Question

The ideal (daytime) noise-level for hospitals is 45 decibels with a standard deviation of 10 db. A simple random sample of 500 hospitals at a moment during the day gives a mean noise level of 46 db. Assume that the standard deviation of noise level is really 10 db.

Part One.
Assuming that the average noise level of hospitals is what it's supposed to be, what is the probability of a sample of 500 hospitals producing an average as high as our sample's (p-value)? (_)

Which comes from a test-statistic of z= (_) (Without Sign)

Part Two:
Assuming that the average noise level of hospitals is what it's supposed to be, what is the probability of a sample of this many hospitals producing an average as far from the truth as is our sample's (p-value)? (_)

Answer 1

Part one: Here test will be one tailed.

Part 2:

----------------------------------------------------------------------