In a large Business Statistics class, the professor has each person select stock

Question

In a large Business Statistics class, the professor has each person select stocks by using computer-generated random numbers. The stocks were from a Journal in which exactly half the publicly traded stocks went up and half went down. The students then check to see whether their stock picks rose or fell the next day and report their proportion of "successes." Complete parts (a) through (d) below. a) The students use computer-generated random numbers to choose 36 stocks each. Use the 68-95-99.7 Rule to describe the sampling distribution model. About 68% should have proportions between _______ and _______, and about 99.7% between b) Confirm that you can use a Normal model here. A Normal model (1) ______ be used here because np = ______ and nq = _____. (Type integers or decimals.) c) They increase the number of stocks picked to 64 each. Draw and label the appropriate sampling distribution model. Choose the correct sampling distribution model below. Check the appropriate conditions to justify your model. Choose the correct answer below. A. Samples are random and stock movements are independent, but np and nq are less than 10. B. Samples are not random and stock movements might not be independent. However, both np and nq are greater than or equal to 10. C. Samples are random and stock movements are independent. Both np and nq are greater than or equal to 10. D. Samples are random, but stock movements might not be independent. Both np and nq are greater than or equal to 10. d) Explain how the sampling distribution model changes as the number of stocks picked increases. Choose the correct answer below. A. The sampling distribution does not change as the number of stocks picked increases. B. The sampling distribution becomes wider (more spread around the center) as the number of stocks picked increases. C. The sampling distribution becomes narrower (less spread around the center) as the number of stocks picked increases. (1) cannot can

Explanation / Answer

a. According to emperical rule, about 68% of data should be within 1 standard deviation of mean, 95% of dat ashould be 2 standard deviations of mean and 99.7% of data will be within 3 standard deviations of mean. The mean and standard deviation of computer generated data are 0.50908 and 0.0478 [Note, while generating 36 normally distributed random data, the mean is phat=0.5, and standard deviation is:sqrt[phat(1-phat)/sqrtn]=0.0442] . Therefore, about 68% have proportions between mu-1sigma=0.50908-1*0.0478=0.461 and mu+1sigma=0.50908+1*0.0478=0.557, about 95% between 0.413 and 0.605, about 99.7% between 0.366 and 0.653.

b. A normal model is used, because, np=36*0.5=18 and nq=36*(1-0.5)=18 are atleast 10.

d. According to central limit theorem, with mean=phat and variance=phat(1-phat)/sqrt N, the sampling distribution approaches normality as sample size increases. Thus, the sampling distribution becomes narrower. Option C. Options A and B are discarded.

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