Calculate and interpret a 95% confidence interval for the mean bp in the pop of ALL anabolic-steroid using athletes:
random sample of 9 athletes resulting in a sd of 207.8, and 109 respectively. When random sample is less than 30, don't I find a t score?
To calculate a confidence interval for the mean blood pressure (bp) in the population of all anabolic-steroid using athletes, we need to follow these steps:
1. Calculate the sample mean (x̄): This is the average blood pressure of the 9 randomly sampled athletes. Let's say the sample mean is x̄ = 120 (hypothetical value).
2. Calculate the standard deviation (s): You mentioned two numbers, 207.8 and 109. Since there are two values given, it's not clear which one is the standard deviation for the blood pressure. Please clarify which value represents the sample standard deviation for the blood pressure.
3. Determine the sample size (n): The number of athletes in the random sample is 9.
4. Determine the confidence level: In this case, it's specified as 95%.
Now, to address your question regarding the t-score calculation, you are correct. For small sample sizes (usually considered as less than 30), it is recommended to use a t-distribution instead of the standard normal distribution (Z-distribution) to calculate the confidence interval.
The t-score accounts for the additional uncertainty in estimating the population mean when we have a small sample size.
To calculate the confidence interval, we can use the following formula:
Confidence Interval = x̄ ± (t * (s / √n))
Where:
x̄ = sample mean
t = t-score corresponding to the desired confidence level and degrees of freedom
s = sample standard deviation
n = sample size
The degrees of freedom can be calculated as (n - 1) since we are estimating the population mean from the sample mean.
Once you clarify the correct standard deviation value (either 207.8 or 109), I can assist you with calculating the specific values for the confidence interval and interpreting the results.