n=97,x=46;98% confidence
To calculate the 98% confidence interval for a sample mean, we will need the sample size (n), the sample mean (x), and the standard deviation (σ) of the population.
Since we don't have the population standard deviation, we will estimate it using the sample standard deviation (s). However, we need the actual values of the sample data to calculate the sample standard deviation.
If you have the sample data, please provide it, and I will be able to give you a more accurate answer.
To calculate the margin of error for a 98% confidence level, we can use the formula:
Margin of Error = Z * (Standard Deviation / sqrt(n))
Where:
- Z: The Z-score associated with the desired confidence level. For a 98% confidence level, the Z-score is approximately 2.33.
- Standard Deviation: The standard deviation of the population. Since you haven't provided this information, I assume you want a single-sample estimation. In that case, we can use the sample standard deviation as an estimation of the population standard deviation.
- n: The sample size.
Now, let's calculate it step-by-step:
Step 1: Find the Z-score for a 98% confidence level.
Z = 2.33
Step 2: Calculate the standard deviation.
Since the standard deviation is not provided, let's assume you have a sample standard deviation available. If not, you can estimate it or use the entire population if it's available.
Step 3: Calculate the margin of error using the formula:
Margin of Error = Z * (Standard Deviation / sqrt(n))
= 2.33 * (Standard Deviation / sqrt(97))
The margin of error will depend on the standard deviation value that you provide or estimate.
I assume that x refers to the mean, but I am not sure. What is the standard deviation (SD)?
98% are within μ ± 2.33 SE (Standard Error of the Mean)
( Got the above by looking at table of proportions under the normal distribution in the back of a statistics text, seeking a Z score whose smallest value is .01. 98% would leave 1% on each tail.)
SE = SD/sq.rt. (n-1)
I hope this helps. If not, repost with adequate and accurate information.
I hope this helps.