T7 SOLUTIONS_Combined_1_2018.pdf

# Solution finally now this is the part that you need

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Solution: FINALLY, NOW THIS IS THE PART THAT YOU NEED TO ANSWER: Q7.3 (c) If you were attempting question Q7.3 (b) WITHOUT THE USE OF EXCEL , what degrees of freedom would you use when consulting the table? How inaccurate do you think your answer might be? t: -2.0106 2.0106

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ETF1100 Business Statistics SOLUTIONS Tutorial 7 6 Solution: The correct degrees of freedom are 48. 45 and 50 degrees of freedom are provided in the table, and the corresponding critical values are 2.014 and 2.009 respectively. To 3 decimal places, the correct critical value for 48 degrees of freedom is 2.011, a difference of 0.003 from the 45 degrees of freedom answer and 0.002 from the 50 degrees of freedom answer. For this particular problem, either of these will result in a change to the confidence limits that makes a difference only at the 4th decimal place, which means the answer would still be acceptable accurate. Q7.4 A random sample of 20 petrol stations, on a Tuesday, in the city of Casey, found that the mean price per litre of petrol was \$1.52. Assume that the price of petrol is normally distributed. (a) Assuming the population standard deviation was 3 cents, find a 99% confidence interval for the mean price of petrol in Casey on a Tuesday. Solution: Let X=price per litre of petrol (\$) Assume ) 03 . 0 , ( ~ N X (b) 0.005 2 X 1.52 0.03 n 20 1 0.99 0.01 z z 2.576     99% Z: -2.576 2.576 2 2 X Z X Z n n 0.03 0.03 1.52 2.576* 1.52 2.57* 20 20 1.52 0.01728 1.52 0.01728 1.5027 1.5373            
ETF1100 Business Statistics SOLUTIONS Tutorial 7 7 We can state with 99% confidence that the mean price of petrol per litre in Casey on a Tuesday is between \$1.50 and \$1.54. (b) Now, calculate a 90% confidence interval for the mean price of petrol, on a Tuesday, in the City of Casey. Solution: To obtain a 90% confidence interval, just need to change the critical value to 0.05 2 X 1.52 0.03 n 20 1 0.90 0.10 z z 1.645     We can state with 90% confidence that the mean price of petrol per litre in Casey on a Tuesday is between \$1.51 and \$1.53. (c) Describe the difference between the confidence intervals in parts (a) and (b) above and the impact this has on the interval estimate. Z: -1.645 1.645 90% 2 2 X Z X Z n n 0.03 0.03 1.52 1.645X 1.52 1.645X 20 20 1.52 0.01103 1.52 0.01103 1.509 1.531            

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ETF1100 Business Statistics SOLUTIONS Tutorial 7 8 Solution: When the required confidence level is decreased, the interval becomes narrower meaning the interval range where we can find the true mean is narrower (If the interval is wider, more values are included so the mean is more likely to be there.) This if due to the z critical value
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