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Economics- Probability and stats

1. Find the value of the 75th percentile of the following array: 5,10,43,9,8,6,2,5 A) 8 B) 9 C) 9.5 D) 8.5 2. Two independent events, A and B, where the P(B) is 0.44 and the probability that A does not occur or B occurs is 0.74. What is the probability that event A occurs? A) 0.3 B) 0.54 C) 0.46 D) 0.28 3. Which of the following is FALSE? A) B) A sampling distribution is a probability distribution for a sample statistic. As the sample size increases, the effect of an extreme value on the sample mean becomes smaller As the sample size increases the standard error of the mean increases The standard error of the mean is also known as the standard deviation of the sampling distribution of the sample mean C) D) 4. Consider the two sets: X 2,4,8,9) Y-(1,0,8, 9,5,6) Which of the following is TRUE? A) XUY-[0,1, 2, 4, 5, 8,9) D) XuY-[0,1, 2, 4, 5, 6, 8, 9)

5. The discrete random variable Z has the following probability distribution 2 0.2 4 P(Z) 0.1 0.25 0.05 0.3 Which of the following is FALSE? A) P(Z < 2) 0.55 B) P(Z 2 4)- 0.45 C) P(Z 4)=0.9 D) P(Z3)-0.05 6. A random sample of 100 first-year students was selected to determine the average GPA they achieved at a university. A 95% confidence interval for the average GPA of the first-year students was 5.2 < H < 6.8 based on sample statistics. The confidence can be interpreted as A) if all possible samples of 100 are drawn from the population, 95% of the confidence intervals developed will show that the sample mean will fall between 5.2 and 6.8 if all possible samples of 100 are taken from the population, 95% of the confidence intervals developed will show that the population mean is between 5.2 and 6.8 if all possible samples of 100 are taken from the population, 95% of the intervals developed will include the population mean 95% of first-year students have GPA between 5.2 and 6.8 B) C) D) 7. Which of the following is TRUE? A) The closer the correlation coefficient is to zero, the stronger the linear B) relationship between the two variables The correlation coefficient must lie in the range -1 to 1 The range of possible values for the coefficient of determination is -1 to C) D) Both B) and C) are correct.

FOR THE NEXT FOUR QUESTIONS (QUESTIONS 8-11) USE THE FOLLOWING INFORMATION The CEO of a cosmetic company claims that 75% of her current customers are satisfied with the products they buy. To test her claim, a research group surveyed 350 customers, using simple random sampling. The results revealed that 280 customers said that they are very satisfied with the products. 8. The null hypothesis test is ) μ=0.75 B) p=0.75. C) p 0.75 D)p>0.75 9. The variance of the random sample is A) 0.160000 B) 0.021381 C) 0.012547 D) 0.000457 10. The calculated z test statistics is A) 1.628 B) 2.339 C) 109.375. D) 1.587 11. Which of the following statements is TRUE? A) B) C) The null hypothesis is not rejected at 5% level of significance The null hypothesis is not rejected at 1% level of significance The null hypothesis is rejected at 5%, but not rejected at 1% level of significance The null hypothesis is rejected at both 1% and 5% level of significance D) 12.If the p-value is greater than α in a two-tailed test, then A) the null hypothesis should be rejected B) the null hypothesis should not C) no conclusion should be made. D) a one-tailed test should be used be rejected.

FOR THE NEXT TWO QUESTIONS (QUESTIONS 19-20) USE THE FOLLOWING INFORMATION: A company has produced cans of soup for many years, with an average weight of 375g and the variance of 225 g. Previous experience has also shown that 9% of the cans become slightly scratched during production 19. From a sample 100 cans of soup, the probability the sample mean is larger than 380g is: A) 0.1293. B) 0.0006. C) 0.3707 D) None of the above. 20. The probability that the sample proportion of slightly scratched cans is more than 15% in a sample of 100 cans of soup is: A) 0.0179. B) 0.0465. C) 0.4535. D) 0.1521

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