Stats 309 PPT 11.1b

Stats 309 PPT 11.1b - Example 11.1 page 329 The store...

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Example 11.1 page 329 The store manager needs to find out if the average monthly balance is more than $170. This is the alternative hypothesis. So our null and alternative hypotheses are: H o : µ = 170 H a : µ > 170 We also know that σ = 65 and the accounts are normally distributed. Then she sampled 400 accounts and got a sample mean of $178. The big question is: Is a sample mean of 178 sufficiently big enough to say that the population mean is > 170? There are two ways to answer this question: The rejection region method The p-value method We will start with the rejection region method: It seems reasonable to reject the null hypothesis in favor of the alternative if the value of the sample mean is large relative to 170. For example, if we had calculated the sample mean to be 500, it would be obvious that the null hypothesis is false and we would reject it.
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On the other hand, sample means close to 170, such as 171, do not allow us to reject the null hypothesis because it is entirely possible to observe a sample mean of 171 from a population whose mean is 170. Unfortunately, the decision is not always so obvious, as in getting a sample mean of 178. To make a decision about this, we set up a
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Stats 309 PPT 11.1b - Example 11.1 page 329 The store...

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