Exercise 2: The school board of Two Guns, Texas is deeply concerned that their public school teachers are quitting their jobs and accepting teaching positions in other parts of the state. Some members of the school board think that the reason why teachers are quitting is because their weekly salaries are lower than those offered by other school boards in the state. The school board hires you to conduct a significance test. The research question: Do teachers in other parts of Texas earn higher average weekly salaries than those working in the Two Guns school district? There is no estimate of the population standard deviations. The significance level will be set at 5%. Step 1: Test Set-up Question 1: How large a sample is needed to achieve 80% statistical power? Based on past research Cohen's d effect size is estimated at 0.40, which is a small effect. See the table below: Cohen's d ES Thresholds Small 0.2 Medium 0.5 | Large 0.8 Here are the results of an a priori power analysis run using G*Power or the tool on the Statistics Kingdom website. Input parameters Output parameters Tails) ) One oncentrality parameter 6 2.4979992 Determine Effect size d 1.6548084 0.4 Criticalt a err prob 0.05 Df 154 Power (1-8 err prob) 0.8 Sample size group 1 78 Allocation ratio N2/N1 1 Sample size group 2 78 Total sample size 156 Actual power 0.8001474 Will a sample of 80 teachers for Two Guns and 80 teachers from other parts of Texas achieve statistical power of 80% or more? Place and X in the appropriation box: Answer: Yes No What would happen to statistical power if the estimate of Cohen's d effect size is wrong? Question 2: What two-sample test statistic should you use and why? Place an X in the correct box. Provide the reason for your answer below the checklist. z-test for z-test for Unequal s² Pooled s? means proportions t-test t-test Please Note: If you state that you should conduct a t-test for independent means, you must run and F-test for equality of variance to determine which two-sample t-test for independent means to use. Show your work in Excel below. What is your rationale for this answer?
Exercise 2: The school board of Two Guns, Texas is deeply concerned that their public school teachers are quitting their jobs and accepting teaching positions in other parts of the state. Some members of the school board think that the reason why teachers are quitting is because their weekly salaries are lower than those offered by other school boards in the state. The school board hires you to conduct a significance test. The research question: Do teachers in other parts of Texas earn higher average weekly salaries than those working in the Two Guns school district? There is no estimate of the population standard deviations. The significance level will be set at 5%. Step 1: Test Set-up Question 1: How large a sample is needed to achieve 80% statistical power? Based on past research Cohen's d effect size is estimated at 0.40, which is a small effect. See the table below: Cohen's d ES Thresholds Small 0.2 Medium 0.5 | Large 0.8 Here are the results of an a priori power analysis run using G*Power or the tool on the Statistics Kingdom website. Input parameters Output parameters Tails) ) One oncentrality parameter 6 2.4979992 Determine Effect size d 1.6548084 0.4 Criticalt a err prob 0.05 Df 154 Power (1-8 err prob) 0.8 Sample size group 1 78 Allocation ratio N2/N1 1 Sample size group 2 78 Total sample size 156 Actual power 0.8001474 Will a sample of 80 teachers for Two Guns and 80 teachers from other parts of Texas achieve statistical power of 80% or more? Place and X in the appropriation box: Answer: Yes No What would happen to statistical power if the estimate of Cohen's d effect size is wrong? Question 2: What two-sample test statistic should you use and why? Place an X in the correct box. Provide the reason for your answer below the checklist. z-test for z-test for Unequal s² Pooled s? means proportions t-test t-test Please Note: If you state that you should conduct a t-test for independent means, you must run and F-test for equality of variance to determine which two-sample t-test for independent means to use. Show your work in Excel below. What is your rationale for this answer?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:Exercise 2:
The school board of Two Guns, Texas is deeply concerned that
their public school teachers are quitting their jobs and
accepting teaching positions in other parts of the state. Some
members of the school board think that the reason why
teachers are quitting is because their weekly salaries are lower
than those offered by other school boards in the state. The
school board hires you to conduct a significance test. The
research question: Do teachers in other parts of Texas
earn higher average weekly salaries than those working in
the Two Guns school district? There is no estimate of the
population standard deviations. The significance level will be
set at 5%.
Step 1: Test Set-up
Question 1: How large a sample is needed to achieve 80%
statistical power? Based on past research Cohen's d effect size
is estimated at 0.40, which is a small effect. See the table
below:
Cohen's d ES
Thresholds
Small
0.2
Medium
0.5
Large
0.8
Here are the results of an a priori power analysis run using
G*Power or the tool on the Statistics Kingdom website.
Input parameters
Output parameters
Tail(s) One
Noncentrality parameter 6
2.4979992
Determine
Effect size d
0.4
Criticalt
1.6548084
a err prob
Df
154
a
0.05
Power (1-B err prob)
0.8
Sample size group 1
78
Allocation ratio N2/N1
1
Sample size group 2
78
Total sample size
156
Actual power
0.8001474
Will a sample of 80 teachers for Two Guns and 80 teachers
from other parts of Texas achieve statistical power of 80%
or more? Place and X in the appropriation box:
Answer:
Yes No
What would happen to statistical power if the estimate of
Cohen's d effect size is wrong?
Question 2: What two-sample test statistic should you use
and why? Place an X in the correct box. Provide the reason
for your answer below the checklist.
z-test for
z-test for
Unequal s?
Pooled s?
proportions
t-test
t-test
means
Please Note: If you state that you should conduct a t-test for
independent means, you must run and F-test for equality of
variance to determine which two-sample t-test for
independent means to use. Show your work in Excel below.
What is your rationale for this answer?
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