Please write detailed steps

1. The Pharmacy Department of Serdang Hospital reported that the average annual

spending on medicines was different from RM838 per patient. A random sample of 60

patients was selected and found that the average annual spending on medicines was

RM745 per patient with a standard deviation of RM300.

(i) At the 5% level of significance, can the department report be rejected?

(ii) Explain the Type I and Type II error in this test.

2.

The local government often faces the problem of not enough money to pay for the

services that it provided. One way to deal is to raise the taxes and another way is to

reduce services. When the local poll asked a random sample of 1200 residents, the

results show that 52% favouring to raise taxes and 48% favouring to reduce services.

Test whether the proportion of residents who choose to raise taxes is different from 50%.

Test at 1% significance level.

3.

A university claims that the percentage of its graduates who fail to get a job after

one year of graduation is less than 10%. A sample of 200 graduates from the university

was randomly selected and found that 16 graduates fail to get a job after one year of

graduation. Is there enough evidence to support the university's claim? Test at 5%

significance level.

4.

The quality manager of a factory wants to determine the life expectancy for

manufactured lamps of his factory and found the mean is 375 hours. The standard

deviation of the population is 100 hours. A sample of 64 lamps showed a mean life time

of 350 hours. At the 5% level, prove that the mean life expectancy is less than 375 hours.