A study of 29 female Sumatran elephants provided a 95% confidence interval for the mean shoulder height as (197.2, 235.1) cm. Consider a new study to estimate the mean shoulder height of male Sumatran elephants. Assuming the standard deviations of shoulder heights are similar for males and females, how many male elephants should be sampled so that the 95% confidence interval for the mean shoulder height of males will have a margin of error of 10 cm?
I know the formula to determine the sample size is:
n=((1.96∙?)/10)
How do I guess the Standard Deviation? I cannot find anything in any scientific literature that has a similar SD.
Thanks for you help.
A confidence interval is found by adding and subtracting the margin of error.
If we take the difference of 235.1 and 197.2 and divide by 2 we have the margin of error.
this margin of error is found by taking 1.96 times the standard deviation.
To find the standard deviation divide 1.96 in to the answer from above. Now, you will have the sd for the next part of the problem.
Thanks John :)
You are welcome.
To estimate the sample size required for the new study, you will need an estimate of the standard deviation of the shoulder heights of male Sumatran elephants. Since you mentioned that you cannot find a similar standard deviation in scientific literature, you have a few options:
1. Pilot Study: You can conduct a small pilot study on a few male Sumatran elephants to estimate their shoulder height standard deviation. This will provide you with a more accurate estimate specific to male elephants.
2. Use the Female Standard Deviation: If no other option is available, and you assume that the standard deviations are similar for males and females as stated in the question, you can use the standard deviation from the existing study of female elephants as an estimate for male elephants. Although this is not ideal, it can provide a rough approximation.
3. Expert Knowledge: If you have expert knowledge or advice from experienced wildlife researchers or veterinarians, they may be able to provide an estimate of the standard deviation based on their experience with male Sumatran elephants.
Remember, the more accurate your estimate of the standard deviation, the more precise your sample size calculation will be. Without a reliable estimate, it may be challenging to obtain an accurate sample size determination.
"John"'s answer is incomplete. The real solution is:
W_female: (235.1 - 197.2)/2 = 18.45
t-value for females: 2.048
SD_female: (W*sqrt(n))/t = (18.45*sqrt(29))/2.048 = 48.5
As stated, the margin of error for males is 10. We assume the t-value for males is 2 based on the female value. So,
10 = 2*(48.5/sqrt(n))
n = 9409/100 = 94.09 male elephants
OR you can say:
n = (4.85 * 2)^2 = 94 male elephants.
Either way, this is your answer.