Question

In a sample of 14 CEOs, they spent an average of 12.9 hours each week looking into new product opportunities with a standard deviation of 4.9 hours. Find the 95% confidence interval.a. (10.3, 15.5)b. (8.0, 17.8)c. (10.1, 15.7)d. (9.9, 15.9)

Answer 1

c. (10.1, 15.7)

Explanation:

The calculation of the 95% confidence interval is shown below:

Given that

n = sample = 14

average =
`\bar x` = 12.9

Standard deviation = s = 4.9

Based on the above information

`\alpha = 1 -0.95 = 0.05`

n - 1 = 14 - 1 = 13

`t_(\alpha)\ value = 2.16`

Now the 95% confidence interval is

`= \bar x + \pm\ t * (s)/(√(n) ) \\\\= 12.9 \pm 2.16 * (4.9)/(√(14) ) \\\\= 12.9 \pm 2.8287`

= (10.1, 15.7)

hence, the correct option is c.