LAB ACTIVITY 13

Due Friday, Nov. 18 at 11:59pm

(Use ‘cholesterol.mtw’ dataset)

Activity 1 (Requires Minitab): Performing hypothesis tests

Open the data set cholesterol.mtw in Minitab. This data set includes cholesterol levels for heart attack patients and for a group of control patients. It is recommended that people try to keep their cholesterol level below 200. We want to answer the question: Does the control group follow this recommendation?

  1. In words, we are testing the alternative hypothesis that the mean cholesterol level of the control group is less than 200. Let µ=the mean cholesterol level of the control group. Write the null and alternative hypotheses in terms of µ:

H0: ______

Ha: ______

  1. Use Minitab to find descriptive statistics for the variable ‘control’, which is what we’re interested in.

x-bar = ______

s = ______

n = ______

  1. What is the standard error of the mean? ______
  2. Calculate the test statistic and tell how many degrees of freedom we use for the corresponding t distribution.
  3. The p-value will be the probability that a random variable from the t distribution in part d is smaller than the test statistic in part d. Sketch a picture of the p-value. Find the p-value by having Minitab perform the hypothesis test. (You will find the 1-sample t test in the Stat  Basic Statistics menu. You will have to figure out how to configure and run the test; make sure you set the correct alternative hypothesis!) The p-value is ______.
  1. Recall that the significance level, alpha, tells us what to compare the p-value to. If the p-value is less than alpha, we can reject the null. In lectures and labs, we’ve generally used alpha = 0.05.
    Using a significance level of 0.05, what is the conclusion for this hypothesis test?
  1. If we use a significance level of 0.10, does our conclusion change?
  1. If we used alpha=0.05, which of the two types of error is possible?
  1. If we used alpha=0.10, which of the two types of error is possible?
  2. If this had been a two-sided hypothesis test, what would the p-value have been?

Activity 2 (Requires Minitab): What impacts the p-value?

  1. Consider testing the null and alternative hypotheses below:

H0: µ=10

Ha:µ < 10

Remember how to calculate the t-statistic for this hypothesis test. Because of the direction of this alternative hypothesis, smaller t-statistics correspond to more extreme sample data. Think about what will happen to the p-value when the sample mean (and thus the test statistic) gets smaller.

  1. Complete the table below. (Use stat  basic stat  1-sample-t  select ‘summarized data’ from the drop down menu  enter info  select correct options  OK. Make sure to correctly set the hypothesized mean and the alternative hypothesis and to recognize that you’re asked to enter the sample size, not the degrees of freedom.)

Sample mean (x-bar) / Sample size / Standard deviation / Test Statistic / p-value
9.5 / 20 / 2
9.0 / 20 / 2
8.5 / 20 / 2
  1. Based on this table, what happens to the test statistic and the p-value when the sample mean gets smaller but nothing else changes?
  2. What would happen to the test statistics and p-values if the alternative hypothesis were “>” instead of “<”?
  1. Consider the same null and alternative hypotheses as in Question 1. Now think about what will happen to the test statistic and p-value if the sample mean and standard deviation stay fixed but the sample size increases.
  1. Complete the table below:

Sample mean (x-bar) / Sample size / Standard deviation / Test statistic / p-value
9.5 / 20 / 2
9.5 / 50 / 2
9.5 / 100 / 2
  1. Based on the table above, what happens to the test statistic and the p-value as the sample mean and standard deviation remain fixed while the sample size increases?

Activity 3 (Does not require Minitab): More practice with the z-table

Use the standard normal table, or z-table, given on the next page to answer the following questions. Because the table has “gaps,” sometimes you may need to approximate.

  1. For testing H0: p = 0.4 vs. Ha: p ≠ 0.4, if the test statistic equals 2.05, what is the p-value?
  1. For testing H0: p1 – p2 = 0 vs. Ha: p1 – p2 > 0, if the test statistic equals 1.17, what is the p-value?
  1. For testing H0: p1 – p2 = 0 vs. Ha: p1 – p2 ≠ 0, if the test statistic equals –2.6, what is the p-value?
  1. For testing H0: p = 0.5 vs. Ha: p< 0.5, if the test statistic equals -1.98, what is the p-value?