Utility Company claims that the average monthly utility bills for 4-room HDB flat households is $63. However, a random sample of 50 house households' bills gives an average of $65 with a standard deviation $11.98.

(i) Use the p-value approach to test whether or not the sample statistics support the claim of the utility company. The level of significance is 5%. In your test, you are required to state the hypotheses H0 AND HA, compute the test statistic and the p-value and state your conclusion.

(ii) Determine the 90.1 percent confidence interval on the average monthly utility bills.

(c) With the aid of a diagram describe the operation of Newton's method for finding the roots of a function. Under what situation does this method fail in getting a root?