Research is conducted regarding the average age at retirement for four careers. A total of 700 people who recently retired are randomly selected. The resulting data are displayed in the contingency table below. The research question is: Are there differences in the retirement age for the four career types? a. What statistical test is most appropriate to answer this question? Identify the relevant assumptions and conditions and state how these have or have not been met b. Write an appropriate null and alternative hypothesis

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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Research is conducted regarding the average age at retirement for four careers. A total of 700 people who recently retired are randomly selected. The resulting data are displayed in the contingency table below. The research question is: Are there differences in the retirement age for the four career types?

a. What statistical test is most appropriate to answer this question? Identify the relevant assumptions and conditions and state how these have or have not been met

b. Write an appropriate null and alternative hypothesis for this question. 

c.Assuming a 5% significance level, what is the appropriate decision for this test and why?

d. Write a one-sentence conclusion statement

e.Examine the standardized residuals presented in the table below and discuss any significant results in 2-4 sentences 

 

Age of retirement
50-55
56-60
61-65
65+
Sales
10
40
75
40
=
Professor
50-55
5
30
80
60
Career type
Expected cell frequency:
Sales
Professor
Nurse
Data analyst 14.04000 41.34000 74.88000 51.74000
61-65
Nurse
21
45
63
49
65+
56-60
12.72857 37.47857 67.88571 46.90714
15:22:2
13.50000 39.75000 72.00000 49.75000
13.73143 40.43143 73.23429 50.60286
The appropriate test was performed in R. The results are shown below:
data: observed
X-squared 20.771, df
9, p-value = 0.01371
Data analyst
18
44
70
50
Transcribed Image Text:Age of retirement 50-55 56-60 61-65 65+ Sales 10 40 75 40 = Professor 50-55 5 30 80 60 Career type Expected cell frequency: Sales Professor Nurse Data analyst 14.04000 41.34000 74.88000 51.74000 61-65 Nurse 21 45 63 49 65+ 56-60 12.72857 37.47857 67.88571 46.90714 15:22:2 13.50000 39.75000 72.00000 49.75000 13.73143 40.43143 73.23429 50.60286 The appropriate test was performed in R. The results are shown below: data: observed X-squared 20.771, df 9, p-value = 0.01371 Data analyst 18 44 70 50
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