14B Coreq

In the next preview assignment and in the next class, you will need to be able to set up  hypothesis tests and use P-values to draw conclusions about population means. You  will also need to know how to calculate ratios to determine the test statistic for an  ANOVA.

Hypothesis Testing for Means

Question 1

1) We want to test if there is a difference in the mean typing speed (in words per  minute) between people who are left-handed and those who are right-handed.

Part A: How many groups/populations are we comparing? Name the  groups/populations.

Part B: Define the parameters of interest in the context of the problem and include  the symbols to represent them.

Part C: What mathematical symbol should the null hypothesis always include? Part D: State the null hypothesis in symbolic form.

Part E: What question are we trying to answer?

  1. a) Is the mean typing speed for left-handed people different than the mean  typing speed for right-handed people?
  2. b) Is the mean typing speed for left-handed people greater than the mean typing speed for right-handed people?
  3. c) Is the mean typing speed for left-handed people less than the mean typing  speed for right-handed people?

Part F: State the alternative hypothesis in symbolic form.

Part G: If the P-value is less than the level of significance (�, or alpha), what should  you do?

  1. a) Reject the null hypothesis.
  2. b) Fail to reject the null hypothesis.
  3. c) Accept the null hypothesis.

Part H: If the P-value is greater than the level of significance (�, or alpha), what  should you do?

  1. a) Reject the null hypothesis.
  2. b) Fail to reject the null hypothesis.
  3. c) Accept the null hypothesis.

Question 2

2) Suppose the researcher in Question 1 set the level of significance (�, or alpha) to  0.05. In each of the following scenarios, state whether or not the null hypothesis  should be rejected.

Part A: P-value = 0.4765

Part B: P-value = 0.0215

Question 3

3) Return to the original scenario in Question 1, and suppose we got a P-value of  0.0162.

Part A: What would be your conclusion in the context of the problem with � = 0.05?

Part B: Suppose that the level of significance was changed to 0.01. Using the same  P-value as Part A, what would the conclusion be in the context of the  problem?

Ratios 

In order to make calculations for an ANOVA, we will need to use ratios.

Question 4

4) Label which ratio has the greatest value, which ratio has the least value, and which  ratio is closest to 1.

Part A: #$.&

#’.$

Part B: ‘.()

#.)

Part C: )*.#’

#+.&

Question 5

5) Use the ratio � = -.to answer the following questions.

Part A: If � remains the same, what would you expect to happen to the value of � if  you increase the numerator, �?

Part B: If � remains the same, what would you expect to happen to the value of � if  you increase the denominator, �?

Part C: If � remains the same, what would you expect to happen to the value of � if  you decrease the numerator, �?

Part D: If � remains the same, what would you expect to happen to the value of � if  you decrease the denominator, �?