the average of the hemoglobin reading for a sample of 20 teachers was 16 gram per 100 milliliters, with a sample standard deviation of 2 grams. find the 99% confidence interval of the population mean.
99% = mean ± 2.575 SEm
SEm = SD/√n
To find the 99% confidence interval of the population mean, we can use the following formula:
Confidence interval = X̄ ± Z * (σ/√n)
Where:
X̄ is the sample mean
Z is the Z-score corresponding to the desired confidence level (99%)
σ is the population standard deviation
n is the sample size
Given information:
Sample mean (X̄) = 16 grams
Sample standard deviation (σ) = 2 grams
Sample size (n) = 20
First, we need to find the Z-score corresponding to the 99% confidence level. The Z-score can be obtained using a Z-table or a statistical calculator. For a 99% confidence level, the Z-score is approximately 2.576.
Now, we can calculate the confidence interval:
Confidence interval = 16 ± 2.576 * (2/√20)
Confidence interval = 16 ± 2.576 * (2/4.472)
Confidence interval = 16 ± 2.576 * 0.447
Confidence interval = 16 ± 1.151
The 99% confidence interval for the population mean is approximately (14.849, 17.151).
Therefore, we can say with 99% confidence that the true population mean lies within the range of 14.849 grams to 17.151 grams.
To find the 99% confidence interval of the population mean, we can use the formula:
Confidence Interval = Sample Mean ± (Z * Sample Standard Deviation / √n)
Where:
- Sample Mean is the average of the hemoglobin reading for the sample (16 grams per 100 milliliters).
- Z is the z-score related to the desired confidence level (99% = 2.58 for a large enough sample size).
- Sample Standard Deviation is the standard deviation of the sample (2 grams).
- n is the sample size (20 teachers).
Calculating the confidence interval:
Confidence Interval = 16 ± (2.58 * 2 / √20)
1. Calculate the value inside the parentheses:
= 2.58 * 2 / √20
= 1.4482
2. Calculate the lower bound of the confidence interval:
Lower bound = 16 - 1.4482
= 14.5518
3. Calculate the upper bound of the confidence interval:
Upper bound = 16 + 1.4482
= 17.4482
Therefore, the 99% confidence interval of the population mean is (14.5518, 17.4482).