Answer Happy

A major manufacturing firm producing polychlorinated biphenyls
(PCBs) for electrical insulation discharges small amounts from the
plant. We assume that the amount of PCB discharge per water
specimen is normally distributed with known population standard
deviation of 0.4 ppm. Production will be halted if there is
evidence that the mean PCB amount discharged in the water exceeds
3.4 ppm (parts per million). A random sample of 25 water specimens
produced a sample mean of 3.5 ppm. Answer the following questions
for a one-sided hypothesis test with alpha of 5%.
Find the z-score test statististic to two decimal
places.
Find the p-value of the test to four decimal places.
Should you reject the null hypothesis?
yes
no
What is the probability of a type I error to two decimal places
(as a decimal, not a percent)?
Find the critical value used in the power calculation to two
decimal places.
Find the power of the test against an alternative mean of 3.6 to
four decimal places.
Find the probability of a type II error to four decimal
places.
Assuming the amount of PCB discharge per water specimen is
normally distributed with known population standard deviation of
0.4 ppm, a random sample of 25 water specimens produced a sample
mean of 3.5 ppm. Find the lower bound of a 95% confidence interval
to two decimal places.
Find the upper bound of a 95% confidence interval to two decimal
places.
Assuming the amount of PCB discharge per water specimen is
normally distributed with known population standard deviation of
0.4 ppm, what sample size is necessary to ensure a margin of error
of less than 0.10 ppm for a 95% confidence interval?