*Introduction to Statistical Methods for the Life and Health Sciences*

http://www.stat.ucla.edu/~dinov/ |

Statistical Testing

**Objective: **In this lab, you will perform and
interpret a 1-sample t-test.

Go to http://www.stat.ucla.edu/projects/datasets and read about the cardiac study.In this exercise we will focus on the variable, basebp.This variable measure the systolic blood pressure at baseline, before implementation of any treatment.

Imagine that several years ago, the baseline systolic blood pressure for the population of individuals with heart disease was 134 (m = 134).We now wish to test the null hypothesis that the population mean baseline blood pressure is equal to 134 using data on systolic blood pressure collected more recently on individuals with heart disease.

1.Graph the variable and describe the shape of its distribution.Are there outliers?Find the mean and standard deviation of the variable.Is it appropriate to use a t-test to test the null hypothesis that m = 134?

Type

graph basebp

summarize basebp

2.Give
an example of a research question for the condition when H_{1}: m
> 134.

Give
an example of a research question for the condition when H_{1}: m
< 134

3.Compute the t test statistic by hand.How many degrees of freedom are there?Don’t worry about the p-value yet.

Now let’s use STATA to perform the t-test.

Type

ttest basebp=134[this performs a tttest with m = 134]

Discuss and interpret the output of the statistical test.

4.When H_{1}:m
> 134, what is the p-value according to the STATA output?Draw
a sketch of the t distribution, identify m
and x, and the region covering the p-value.Using a
= .05 as your decision criteria, what do you conclude about the null hypothesis?What
do you conclude about your research question?

5.Use the t test statistic that you computed by hand and the t-table to compute the p-value for this null hypothesis.What is your best estimate of the p-value?

6.When H_{1}:m
< 134, what is the p-value?Draw
a sketch of the t distribution, identify m
and x, and the region covering the p-value.Using a
= .05 as your decision criteria, what do you conclude about the null hypothesis?What
do you conclude about your research question?

7.Use the t test statistic that you computed by hand and the t-table to compute the p-value for this null hypothesis.What is your best estimate of the p-value?

8.Now compute the 95% CI for the true population mean systolic blood pressure.Is 134 contained in that interval?Is this CI consistent with the 2-tailed t-test result?

9.Now compute
the z-statistic, using H_{1}: m
> 134.What is the p-value?How
does this p-value compare to the p-value obtained using the t distribution?Explain
why the two p-values are similar or different.