Workshop 7 Solutions(5) - Workshop 7 Solutions THE...

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Workshop 7 Solutions T HE U NIVERSITY OF S YDNEY Q UANTITATIVE B USINESS A NALYSIS Prepared by: Scott Liu Workshop Aims 1. Understand the reasons why a sample is used and not a population. 2. Understand the concept of a simple random sample (SRS). 3. Enumerate the sample space for a discrete distribution for samples of size 2 or 3. 4. Determine the sampling distribution of the mean after enumerating the sample space. 5. Calculate the mean and the variance of the sample mean. 6. Calculate a point estimate for the mean and variance; be able to explain the meaning of a point estimate, and what it is estimating. 7. Use Excel to create a set of random numbers to enable taking a sample. 8. Use the random number generator in Excel to produce random numbers from a normal or uniform distribution. 9. Demonstrate, using expectations, that E ( ¯ x ) = μ and V ( ¯ x ) = æ 2 n . 10. Choose the distribution to be used and explain why the choice was made. 11. Understand HOW the Central Limit Theorem is used. 12. Understand when the Central Limit Theorem is used and how to use it. 13. Calculate an interval estimate for the population mean using the Central Limit Theorem. 14. State the assumptions for the choice of distribution when calculating an interval estimation for the population mean. 15. Interpret the interval estimation obtained for the population mean.
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BUSS1020 Quantitative Business Analysis Workshop 7 Solutions Workshop 7 Question 2 (BLS Q15, p. 281) The goal of corporate sustainability is to manage the environmental, economic and social effects opf a corporation’s operations so it is profitable over the long termw hile acting in a responsible manner towards soceity. A Hill + Knowlton Strategies survey found that 57% of U.S. respondents are more likely to buy stock in a U.S. corporation, or shop at its stores, if it is making an effort to publicly talk about how it is becoming more sustainable. Suppose you select a smaple of 100 U.S. respondents. (a) What is the probability that in the sample, fewer than 57% are more likely to buy stock in a U.S. corporation, or shop at its stores, if it is making an effort to publicly talk about how it is becoming more sustainable? Assumption of normality : In your assignments, you have to show that the distribution is approximately normal. For the purposes of these solutions, I will assume everything is a normal distribution. Below is how you prove normality for a population proportion: n º = 100(0.57) = 57 > 5, n (1 ° º ) = 100(1 ° 0.57) = 43 > 5 ) distribution is approximately normal. Calculate the Z -score: Z p = 0.57 = p ° º r º (1 ° º ) n = 0.57 ° 0.57 r 0.57(1 ° 0.57) 100 = 0 Compute the probability: P ( p > 0.57) = 1 ° P ( p < 0.57) = 1 ° P ( Z < 0) = 1 ° 0.50 = 0.50 (b) What is the probability that in the sample, between 52% and 62% are more likley to buy a stock in a U.S. corporation, or shop at its stores, if it is making an effort to publicly talk about how it is becoming more sustainable?
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