Question

In a study, researchers wanted to estimate the true mean skidding distance along a new road in a European forest. The skidding distance (in meters) were measured at 20 randomly selected road sites. The 95% confidence interval constructed based on the data collected was (303.3, 413.6). A logger working on the road claims that the mean skidding distance is at least 425 meters. Does the confidence interval supports the loggers claim

Answer 1

`303.3 \leq \mu \leq 413.6`

We need to remember that the confidence interval for the true mean is given by:

`\bar X \pm t_(\alpha/2)(s)/(√(n))`

Since the upper limit for the confidence interval is lower than the value of 425 we don't have enough evidence to conclude that the the mean skidding distance is at least 425 meters at the 5% of signficance used so then the confidence interval not support the loggers claim

Explanation:

We know that they use a sample size of n =20 and the confidence interval for the true mean skidding distance along a new road in a European forest is given by:

`303.3 \leq \mu \leq 413.6`

We need to remember that the confidence interval for the true mean is given by:

`\bar X \pm t_(\alpha/2)(s)/(√(n))`

Since the upper limit for the confidence interval is lower than the value of 425 we don't have enough evidence to conclude that the the mean skidding distance is at least 425 meters at the 5% of signficance used so then the confidence interval not support the loggers claim