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/madonna.blackboard.com/bbcswebdav/pid-780436-dt-content-rid | a search - + Automatic Zoom 96 CHAPTER9 Fundamentals of Hypothesis Testing One Sample Tests this section, you tested whether the population mean fill amount was different from 368 grams by using Equation (9.1) on page 290 Instead of testing the null hypothesis that = 368 grams, you can reach the same conclu- sion by constructing a confidence interval estimate of . If the hypothesized value of -368 is contained within the interval, you do not reject the null hypothesis because 368 would not be considered an unusual value. However, if the hypothesized value does not fall inio the interval, you reject the null hypothesis because = 368 grams is then considered an unusual value. Using Equation (8.1) on page 252 and the following results: n= 25,2 372.5 grams. = 15grams for a confidence level of 95% (ie, -005), 15 3725 ± (1.96) 372.5 ± 5.88 so that 36662 37838 Because the interval includes the hypothesized value of 368 grams, you do not reject the null hypothesis. There is insufficient evidence that the mean fill amount for the entire filling pro- cess is not 368 grams.You reached the same decision by using a two-tail hypothesis test. Can You Ever Know the Population Standard Deviation? The end of Section 8.1 on page 254 discussed how learmning a con- and then test that hypothesis. So why study a hypothesis test of the fidence interval estimation method that required knowing e, te mean, which requires that ° is inon? Using such a test makes popuiation standard deviation, served as an effective introduction to it much easier to explain the fundamentals of hypothesis testing. the concept of aconfiderce i val. Th section then revealed that itmanown population ndard deaton, you car use the normal you would be unilikely b use that procedure for most practical ap- distribution and compute p-values using the tables of the normal plications for several reasons distribution Likewise, for most practical applications, you are unilikely to use Because it is important that you understand the concapt of hy ahypothesis-testing method that r des knowing ·lf knew hesis tsting when reading terestofthis book, review this sec- the population standard deviation, you would also know the popula tion carefully -even if you anticipate never having a practical reason tion mean and would not need to form a hypothesis about the mean to use the test represented in Equation (9.1) | Problems for Section 9.Explanation / Answer
The critical values are - 1.96 and 1.96.
Since - 0.76 is lies between - 1.96 and 1.96, we fail to reject the null hypothesis H0.
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