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Hypothesis Testing and T-Tests

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Hypothesis Tests Related to Differences Copyright © 2009 Pearson Education, Inc. Chapter 17 - 2 Tests of Differences One Sample Means Proportions Two Independent Samples Paired Samples More Than Two Samples Means Proportions

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The t Distribution The t statistic assumes that the variable is normally distributed and the mean is known (or assumed to be known) and the population variance is estimated from the sample. Assume that the random variable X is normally distributed, with mean and unknown population variance 2, which is estimated by the sample variance s 2. Then, is t distributed with n - 1 degrees of freedom. The t distribution is similar to the normal distribution in appearance. Both distributions are bell-shaped and symmetric. As the number of degrees of freedom increases, the t distribution approaches the normal distribution. Copyright © 2009 Pearson Education, Inc. Chapter 17 - 3

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Hypothesis Testing Using the t Statistic 1.Formulate the null (H 0 ) and the alternative (H 1 ) hypotheses. 2.Select the appropriate formula for the t statistic. 3.Select a significance level, , for testing H 0. Typically, the 0.05 level is selected. 4.Take one or two samples and compute the mean and standard deviation for each sample. 5.Calculate the t statistic assuming H 0 is true. 6.Calculate the degrees of freedom and estimate the probability of getting a more extreme value of the statistic from Table 4 (Alternatively, calculate the critical value of the t statistic). Copyright © 2009 Pearson Education, Inc. Chapter 17 - 4

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Hypothesis Testing Using the t Statistic (Cont.) 7.If the probability computed in step 5 is smaller than the significance level selected in step 2, reject H 0. If the probability is larger, do not reject H 0. (Alternatively, if the value of the calculated t statistic in step 4 is larger than the critical value determined in step 5, reject H 0. If the calculated value is smaller than the critical value, do not reject H 0 ). Failure to reject H 0 does not necessarily imply that H 0 is true. It only means that the true state is not significantly different than that assumed by H 0. 8.Express the conclusion reached by the t test in terms of the marketing research problem. Copyright © 2009 Pearson Education, Inc. Chapter 17 - 5

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Formulate H 0 and H 1 Select Appropriate t-Test Choose Level of Significance, Collect Data and Calculate Test Statistic a) Determine Probability Associated with Test Statistic (TS CAL ) b) Determine Critical Value of Test Statistic TS CR a) Compare with Level of Significance, b) Determine if TS CAL falls into (Non) Rejection Region Reject or Do Not Reject H 0 Draw Marketing Research Conclusion Chapter 17 - 6 Copyright © 2012 Pearson Education, Inc.

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Chapter 17 - 7 Copyright © 2012 Pearson Education, Inc.

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