If bird flu mortality in one sample of 100 is 20% and in another sample of 100 it is 30%. Is the difference in mortality rate is significant? Solve for the statistic value of Z at probability alpha level of 0.05. Please show your solution.
To determine if the difference in mortality rates is statistically significant, we can perform a hypothesis test using a Z-test.
1. State the null hypothesis (H0) and alternative hypothesis (H1):
- H0: The difference in mortality rates between the two samples is not significant.
- H1: The difference in mortality rates between the two samples is significant.
2. Calculate the observed difference in mortality rates:
- Mortality rate in Sample 1 = 20%
- Mortality rate in Sample 2 = 30%
- Observed difference in mortality rates = 30% - 20% = 10%
3. Determine the standard error (SE) of the difference:
- SE = sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)]
- p1 = mortality rate in Sample 1 = 20% = 0.20
- n1 = sample size of Sample 1 = 100
- p2 = mortality rate in Sample 2 = 30% = 0.30
- n2 = sample size of Sample 2 = 100
- SE = sqrt[(0.20 * (1 - 0.20) / 100) + (0.30 * (1 - 0.30) / 100)]
- SE ≈ 0.0436
4. Calculate the Z statistic value:
- Z = (observed difference - expected difference) / SE
- Expected difference = 0 (assuming no difference)
- Z = (0.10 - 0) / 0.0436
- Z ≈ 2.2928
5. Determine the critical Z value at the desired alpha level (α):
- α = 0.05 (given)
- For a two-tailed test, we divide α by 2 to get α/2 = 0.025
- Using a Z-table or a statistical calculator, find the critical Z value at α/2 = 0.025
- The critical Z value for α/2 = 0.025 is approximately 1.96
6. Compare the Z statistic value with the critical Z value:
- Z statistic value = 2.2928
- The critical Z value at α/2 = 0.025 is 1.96
- Since the Z statistic value (2.2928) is greater than the critical Z value (1.96), we can reject the null hypothesis.
7. Interpretation:
- The difference in mortality rates between the two samples is statistically significant at the 0.05 significance level. This suggests that there is a significant difference in bird flu mortality between the two samples.