posted by Jonie .
The world’s smallest mammal is the bumblebee bat. Such bats are roughly
the same size of a large bumblebee. Listed below are the weights (in
grams) from a sample of these bats. Assuming that all such bats have a
standard deviation of .3 grams, use a significance level of .05 to test the
claim that these bats are from the same population with a known mean of
1.8 grams. Do the bats appear to be from the same population ? You may
assume the sample data comes from a population that follows a normal
2.13 1.31 1.91 1.92 1.77 1.64 2.29 1.99 2.33 2.49 2.22
Find the mean of your sample first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to your Z score.