A researcher would like to determine whether any particular age group has a grea
ID: 3223692 • Letter: A
Question
A researcher would like to determine whether any particular age group has a greater risk of related death if in the city, 30% of the population is in the "under 30" bracket, 40% is in "30-60, " and 30% is in "over 60" what does the following breakdown of the 7 influenza deaths suggest? Set this up as a formal inferential proof with the following 7 steps: 1. One tail or two tail. 2. Alternate and null hypotheses. 3. Type of test and why. 4. Critical values (df if needed) at .05 and .01. 5. Compute test. 6. Accept or reject null (Remember to include level if reject.) 7. English conclusion. Include percent for each age group. N = 50Explanation / Answer
Solution:
Here, we have to use the chi square test for goodness of fit.
The null and alternative hypotheses are given as below:
Null hypothesis: H0: The observed frequencies do not follow the population distribution.
Alternative hypothesis: Ha: The observed frequencies follow the population distribution.
This is a two tailed test.
The test statistic formula is given as below:
Chi square = [(O – E)^2/E]
The calculation table is given as below:
Age
O
Prob.
E
(O - E)^2
(O - E)^2/E
<30
10
0.3
15
25
1.666666667
30-60
10
0.4
20
100
5
>60
30
0.3
15
225
15
Total
50
1
50
21.66666667
Chi square test statistic = 21.67
Degrees of freedom = 3 – 1 = 2
P-value = 0.00002
Alpha value = 0.05 and 0.01
Critical value for alpha = 0.05 = 5.99
Critical value for alpha = 0.01 = 9.21
Chi square test statistic > Critical value for alpha = 0.05 and 0.01
So, we reject the null hypothesis at both level of significance or alpha = 0.05 and 0.01
The observed frequencies follow the population distribution.
Age
O
Prob.
E
(O - E)^2
(O - E)^2/E
<30
10
0.3
15
25
1.666666667
30-60
10
0.4
20
100
5
>60
30
0.3
15
225
15
Total
50
1
50
21.66666667
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