Question

Compute the 90% confidence interval for μ if ˉx and s ² were obtained from a sample of 15 observations.

a) Use the t-distribution
b) Use the z-distribution
c) Increase the sample size for accuracy
d) Decrease the confidence level

Answer 1

To compute the confidence interval for μ, we can use either the t-distribution or the z-distribution. Let's calculate it using both.

Step-by-step explanation:

To compute the confidence interval for μ, we can use either the t-distribution or the z-distribution. Let's calculate it using both:

a) Using the t-distribution:

Steps:

1. Calculate the standard error: SE = s/√n
2. Calculate the margin of error: ME = t * SE, where t is the critical value from the t-distribution table for a 90% confidence level and n-1 degrees of freedom
3. Calculate the lower limit: LL = ˉx - ME
4. Calculate the upper limit: UL = ˉx + ME

b) Using the z-distribution:

Steps:

1. Calculate the standard error: SE = s/√n
2. Calculate the margin of error: ME = z * SE, where z is the critical value from the z-distribution table for a 90% confidence level
3. Calculate the lower limit: LL = ˉx - ME
4. Calculate the upper limit: UL = ˉx + ME