Question 4 20 marks A doctor claimed that the average weight of newborn babies 1n City A 15 greater than 3kg He selected a random sample of 16 newborn babies from City A and he found that the sample mean weight of the newborn babies was (3.16 + E) kg. It 15 known that the weights of newborn babies in City A follow a normal distribution with a standard deviation of 0.4 kg. Test the doctor's claim using z-test with critical value method at a level of signicance of 0.011. Carry out the test by completing the following questions. (a) State the hypothesis and identify the claim. Indicate also whether the test is left-tailed, right-tailed or two-tailed. (3 marks) (b) Find the critical value. Correct your answer to 2 decimal places. (3 marks) (c) Find the test value. Correct your answer to 2 decimal places. (3 marks) (d) Make a decision for the test using critical value method. (3 marks) (e) Summarize the result of the test. (3 marks) (1) Find the probability that the null hypothesis is not rejected if it is actually true. Correct your answer to 4 decimal places. (2 marks) (g) If the test is carried out by p-value method instead of critical value method, nd the p-value. Correct your answser to 4 decimal places