Posted: July 17th, 2022

Confidence Intervals and Chi Square discussion

Question description

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Week 4
Confidence
Intervals and Chi Square  (Chs 11 - 12)
  Let's look at some other factors that might
influence pay.

For
question 3 below, be sure to list the null and alternate hypothesis
statements.  Use .05 for your
significance level in making your decisions.
 
 
 
 
 
 
For
full credit, you need to also show the statistical outcomes - either the
Excel test result or the calculations you performed.
 
 
 
 
 
 
 
 
 
 
 
 
1
One question we might
have is if the distribution of 
graduate and undergraduate degrees independent of the grade the
employee?
 
 
 
 
 
 
(Note: this is the same
as asking if the degrees are distributed the same way.)
 
 
 
 
 
 
Based on the analysis of
our sample data (shown below), what is your answer?
 
 
 
 
 
 
 
 
 
 
Ho: The populaton
correlation between grade and degree is 0.
 
 
 
 
 
 
Ha: The population
correlation between grade and degree is > 0
 
 
 
 
 
 
Perform analysis:
 
 
 
 
 
 
OBSERVED
A
B
C
D
E
F
Total
 
 
 
 
 
 
COUNT - M or 0
7
5
3
2
5
3
25
 
 
 
 
 
 
COUNT - F or 1
8
2
2
3
7
3
25
 
 
 
 
 
 
total
15
7
5
5
12
6
50
 
 
 
 
 
 
EXPECTED
 
 
 
 
 
 
7.5
3.5
2.5
2.5
6
3
25

 
 
 
 
 
 
 
 
 
 
 
By using either the
Excel Chi Square functions or calculating the results directly as the text
shows, do we
 
 
 
 
 
 
reject or not reject the
null hypothesis?  What does your
conclusion mean?
 
 
 
 
 
 
Interpretation:
 
 
 
 
 
 
 
 
 
 
 
 
2
Using our sample data,
we can construct a 95% confidence interval for the population's mean salary
for each gender.
 
 
 
 
 
 
Interpret the
results.  How do they compare with the
findings in the week 2 one sample t-test outcomes (Question 1)?
 
 
 
 
 
 
Males
Mean
St error
Low
to
High
 
 
 
 
 
 
52
3.65878
44.4483
59.5517
Results are mean
+/-2.064*standard error
 
 
 
 
Females
38
3.62275
30.5226
45.4774
2.064 is t value for 95%
interval
 
 
 
 
 

 
 
 
 
 
 
Interpretation:
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
3
Based on our sample
data, can we conclude that males and females are distributed across grades in
a similar pattern within the population?
 
 
 
 
 
 
 
 
 
 
 
 
4
Using our sample data,
construct a 95% confidence interval for the population's mean service
difference for each gender.
 
 
 
 
 
 
Do they intersect or
overlap?  How do these results compare
to the findings in week 2, question 2?
 
 
 
 
 
 
 
 
 
 
 
 
5
How do you interpret
these results in light of our question about equal pay for equal work?
 
 
 
 
 
 
 
 
 
 
 
 

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