110年 - 110 國立中央大學_碩士班招生考試_共同科目:統計學#105819

1.Suppose we have a population that is normally distributed, and its standard deviation is unknown. We want to test the following hypotheses: H₀:μ=12 vs Ha:μ≠12. If the value of the test statistic is -1.9 based on a sample of size 20, what type of test statistic is it and what is the corresponding p-value? (A)z statistic, 0.0287; (B)z statistic, 0.0574; (C) t statistic, between 0.025 and 0.05; (D) t statistic, between 0.05 and 0.10.

2. To test the null hypothesisH₀:μ=12 , which alterative hypothesis of following would have the highest testing power? (A)Ha:μ=10; (B)Ha:μ=12; (C) Ha:μ=15; (D) It depends on the sample size.

3.To test the bypotheses H₀:μ=12 vs Ha:μ=10, which following sample size would end up to be the lowest testing power with the specified a = 0.05? (A)n=20; (B)n=30; (C) n=100; (D) It depends on the sample observations.

4. Suppose p-value is equal to 0.0626. The null hypothesis can be rejected (A)if a=0.10 in a two-tailed test; (B)if a= 0.05 in a two-tailed test; (C) if a = 0.05 in a one-tailed test； (D) Not enough information to make a conclusion.

5. In a two-tailed test for population mean u, suppose the p-value is equal to 0.0626. Which one of the following statements is not true? (A)The 90% confidence interval of u contains the hypothesized value uo； (B) The 95% confidence interval of u contains the hypothesized value 4o； (C) The 99% confidence interval of u contains the hypothesized value [4o； (D) The testing power is not determined by p-value.

5. In a two-tailed test for population mean u, suppose the p-value is equal to 0.0626. Which one of the following statements is not true? (A)The 90% confidence interval of u contains the hypothesized value uo; (B)The 95% confidence interval of u contains the hypothesized value po; (C) The 99% confidence interval of u contains the hypothesized value po; (D) The testing power is not determined by p-value.

6.Which of the following statements is not true about the level of significance for a hypothesis test? (A)The level of significance is usually denoted by alpha (a); (B) If the p-value is less than the level of significance, we reject the null hypothesis; (C) The level of significance is the maximum allowable probability of making a Type I error; (D) The level of significan nce is determined by the valuc of the test statistic.

7. Which of the following is incorrect for the linear regression model y= β₀ + β₁x+ε and its predictive equation , if the sample observations are not specified? (A)b₀ and b₁ are random variables; (B)β₀ and β₁ are random variables; (C) yand ε are random variables; (D) is a random variable.

8. Based on the assumptions of an ANO VA procedure, which of the following cannot be determined? (A) The distributions of the populations; .(B)Whether the samples are independent or not; (C) Whether all the population means are different; (D) The variance of the other populations if the variance of one population is known as 10.

9.We have a population that is normally distributed with an unknown variance. A two-tailed hypothesis test was conducted for the population mean. A random sample of size 22 was selected. After setting the level of significance, a, a student wrongly used as the critical value and concluded to reject the null hypothesis. If the student did not make the mistake, what would be the correct conclusion? (A)The conclusion stays the same, that is, the null hypothesis should be rejected; (B)The conclusion is different, that is, the null hypothesis should not be rejected; (C) There is insufficient information to make a conclusion. In other words, the null hypothesis may or may not be rejected; (D) None of the above.

10. It is known that the mean of a population is 105. A sample of size 25 was taken and the sample mean was 100.7. If H₀: μ≤100, and you decided not to reject the null hypothesis, it means (A)you have committed a Type I error; (B)you have committed a Type I error; (C) you have committed a Type III error; (D) you have committed neither Type I nor Type II error.

11. A random sample of 100 people was taken. Fifty-five of the people in the sample favored Candidate A. We are interested in determining whether the proportion of people in the population in favor of Candidate A is less than60%. What is the value of the test statistic? (A)-1.005; (B)-1.02; (C) 1.005; (D) 1.02.

12. You found that the null hypothesis μ1- μ2 ≤ 100 could not be rejected at a = 0.05. If the same sample is used, which of the following is correct? (A)H₀:μ1- μ2 ≤ 95 can never be rejected at a = 0.05; (B)H0:μ1- μ2 ≤ 105 can never be rejected at a = 0.01; (C) H₀: μ1- μ2 ≤ = 100 can never be rejected at a = 0.05; (D) Insufficient data to claim any of the above.

13. From a population that is not normally distributed and whose standard deviation is unknown, a sample of 15 items is selected to develop an interval estimate for the population mean μ. Which of the following is true? (A)The sample size must be increased; (B)The normal distribution may be used; (C) Thet distribution with 14 degrees of freedom can be used; (D) The t distribution with 15 degrees of freedom can be used.

14. Comparing the multiple coeficient of determination, r², and adjusted multiple coefficient of determination, r²a, for the same regression model, which of the following statements is correct? (A)When an additional independent variable is added to the model, r²will always increase; (B)When an additional independent variable is added to the model, r²a will always increase; (C)r²a can be greater than r²; (D) Both (a) and (b) are right.

15. In estimating the population mean, it is known that the necessary sample size is 150 in order to provide a particular margin of error at 98% confidence level. With a 95% confidence level, what is the minimum sample size that needs to be taken if the desired margin of error is balved? (A)213; (B)253; (C) 427; (D) 506.

16. Using the least squares method, the regression line is obtained by minimizing (A). SST : Total sum of squares; (B)SSR : Sum of squares due to the regression; (C) SSE : Sum of squares due to the errors; (D) none of the above.

複選題
17. According to a model regressing a firm's monthly sales (in thousands) of a product on the price of that product, the 90% confidence interval on the average monthly sales is [5.3, 7.7] if the price is $6. Which of the following could be the 90% prediction interval for a single month sales if the price is $6? (A)[4.4,8.2]; (B)[4.4,8.6]; (C) [5.9,7.1]; (D)[5.4,8.4].

18. The assembly times for products in a factory are normally distributed with a mean of 15 minutes and a standard deviation of 6 minutes. What is the probability that the assembly time of a randomly selected product will be exactly 15 minutes? (A)1; (B)0.5; (C) 0.4; (D) 0.

110年 - 110 國立中央大學_碩士班招生考試_共同科目:統計學#105819

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