13. As the sample size becomes larger, the sampling distribution of the sample mean approaches a
(A) Binomial distribution
(B) Poisson distribution
(C) Normal distribution
(D) Chi-square distribution
(E) t distribution

7. As the sample size becomes larger, the sampling distribution of the sample mean approaches a (A) binomial distribution (B) Poisson distribution (C) normal distribution (D) chi-square distribution

14. Which of the following is true? (A) If we draw a simple random sample of any size from any population the sampling distribution of the sample mean will be exactly Normal. (B) If we draw a simple random sample of any size from any population the sampling distribution of the sample mean will be close to Normal. (C) Central limit theorem only applies when sampling from Normal populations. (D) None of the above.

15. A professor of statistics refutes the claim that the average student spends 3 hours studying for the midterm exam. The professor thinks the students spend more time than that. Which hypotheses are used to test the claim? (A) \( H_0: \mu \leq 3 \) vs. \( H_a: \mu > 3 \) (B) \( H_0: \mu = 3 \) vs. \( H_a: \mu \neq 3 \) (C) \( H_0: \mu \neq 3 \) vs. \( H_a: \mu = 3 \) (D) \( H_0: \mu = 3 \) vs. \( H_a: \mu < 3 \) (E) \( H_0: \mu \geq 3 \) vs. \( H_a: \mu = 3 \)

16. We test the null hypothesis $H_0: \mu=10$ and the alternative $H_a: \mu<10$, for a normal population with $\sigma=4$. A random sample of 16 observations is drawn from the population and we find the sample mean of these observations is 12. The $p$-value is closest to (A) 0.0228 (B) 0.0456 (C) 0.1016 (D) 0.9772 (E) 0.9999

17. The nicotine content in cigarettes of a certain brand is normally distributed, with mean (in milligrams) and standard deviation $\sigma = 0.1$. The brand advertises that the mean nicotine content of its cigarettes is 1.5, but measurements on a random sample of 100 cigarettes of this brand give a mean of $\overline{x} = 1.53$. Is this evidence that the mean nicotine content is actually higher than advertised? To answer this, test the hypotheses $H_0: \mu = 1.5, H_a: \mu > 1.5$ at the 5% significance level. You conclude (A) That \( H_0 \) should be rejected. (B) That \( H_0 \) should not be rejected. (C) That \( H_{a} \) should be rejected. (D) There is a \( 5\% \) chance that the null hypothesis is true. (E) There is a \( 5\% \) chance that the alternative hypothesis is true.

18. A certain population follows a normal distribution with mean $\mu$ and standard deviation $\sigma = 2.5$. You collect data and test the hypotheses $H_0: \mu = 1, H_a: \mu \neq 1$. You obtain a p-value of 0.022. Which of the following is true? (A) A \( 90\% \) confidence interval for \( \mu \) will include the value 1. (B) A \( 95\% \) confidence interval for \( \mu \) will include the value 1. (C) A \( 95\% \) confidence interval for \( \mu \) will include the value 0. (D) A \( 99\% \) confidence interval for \( \mu \) will include the value 1. (E) A \( 99\% \) confidence interval for \( \mu \) will include the value 0.

19. Suppose that the significant level of a statistical hypothesis test is $\alpha$. The null hypothesis will be rejected when: (A) \( p \)-value \( \leq \alpha \) (B) \( p \)-value \( >\alpha \) (C) \( p \)-value \( \leq \alpha / 2 \) (D) \( p \)-value \( >\alpha / 2 \) (E) \( p \)-value \( = \frac{\alpha}{2} \)

20. The average monthly rent for one-bedroom apartments in Chattanooga has been $700. Because of the downturn in the real estate market, it is believed that there has been a decrease in the average rental. The correct hypotheses to be tested are (A) \( H_0: \mu \geq 700 \) v.s. \( H_a: \mu < 700 \) (B) \( H_0: \mu = 700 \) v.s. \( H_a: \mu \neq 700 \) (C) \( H_0: \mu > 700 \) v.s. \( H_a: \mu \leq 700 \) (D) \( H_0: \mu < 700 \) v.s. \( H_a: \mu \geq 700 \) (E) \( H_0: \mu < 700 \) v.s. \( H_a: \mu > 700 \) 

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_碩士班一般入學考試試題_統計學系：統計學#147125