(b) Suppose you recommend that the client invests \( 75\% \) in the WSI and \( 25\% \) in the TGB. If the client decides to invest in NT$10,000 in this portfolio, what would be the expected return and standard deviation, in dollars, for the client's investment?

(a) How large was the sample used in the study?

(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.

115年 - 110 國立臺北大學_碩士班一般入學考試試題_企業管理學系甲組：統計學#146951

115年 - 115 國立臺北大學_碩士班一般入學考試試題_金融與合作經營學系：統計學#146920

115年 - [無官方正解]115 國立臺北大學_碩士班一般入學考試試題_經濟學系：統計學#146534

115年 - [無官方正解]115 國立嘉義大學_碩士班招生考試試題_財務金融學系：統計學#143862

115年 - 115 中央警察大學_碩士班入學考試試題：統計學#139759

114年 - 114 國立臺北大學_碩士班一般入學考試試題_企業管理學系甲組：統計學#146907

114年 - 114 中央警察大學_碩士班入學考試試題_警察政策研究所、刑事警察研究所、資訊管理研究所、鑑識科學研究所、行政管理研究所、防災研究所、水上警察研究所海洋科技組：統計學(同等學力加考)#146791

114年 - [無官方正解]114 國立嘉義大學_碩士班招生考試試題_財務金融學系：統計學#144015

114年 - [無官方正解]114 臺灣綜合大學系統_學士班轉學生考試試題:統計學#138278

113年 - 113 國立臺北大學_碩士班一般入學考試試題_自然資源與環境管理研究所：統計學#146880