Question 1 a) In order to estimate the unemployment rate of Hong Kong, a random sample of 8500 people was selected in 2002 and 618 people were found to be unemployed. Find a 95% confidence interval for the unemployment rate of Hong Kong in 2002. Give your answer to the fourth decimal place. b) If you want to be 95% confident of estimating the unemployment rate of Hong Kong in part (a) to within 10.2%, what sample size is needed? c) According to the report given by the Census and Statistics Department of Hong Kong, the actual unemployment rate of Hong Kong in 2002 is 7.3%. In a survey of 620 people in Shatin, 34 people were found to be unemployed. Is there evidence that the Shatin unemployment rate was lower than the Hong Kong unemployment rate at the 0.05 level of significance? Question 2 a) Grant, Inc., a manufacturer of women's dress blouses, knows that its brand is carried in 19 percent of the women's clothing stores in Hong Kong. Grant recently sampled 85 women's clothing stores in mainland China and found that 14 percent of the stores carried the brand. (i) At the 0.05 level of significance, is there evidence that Grant has poorer distribution in mainland China than it does in Hong Kong? (1i ) Interpret the decision you made in (i) in the situation being examined. (iii) What is the p-value in (i)? Do you make the same decision as in (i) at a = 0.05 if you use the p-value approach? (iv) Suppose that the sample size n = $5 is fixed and further suppose that the penalty of committing type II is serious, which a value (0.05 or 0.10) do you choose for the hypothesis testing? Briefly explain your choice. b) From past records, a charity has found that 42% of donors in a year will denote again in the next year. A random sample of 300 donors from last year was taken. (please think of the concept of standard error of the sample mean first, then to this proportion case). (i) What is the standard error of the sample proportion who will donate again this year? What is the probability that the sample proportion is between 0.40 and 0.45? (ii) Without doing the calculations, state in which of the following ranges the sample proportion is more likely to lie: 0.39 to 0.41, 0.41 to 0.43, 0.43 to 0.45.