Statistics_8 - Chapter 8: Hypothesis testing • Steps in...

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Unformatted text preview: Chapter 8: Hypothesis testing • Steps in Hypothesis Testing— Traditional Method • z Test for a Mean • t Test for a Mean • g2257 g2779 Test for a Variance or Standard Deviation Steps in Hypothesis Testing— Traditional Method • A statistical hypothesis is a conjecture about a population parameter. This conjecture may or may not be true. • The null hypothesis , symbolized by g1834 g2868 , is a statistical hypothesis that states that there is no difference between a parameter and a specific value, or that there is no difference between two parameters. • The alternative hypothesis , symbolized by g1834 g2869 , is a statistical hypothesis that states the existence of a difference between a parameter and a specific value, or states that there is a difference between two parameters. Example: State the null and alternative hypotheses for each conjecture. a. A researcher thinks that if expectant mothers use vitamin pills, the birth weight of the babies will increase. The average birth weight of the population is 8.6 pounds. b. An engineer hypothesizes that the mean number of defects can be decreased in a manufacturing process of compact disks by using robots instead of humans for certain tasks. The mean number of defective disks per 1000 is 18. c. A psychologist feels that playing soft music during a test will change the results of the test. The psychologist is not sure whether the grades will be higher or lower. In the past, the mean of the scores was 73. Solution a. g1834 g2868 : μ= 8.6 and g1834 g2869 : μ > 8.6 b. g1834 g2868 : μ= 18 and g1834 g2869 : μ < 18 c. g1834 g2868 : μ= 73 and g1834 g2869 : μ ≠ 73 • A statistical test uses the data obtained from a sample to make a decision about whether the null hypothesis should be rejected. The numerical value obtained from a statistical test is called the test value. • In the hypothesis-testing situation, there are four possible outcomes. • A type I error occurs if you reject the null hypothesis when it is true. • A type II error occurs if you do not reject the null hypothesis when it is false. • when there is a large difference between the mean obtained from the sample and the hypothesized mean, the null hypothesis is probably not true. The question is, How large a difference is necessary to reject the null hypothesis? Here is where the level of significance is used. • The level of significance is the maximum probability of committing a type I error. This probability is symbolized by α. That is, P (type I error) = α. The probability of a type II error is symbolized by β . That is, P (type II error)= β....
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Statistics_8 - Chapter 8: Hypothesis testing • Steps in...

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