(b) What is the probability that the point estimate was within \( \pm 25 \) of the population mean?

(a) What is the \( 95\% \) confidence interval for the population mean amount spent on cigarette?

(b) If the amount spent on cigarette is skewed to the right, what would you expect the median amount spent on cigarette compared to the mean?

IV. (20%) Suppose, in a poll of 910 adults, 503 respondents reported that they were optimistic about the national outlook. The Press Secretary claims that this poll indicates that the majority of adults are optimistic about the nation's outlook. Conduct a hypothesis test using the p-value approach and use α = 0.05 for the level of significance to test the Press Secretary's statement.

(a) Use days to denote the number of days that students are absent and use distance to denote the distance between student's home and school. What is the least squares regression model estimated by the researcher? What is the sample size?

(b) Is there a significant relationship between the two variables? Use \( \alpha = 0.05 \) for the level of significance.

(c) Did the estimated regression provide a good fit? Explain your answer.

(d) Develop a \( 95\% \) confidence interval for the slope of the regression.

VI. (20%) A financial adviser wants to compare the mutual fund performance between two countries. 30 mutual funds from each country were randomly selected and the annual return for the funds were collected for the analysis. The descriptive statistics of the two samples are shown below: Conduct a hypothesis test to test whether the mutual funds from Country A have a higher annual return than the mutual funds from Country B. At the 0.05 level of significance, what is your conclusion? You may use reasonable approximations in your calculation.

1. 以所得面及支出面之名目所得計算式，試推導出開放經濟體系下的「簡單凱因斯模型」？(5%)

2.以「簡單凱因斯模型」說明在開放經濟體系下，影響一國經濟景氣變動的主要成因為何？(5%)

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