Question

The average earnings per share (EPS) for 10 industrial stocks randomly selected from those listed on the Dow-Jones Industrial Average was found to be x ˉ =1.85 with a standard deviation of s=0.395. Calculate a 99% confidence interval for the average EPS.

Answer 1

The student is asked to calculate a 99% confidence interval for the average EPS for 10 industrial stocks listed on the Dow-Jones Industrial Average, with the EPS mean at 1.85 and a standard deviation of 0.395. The calculation involves finding the appropriate t-value for a 99% confidence level and a sample size of 10 and plugging it into the confidence interval formula.

Step-by-step explanation:

The question asks for the calculation of a 99% confidence interval for the average Earnings Per Share (EPS) for 10 industrial stocks randomly selected from those listed on the Dow-Jones Industrial Average, given an average EPS of
`\( \bar{x} = 1.85 \)` ation of
`\( s = 0.395 \)` distribution for a sample size of 10 and a 99% confidence level, we locate the appropriate t-value from a t-table and use the formula for the confidence interval:

`\[ \text{Confidence Interval} = \bar{x} \pm (t \cdot (s)/(√(n))) \]`

Once the t-value is found, it is plugged into the formula along with the given standard deviation and sample size to calculate the confidence interval. Since the sample size is small (n = 10), we use the t-distribution instead of the normal z-distribution.