Answer:The 99% confidence interval is
To find the 99% confidence interval for the mean systolic blood pressure (SBP) level, we use the formula:
CONFIDENCE INTERVAL = Mean ± Z * (Standard Deviation / √n)
Where:
Mean is the sample mean of SBP
Z is the Z-score corresponding to the desired confidence level
Standard Deviation is the population standard deviation
Explanation:
Given that the sample size is 13 and the standard deviation is 10, we need to calculate the sample mean and the Z-score for the 99% confidence level.
First, we calculate the sample mean:
Mean = (129 + 134 + 142 + 114 + 120 + 116 + 133 + 142 + 138 + 148 + 129 + 133 + 140) / 13
= 1724 / 13
≈ 132.62
Next, we need to determine the Z-score for a 99% confidence level. The Z-score can be found 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 = 132.62 ± 2.576 * (10 / √13)
132.62 ± 2.576 * (10 / 3.6056)
≈ 132.62 ± 2.576 * 2.771
≈ 132.62 ± 7.147
Therefore, the 99% confidence interval for the mean SBP level is approximately (125.47, 139.77).