Quitting Smoking: Hypnosis One program to help people stop...

Quitting Smoking: Hypnosis One program to help people stop smoking cigarettes uses the method of posthypnotic suggestion to remind subjects to avoid smoking. A random sample of 18 subjects agreed to test the program. All subjects counted the number of cigarettes they usually smoke a day; then they counted the number of cigarettes smoked the day after hypnosis. (Note: It usually takes several weeks for a subject to stop smoking completely, and the method does not work for everyone.) The results follow. Using a $1 \%$ level of significance, test the claim that the number of cigarettes smoked per day was less after hypnosis.

Quitting Smoking: Hypnosis One program to help people stop smoking cigarettes uses the method of posthypnotic suggestion to remind subjects to avoid smoking. A random sample of 18 subjects agreed to test the program. All subjects counted the number of cigarettes they usually smoke a day; then they counted the number of cigarettes smoked the day after hypnosis. (Note:
It usually takes several weeks for a subject to stop smoking completely, and the method does not work for everyone.) The results follow.
Using a $1 \%$ level of significance, test the claim that the number of cigarettes smoked per day was less after hypnosis.

Key Concepts

p-Value and Decision Rule

The p-value is the probability of obtaining a test statistic as extreme as the one observed, assuming that the null hypothesis is true. In hypothesis testing, if the p-value is less than the chosen significance level, the null hypothesis is rejected. This decision rule helps determine whether the observed data provide sufficient evidence to support the alternative hypothesis.

t-Distribution

The t-distribution is a probability distribution used in situations where the sample size is small and the population standard deviation is unknown. It is applied in the computation of the t-test statistic for hypothesis testing, particularly in paired or independent samples, to account for additional variability introduced by estimating the standard deviation from the sample.

Significance Level

The significance level, often denoted as alpha, is the probability threshold used to decide whether to reject the null hypothesis. It represents the risk of committing a Type I error, which is the error of wrongly rejecting a true null hypothesis. In a one percent significance level test, the criteria for rejecting the null hypothesis are very stringent.

Paired Sample t-Test

The paired sample t-test is used when the same subjects are measured twice, such as before and after an intervention. This test analyzes the differences between paired observations to determine if there is a statistically significant change or effect. It accounts for the fact that the data points are not independent but related.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about population parameters based on sample data. It involves formulating a null hypothesis (which represents no effect or no difference) and an alternative hypothesis (which represents the expected effect or difference), and then using a test statistic to determine whether to reject the null hypothesis in favor of the alternative.

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