I've slowly been building up some confidence on these types of problems but after the easy plug-n-chug I get very confused on what to do. There is a solution I found online for this question (number 1, solution 1) but I get confused on the very last step, where they say .046 > .05.
The question is: A colony of laboratory mice consists of several thousand mice. The average weight of all the mice is 32 grams with a standard deviation of 4 grams. A laboratory assistant was asked by a scientist to select 25 mice for an experiment. However, before performing the experiment, the scientist decided to weigh the mice as an indicator of whether the assistants selection constituted a random sample or whether it was made with some unconscious bias (perhaps the mice selected were the ones that were slowest in avoiding the assistant, which might indicate some inferiority about this group). If the sample mean of the 25 mice was 30.4, would this be significant evidence, at the 5 percent level of significance, against the hypothesis that the selection constituted a random sample?
My steps were:
Ho = mu-not is 32 grams (selection is random)
H1 = mu is not 32 grams (selection is not random)
standard deviation is 4 grams
n = 25 mice
x-bar (sample mean) = 30.4
Confidence Interval is 95% (level of significance is .05)
All I really did was find the p-value using: (x-bar - mu) / (std dev / sqrt(n))
p-value: |30.4 - 32| / (4/5) = 2
The probability of rejecting Ho = (Z > 2)
Value based on the confidence interval would be the level of significance divided by 2 since this is a two-sided confidence interval. Looking this up in a z-table I got 1.96. However, I don't know where to go from here especially since the solutions page has .046 < .05, which I'm not sure how to get. Can someone please explain this?