he could reduce the probability of a Type II
error in his experiment, what would you tell him/her? - - There are two ways
to decrease the probability of Type II error. One could increase alpha, which
is the probability of a Type I error, but that is not a desirable thing to do. One
could also increase the sample size which increases the power of the test
and decreases the probability of a Type II error.
- When conducting a test of hypothesis for a binomial proportion with a large
sample size, on what probability distribution do we base our test statistic? - -
When conducting a test of hypothesis for a binomial proportion the
probability distribution we base our test statistic is by observing outcomes
from an independent trial in which the probabilities of two outcomes do not
change from one trial to the next. For example, two possible categories of
binomial probability can be male vs. female. We base our test statistic on the
z-distribution which is also called the standard normal distribution.
- Explain how one can use the "p-value" from a statistical software program
to make a decision of whether or not there is evidence to reject a null
hypothesis. - - Statistical software programs can give the exact p-value. it is
then compared to the alpha which is determined by the level of significance,
which is usually 5% (so alpha would be 0.05). If the p-value is greater than
alpha, there is not enough evidence to reject the null hypothesis. If the p-
value is less than alpha, there is enough evidence to reject the null
hypothesis.
- What type of data are needed to conduct a paired t-test? - - The key is
that two comparable (commensurate) measurements are taken from each
experimental subject. These may be before and after data or any other
paired data.
- What is the null hypothesis for a paired t-test? - - The null hypothesis for a
paired t-test is that the mean difference between paired observation is zero.
- What assumptions must we make in order to use a t-test for two
independent groups? - - When using the t-test for two independent groups,
we assume that the dependent variable being tested follows a normal
