Question

Veterinary researchers at a major university veterinary hospital calculated a 99% confidence interval for the average age of horses admitted for laminitis, a foot disease that leaves the horse severely lame, as 6.3 to 7.4 years. Based on this information we conclude that:
a) All of the above
b) we can be 100% sure that the average age of horses admitted with laminitis is between 6.3 and 7.4 years.
c) we are 99% confident that the true mean age of horses with laminitis is between 6.3 and 7.4 years old.
d) 99% of all horses admitted for laminitis are between 6.3 and 7.4 years old.

Answer 1

Answer:

c) we are 99% confident that the true mean age of horses with laminitis is between 6.3 and 7.4 years old.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample  

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$   (1)

For this cafter calculate the 99% confidence interval they provided the following results:

$6.3 \leq \mu \leq 7.4$

And on this case the best interpretation is:

c) we are 99% confident that the true mean age of horses with laminitis is between 6.3 and 7.4 years old.

Because the confidence interval is for the true mean (parameter of interest) not for the all possible horses.