Question

Your manager has collected some data regarding spare time of workers in minutes from a sample of 20 workers. The average spare time is 7 minutes with the sample standard deviation of 2 minutes 1. Construct the 90% confidence interval of spare time in the factory. 2. How confident are you that the average spare time is within the range that you found?

Answer 1

1)

Answer:

$\text{90\% CI}=(6.2267,7.7733)$

Explanation:

Since the population standard deviation is not known, the t distribution is used to construct the confidence interval for the mean spare time,

The confidence interval for the mean spare time is obtained using the following formula,

$\text{CI}=\overline{x}\pm t_c\times \frac{s}{\sqrt{n}}$

The t critical value is obtained from t distribution table for significance level = 0.10 and degree of freedom = n -1 = 20 - 1 = 19. In excel use function =T.INV.2T(0.1,19).

$t_c=t_{0.10,11}=1.7291$

now,

$\text{90\% CI}=7\pm 1.7291\times \frac{2}{\sqrt{20}}$

$\text{90\% CI}=(6.2267,7.7733)$

2)

Answer:

We are 90% confident that the mean spare time will lie between 6.2267 and 7.7733 minutes.

Explanation:

For a 90% confidence interval, we are 90% confident that the mean spare time will lie between 6.2267 and 7.7733 minutes such that if we do repeated measures, then there will be 90% chance that the mean spare time will lie in this range.