Preliminary data analyses indicate that use of a paired...

Preliminary data analyses indicate that use of a paired t-test is reasonable. Perform each hypothesis test by using either the critical-value approach or the P-value approach. Anorexia Treatment. Anorexia nervosa is a serious eating disorder. particularly among young women. The following data provide the weights, in pounds, of 17 anorexic young women before and after receiving a family therapy treatment for anorexia nervosa. Isounce: D. Hand et al. (ed.) A Handbook of Small Data Sets, London: Chapman \& Hall, 1994; raw data from B. Everitt (personal communication)] Does family therapy appear to be effective in helping anorexic young women gain weight? Perform the appropriate hypothesis test at the $5 \%$ significance level.

Preliminary data analyses indicate that use of a paired t-test is reasonable. Perform each hypothesis test by using either the critical-value approach or the P-value approach.
Anorexia Treatment. Anorexia nervosa is a serious eating disorder. particularly among young women. The following data provide the weights, in pounds, of 17 anorexic young women before and after receiving a family therapy treatment for anorexia nervosa. Isounce: D. Hand et al. (ed.) A Handbook of Small Data Sets, London: Chapman \& Hall, 1994; raw data from B. Everitt (personal communication)]
Does family therapy appear to be effective in helping anorexic young women gain weight? Perform the appropriate hypothesis test at the $5 \%$ significance level.

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to make inferences about populations using sample data. It involves setting up a null hypothesis, which assumes no effect or difference, and an alternative hypothesis, which represents the effect or difference of interest. The process determines whether the observed data provide sufficient evidence to reject the null hypothesis in favor of the alternative.

Paired t-test

The paired t-test is a statistical procedure used to compare the means of two related groups, such as measurements taken on the same subjects before and after an intervention. This test accounts for the dependency between the paired observations by focusing on the differences within each pair, thereby reducing variability and providing a more accurate assessment of the treatment effect.

P-value and Critical-value Approaches

These are two common methods for conducting hypothesis tests. The P-value approach involves calculating the probability of observing a test statistic at least as extreme as the one obtained, assuming the null hypothesis is true, and then comparing this probability with a predetermined significance level. In contrast, the critical-value approach determines a threshold value (critical value) from the sampling distribution, and if the computed test statistic exceeds this threshold, the null hypothesis is rejected.

Significance Level

The significance level, often denoted by alpha (?), is a threshold that defines the maximum acceptable probability of making a Type I error—rejecting a true null hypothesis. In hypothesis testing, a common significance level is 5% (0.05), meaning there is a 5% risk of concluding that there is an effect when there is none. This level is set prior to the test to help guide decision making.

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