5. (10%) The following results come from two independent random samples taken of two different normal populations. Assume that two variances are unknown, but they are the same.

| Sample 1 | Sample 2 |
| --- | --- |
| n=15 | m=10 |
| x̄ = 13.6 | ȳ = 11.6 |
| S_x = 2.2 | S_y = 3.0 |

(a) \((5\%)\) What is the point estimate of the difference between the two population means?

(b) \((5\%)\) Find a \(95\%\) confidence interval for the different between the two population means.

6. (10%) The following table contains observed frequencies of a sample of 500. Test for independence of the row and column variables using α=0.01 level of significance.

7. (10%) In an experiment to investigate the performance of four different brands of tires for 125-cc motorcycles, five tires of each brand were tested and number of miles until failure was observed. A partially completed ANOVA table is given: | Source of variation | Sum of Squares | Degrees of Freedoms | Mean Square | F-value | | --- | --- | --- | --- | --- | | Treatments | (?) | (?) | (?) | (?) | | Error | 235419 | (?) | (?) | | | Total | 310501 | (?) | | | (a) \((7\%)\) Complete the ANOVA table.

(b) \((3\%)\) At the \(\alpha = 0.05\) level of significance, test whether the average number of miles until failure for the four different brands of tires are equal.

8. (20%) Given are following observations collected in a regression study on two variables. Consider the linear regression model $$Y = \beta_0 + \beta_1X + \varepsilon$$ | $$x_t$$ | 2 | 3 | 4 | 5 | 6 | | --- | --- | --- | --- | --- | --- | | $$y_t$$ | 3 | 7 | 5 | 11 | 14 | (a) \((5\%)\) Find the estimated regression equation for these data.

(b) \((5\%)\) Use the estimated regression equation to predict the value of \(y\) when \(x = 7\).

(c) \((5\%)\) Find the coefficient of determination \(R^2\)

(d) (5%) Use F test to test the hypotheses \( H_0 \): \( \beta_1 = 0 \) vs. \( H_a \): \( \beta_1 \neq 0 \) at 0.05 level of significance.

The following table is the cumulative probabilities for the standard distribution

作文題目一：Effects of Coronavirus Disease 2019 (COVID-19) in Taiwan (250-300 words; 70%)

115年 - 115 國立臺北大學_學士班曁進修學士班轉學生招生考試試題_統計學系日間學士班2、3年級、金融與合作經營學系日間學士班3年級：統計學#147967

115年 - 115 國立臺北大學_日間學士班轉學生招生考試試題_統計學系日間學士班2、3年級 金融與合作經營學日間學士班3年級：統計學#147585

115年 - 115 國立臺北大學_碩士班一般入學考試試題_國際企業研究所：統計學#147120

115年 - 115 國立臺北大學_碩士班一般入學考試試題_統計學系：統計學#147104

115年 - 115 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#146969

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