I NEED HELP ASAP

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 tha 0.10 ppm for a 95% confidence interval?