1. An international business uses a simple linear regression model to establish the relationship between its sales (Y) and the volume of advertisements (X).

Given the following 10 sets of data (y1, x1),...(y10, x10), where yi is the sales in the ith month, and xi is the number of advertisements in the ith month. According to the information:

10 sales data y1,..., y10, the average value of yi is 130, and the variance is 1748. The number of advertisements for 10 advertisements is x1,...,x10, and the average value of xi is 14. In addition, the sales data y1,...,y10, and the advertisement frequency data x1,...,x10, the covariance is 316.

Using the least squares method, the estimated regression relationship is Y = 60 + 5X.

(1) If the sales in the third month are y3 = 88 and the volume of advertisements performed is x3 = 8, please try to calculate the fitted value and residual value of this month's sales. (5 points)

(2) Please calculate the coefficient of determination R², and sales data y1,...,y10, and the correlation coefficient of the volume of advertisements x1,..., x10. (5 points)

(3) At the significance level α=0.05, use the t test method to test whether the volume of advertisements will affect sales, that is, test whether the slope of the linear relationship of the regression is 0. (5 points)

2. Assuming that there are 3 possible variants during a disease epidemic related to COVID-19: A, British variant, B, South African variant, and C, American variant of COVID-19 disease. Among them, the probability of infected patients is that the probability of the A British variant new coronary pneumonia disease is 0.6, the B South African variant new coronary pneumonia disease probability is 0.3, and the C American variant new coronary lung disease probability is 0.1. These three types of new coronary pneumonia diseases may have fever and cough symptoms. Among them, 20% of patients with A: British variant have fever, 60% of patients with B: South African variant have fever, and 80% of patients with C: American variant have fever; And 50% of patients with variant A in the UK have cough symptoms, 35% of patients with variant B in South Africa have cough symptoms, and 25% of patients with variant C in the United States have cough symptoms. An existing patient who is infected has fever symptoms. Please calculate the probability of this patient to have these three types of new coronary pneumonia, and determine which type of new coronary pneumonia the patient is most likely to have. (10 points)

3. A Taiwan mask manufacturer received an order worth 50 million yuan from a politically unstable country (India). Given a probability of 0.7 this manufacturer can receive payment for the 50 million yuan order. There is a probability of 0.15 that you can only receive a payment of 30 million yuan, a probability of 0.1 that you can only receive a payment of 10 million yuan, and a probability of 0.05 that you will not receive any payment. For the sake of insurance, this Taiwanese manufacturer insures an accident insurance and pays an insurance premium of 10 million yuan first. The Japanese insurance company underwriting will pay any shortfalls in the company's receivables. If the random variable X represents the amount of money spent or earned by this Taiwanese mask manufacturer finally insuring here. Please calculate the expected value E(X) of X. (10 points)

4. An international business wants to choose one of the two recommended by its A branch and B branch to be promoted to a supervisory position. The performance information of the employees of these two branches is as follows: (1) Branch A: The z-score for the branch with a performance score of 84 points is 0.5, and the z-score for the branch with a performance score of 72 points is -2.5. The recommended employee's performance score in his branch is 90.0 points. (2) Branch B: The z-score for the branch with a performance score of 84 points is 3.0, and the z-score for the branch with a performance score of 72 points is -1.0. The recommended employee's performance score in his branch is 82.5 points.

The HR supervisor decided to use the z score to determine the candidate for promotion. May I ask which branch company recommended the employee to be promoted, and please explain the reason (10 points).

5. To compare whether the average lifespan of cell phone batteries of three different brands is the same, randomly test 5 batteries of each brand of cell phone batteries and record their life. The average life spans of the three groups of samples are 3.0, 4.5, and 3.6, and the standard deviations of life spans are 1.5, 1.0, and 15.0, respectively. At the significance level α=0.05, please use one-way ANOVA to check whether the average battery life of these three brands of mobile phones is consistent, that is, check: The null hypothesis H0: μ1 = μ2 = μ3, the opposite hypothesis H1: μ1, μ2, and μ3 are not completely equal. Among them, μ1, μ2 and μ3 are the average lifespans of these three brands of mobile phone batteries. (5 points)

6. Alice's Shop in Oxford, UK, is one of the most famous little shops in the world. It sells Alice in Wonderland themed gifts, souvenirs and memorabilia. One of the popular items is the Tea Party paper bookmark. The average of the Tea Party paper bookmark sold in a week is 2100 units. Supposed the weekly demand is approximately normally distributed, with a standard deviation of 200 units. The manager wants to limit the probability of being out of stock of the Tea Party paper bookmark. Please help to solve his problems below. You need to show your calculations. Remember to use four decimal places. a. If the manager wants to limit the probability of being out of stock of the Tea Party paper bookmark to no more than \(5\%\) in a week, how many units of the bookmarks should he keep at the start of the week? (5 points) b. If the Shop has 2500 units on hand at the start of week, what is the probability that weekly demand will be greater than the inventory? (5 points) c. What is the probability that the Shop sells between 2000 and 2500 Tea Party paper bookmarks in a typical week? (6 points) d. If the standard deviation of weekly demand for the toy increases from 200 units to 350 units, how many more Tea Party paper bookmarks would have to be stocked to ensure that the probability of weekly demand exceeding inventory is no more than \(10\%\)? (5 points) 7. In 2020, the COVID-19 pandemic created a huge problem globally. More than 2 million people died from this disease as of Jan. 15, 2021. Some people say the elderly people are more likely to be infected (Claim A), and the survivors are mostly younger (Claim B). We would like to take a case from a country to see if these claims are reliable. City B had few hundreds of COVID-19 infected cases in 2020, and we took the COVID-19 cases in Hospital C in this city for the calculation. These are the figures of the confirmed infected cases in C hospital: Survival cases' age: 65, 88, 23, 8, 45, 55, 32, 22, 42, 65, 51, 15, 27, 65, 34, 13, 25, 31, 58, 32, 45, 67, 30, 58, 74 Confirmed death cases' age: 90, 18, 43, 67, 88, 89, 28, 55, 32, 66, 42, 49, 76, 59, 63, 2, 60, 84 The questions are to follow: a. First of all, from the age figures of the infected cases above, can you tell us if the infected cases' age is normally or skewed distributed (please show the calculations)? (5 points)

b. What does the above result mean in plain language? (3 points)

c. In terms of the infected cases, we would like to check them more closely. We would you to create a box and whisker plot for each of the case: the survival cases, and the confirmed death cases. (8 points)

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

114年 - 114 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#147628