The average hemoglobin reading for a sample of 20 nurses was 16 grams per 100 mL, with a sample standard deviation of 2 g. Assume the hemoglobin readings are approximately normally distributed. The 98% confidence interval for the true mean hemoglobin reading for nurses is closest to
To find the 98% confidence interval for the true mean hemoglobin reading for nurses, we can use the formula:
Confidence interval = (sample mean) ± (critical value) * (standard deviation / sqrt(sample size))
First, let's calculate the critical value. Since we want a 98% confidence level, we need to find the z-score associated with that level. The z-score can be found using a standard normal distribution table or a calculator. For a two-tailed test with a 98% confidence level, the critical value is approximately 2.33.
Next, we'll plug in the given values into the formula:
- Sample mean (x̄) = 16 grams per 100 mL
- Standard deviation (σ) = 2 grams
- Sample size (n) = 20
Confidence interval = 16 ± 2.33 * (2 / sqrt(20))
Now, let's solve the equation:
Confidence interval = 16 ± 2.33 * (2 / 4.47)
Simplifying further:
Confidence interval = 16 ± 2.33 * 0.448
Finally, we can calculate the confidence interval:
Confidence interval = 16 ± 1.044
Therefore, the 98% confidence interval for the true mean hemoglobin reading for nurses is approximately 14.956 to 17.044 grams per 100 mL.