Final answer:
To calculate the mean and 90% confidence interval for a dataset, follow these steps: calculate the sample mean and standard deviation, and use the formula CI = mean +/- (z * (std dev / sqrt(n))) to construct the interval.
Step-by-step explanation:
To calculate the mean and 90% confidence interval for a dataset, you need to follow these steps:
- Calculate the sample mean by summing up all the values in the dataset and dividing by the number of values.
- Calculate the sample standard deviation, which measures the spread of the data around the mean.
- With the sample mean and known population standard deviation, you can construct a confidence interval using the formula: CI = mean +/- (z * (std dev / sqrt(n))). Here, z represents the z-score for the desired confidence level (e.g., for 90% confidence, z = 1.645), std dev is the population standard deviation, and n is the sample size.
For example, if the mean is 10, the sample standard deviation is 2, and the sample size is 50, the 90% confidence interval would be 10 +/- (1.645 * (2 / sqrt(50))).