CAN 22 S2 Power

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School

St. John's University *

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Course

1013

Subject

Statistics

Date

Apr 3, 2024

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pdf

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2

Uploaded by ChancellorMoonVulture41

Name: CAN 22 Power Will Mr. Moore Prove Himself?? 1. Write the appropriate hypotheses for the significance test. Be sure to define the parameter of interest. 2. Describe a Type II error in this setting. 3. Suppose that Mrs. Moore’s true free throw percentage is actually 66% (H a is true!). Enter all information into the applet at https://istats.shinyapps.io/power/ . Click to Display Type II error. It will show as a blue shaded region. (a) If Ha is true, what is the probability of a Type II error (bad decision)? _______ (b) If Ha is true, what would be the probability of a good decision here? _______ (c) Interpret the probability of this good decision in the context of the problem. 4. Click Display Power. We want to increase the power of our test. How could we adjust each of the following factors to increase our power? Use the applet to explore each. a. Sample size: b. Alpha level: c. Alternative p:
Power of a Test Check Your Understanding A statistics major and a finance major decide to get married. In order to investigate their per person expenses they select a random sample guests they have invited to the wedding and records whether or not each person plans to attend the wedding. They decide to test H 0 : p = 0.75 versus H a : p ≠ 0.75 where p = the true proportion of all guests that will attend the wedding. a. The power of the test to reject H 0 : p = 0.75 when p = 0.70 using α = 0.05 and n = 25 subjects is 0.10. Interpret this value. b. Find the probability of a Type I error and the probability of a Type II error for the test in part (a). c. Determine whether each of the following changes would increase or decrease the power of the test. Explain your answers. ● Use α = 0.01 instead of α = 0.05. ● Use n = 100 instead of n = 25.
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