Tut sol week10

# Tut sol week10 - BES Tutorial Sample Solutions, S1/10 WEEK...

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1 BES Tutorial Sample Solutions, S1/10 WEEK 10 TUTORIAL EXERCISES (To be discussed in the week starting May 10) 1. State whether the normal distribution, t distribution or neither would be used to test hypotheses regarding the population mean in the following situations: (a) Population normally distributed, σ 2 unknown, sample size less than 30. t ­ distribution (b) Population normally distributed, σ 2 unknown, sample size greater than 30. t ­ distribution although as the sample size gets very large this effectively becomes the same as using the normal. (c) Population normally distributed, σ 2 known, sample size less than 30. Normal distribution (d) Population not normally distributed, σ 2 unknown, sample size greater than 30. Because the sample size is large you can invoke the CLT and use the fact that s 2 is a consistent estimator of σ 2 to justify using the normal distribution. (e) Population not normally distributed, σ 2 unknown, sample size less than 30. Here the sampling distribution is unknown and hence we don’t know how to test a hypothesis about in this circumstance. In practice you could either assume the population is approximately normally distributed and proceed as in (a); or alternatively invoke the CLT and proceed as in (d). How well either of these solutions works ultimately depends on the (unknown) extent of non ­ normality of the population distribution.

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2 2. Reconsider Question 2 of the Week 9 exercises. In that exercise, a real estate expert claimed the current mean value of houses in a particular area was more than \$250,000. A random sample of 150 recent sales prices in the area yielded a sample mean of \$265,000 and it is known that house values in the area are approximately normally distributed with a standard deviation of \$50,000. (a)
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## Tut sol week10 - BES Tutorial Sample Solutions, S1/10 WEEK...

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