To construct the confidence interval for the difference between the two population proportions, we can use the formula:
Margin of Error (ME) = Z * sqrt(p1(1-p1)/n1 + p2(1-p2)/n2)
Where:
- ME is the margin of error
- Z is the z-score associated with the desired level of confidence (in this case, for a 99% confidence interval)
- p1 is the proportion in sample 1 (males)
- p2 is the proportion in sample 2 (females)
- n1 is the sample size of sample 1 (males)
- n2 is the sample size of sample 2 (females)
First, let's calculate the proportions and sample sizes:
p1 = 31/100 = 0.31
p2 = 24/100 = 0.24
n1 = 100
n2 = 100
Next, we need to find the z-score associated with a 99% confidence level. For a 99% confidence level, the z-score is approximately 2.576.
Plugging in the values:
ME = 2.576 * sqrt(0.31 * (1-0.31)/100 + 0.24 * (1-0.24)/100)
ME ≈ 0.0779
Finally, we can construct the confidence interval:
CI = (p1 - p2) ± ME
CI = (0.31 - 0.24) ± 0.0779
Since we want the upper limit of the confidence interval, let's calculate the upper limit:
Upper Limit = (0.31 - 0.24) + 0.0779
Upper Limit ≈ 0.1479
Therefore, the upper limit of the 99% confidence interval for the difference between the two population proportions is approximately 0.1479.
A random sample of 100 males shows that 31 males have a certain minor blood disorder, while a random sample of 100 females shows that only 24 have the disorder. Construct a 99% confidence interval for the diffrences between the two population proportions. Give the the upper limit.
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