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ECON634 Econometrics And Business Statistics

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Questions:

1. It is reported that the average numeracy score achieved by Year 5 classes in the recent Naplan tests of 2016 is 493 with a standard deviation of 60. Calculate the probability that a randomly selected sample of 30 Year 5 classes in Australia in 2016 had an average numeracy score less than 500. Justify any assumption you make. Shade in the diagram to represent the probability you have calculated.

2. Assume that 50% of students scored above 493 in the numeracy test. Calculate the probability that, in a randomly selected sample of 200 Year 5 children, more than 115 of them scored over 493 in the numeracy test. Justify any assumption
you make. Shade in the diagram to represent the probability you have calculated.

3. It is reported that the average numeracy score achieved by Year 5 classes in the Naplan tests of 2016 is 493. From the sample of 59 schools in 2015, the average score was found to be 506.63 with a standard deviation of 36.76. Test the hypothesis that the average numeracy scores of Year 5 classes in 2015 in the three major capital cities differs from the average numeracy score in 2016. Test your claim at the 5% significance level.

5. Calculate a 95% confidence interval to estimate the average numeracy score of all grade 5 classes in the major capital cities in 2015. Interpret this interval.
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