Researchers collected data on 100 days for the number of asthma emergency depart
ID: 3265306 • Letter: R
Question
Researchers collected data on 100 days for the number of asthma emergency department visits for children in Seattle. Their sample is summarized in the table below:
Number of visits 0 1 2 3 4 5 6
Observed frequency 12 24 36 16 9 2 1
Based on these observations, is a Poisson distribution with a mean of 2.3 an appropriate model? Perform a goodness of fit test with a significance level of 0.10. In order to receive full credit, you must clearly state the hypotheses, the test statistic, the p-value, and the rejection decision.
Explanation / Answer
Hypothesis:-
Ho: Poisson distribution is well fit to the given data.
H1: Poisson distribution is not well fit to given data.
Test Statistics :
Chi-Square = (Oi-Ei)2/Ei
Oi= Observed frequency
Ei=Expected Frequency
Calculations:-
Number of Visit
Observed
Poisson Probability
Expected
Contribution to Chi-Sq
0
12
0.140858
14.0858
0.30887
1
24
0.276083
27.6083
0.47158
2
36
0.270561
27.0561
2.95658
3
16
0.176766
17.6766
0.15903
4
9
0.086616
8.6616
0.01322
5
2
0.033953
3.3953
0.57342
6
1
0.015163
1.5163
0.17580
N
N*
Df
Chi-Sq
P-Value
100
0
5
4.65851
0.459
Result:- Here We observed that The p-values(0.459) > Level of significance (0.01) There for we accept the null Hypothesis i.e . The Poisson distribution is well fit to data.
Number of Visit
Observed
Poisson Probability
Expected
Contribution to Chi-Sq
0
12
0.140858
14.0858
0.30887
1
24
0.276083
27.6083
0.47158
2
36
0.270561
27.0561
2.95658
3
16
0.176766
17.6766
0.15903
4
9
0.086616
8.6616
0.01322
5
2
0.033953
3.3953
0.57342
6
1
0.015163
1.5163
0.17580
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