Question 884233
test assumption is that the mean is not equal to 500.
sample size = 81
sample mean = 492
population standard deviation = 36.


standard error = population standard deviation divided by square root of sample size = 36 / sqrt(81) = 36/9 = 4


z score = (sample mean minus popjulation mean) / standard error = (492 - 500) / 4 = -8/4 = -2


test alpha = .0228 from the z score table.  this is the area under the distribution curve that is to the left of a z score of -2.


since the critical alpha = .02 and the test alpha is greater than this, the results are not  statistically significant and you do not reject the null hypothesis in favor of the alternate hypothesis.


z score table used can be found at the following link:
<a href = "http://lilt.ilstu.edu/dasacke/eco148/ztable.htm" target = "_blank">http://lilt.ilstu.edu/dasacke/eco148/ztable.htm</a>