Biostatistics Exam #2 Study Guide with
correct answers A+ rated
Which is wider, a 95% confidence interval or a 90% confidence interval? Why? - correct answer ✔✔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? - correct answer ✔✔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? - correct answer ✔✔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? - correct answer ✔✔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? - correct answer ✔✔A
student's t-distribution converges to normal distribution as the degrees of freedom increases.
What is a null hypothesis? - correct answer ✔✔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? - correct answer ✔✔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? - correct answer ✔✔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? - correct answer ✔✔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? - correct answer ✔✔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? - correct answer ✔✔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? - correct answer ✔✔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. - correct answer ✔✔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? - correct answer ✔✔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.
correct answers A+ rated
Which is wider, a 95% confidence interval or a 90% confidence interval? Why? - correct answer ✔✔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? - correct answer ✔✔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? - correct answer ✔✔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? - correct answer ✔✔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? - correct answer ✔✔A
student's t-distribution converges to normal distribution as the degrees of freedom increases.
What is a null hypothesis? - correct answer ✔✔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? - correct answer ✔✔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? - correct answer ✔✔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? - correct answer ✔✔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? - correct answer ✔✔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? - correct answer ✔✔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? - correct answer ✔✔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. - correct answer ✔✔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? - correct answer ✔✔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.
