Question
In: Statistics and Probability
Using the data below and the 5 steps of null hypothesis testing for a chi-square goodness...
- Using the data below and the 5 steps of null hypothesis testing for a chi-square goodness of fit test examine if the frequency of confirmed COVID-19 cases are equally proportionate between the states of Wyoming, North Dakota, Nebraska, and South Dakota (p < .05).
**Data retrieved from Center for Disease Control (April 22, 2020)**
|
Observed Frequencies |
|
|
Wyoming |
430 |
|
N. Dakota |
627 |
|
Nebraska |
1648 |
|
S. Dakota |
1675 |
Solutions
Expert Solution
Null hypothesis : The 4 states have equal proportion of cases
Alternate hypothesis: At least one state have different proportion
alpha = 0.05
| Event | Observed Frequency(O) | Expected Probability | Expected Frequency ( E) | ( O-E)^2 | ( O-E)^2/E |
| Wyoming | 430 | 0.25 | 1095 | 442225 | 403.8584475 |
| N. Dakota | 627 | 0.25 | 1095 | 219024 | 200.0219178 |
| Nebraska | 1648 | 0.25 | 1095 | 305809 | 279.2776256 |
| S. Dakota | 1675 | 0.25 | 1095 | 336400 | 307.2146119 |
| Total | 4380 | 1 | 4380 | 1303458 | 1190.372603 |
The chi square statistic = 1190.372
The corresponding p value is 0.00000
Since p < alpha ( 0.05 )
We reject the null hypothesis
or, At least one state have different proportion
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