An experiment was performed to see whether sensory...

An experiment was performed to see whether sensory deprivation over an extended period of time has any effect on the alpha-wave patterns produced by the brain. To determine this, 20 subjects, inmates in a Canadian prison, were randomly split into two groups. Members of one group were placed in solitary confinement. Those in the other group were allowed to remain in their own cells. Seven days later, alpha-wave frequencies were measured for all subjects, as shown in the following table. (P. Gendreau et al., “Changes in EEG Alpha Frequency and Evoked Response Latency During Solitary Confinement,” Journal of Abnormal Psychology 79 [1972]: 54–59) (TABLE CAN'T COPY) a) What are the null and alternative hypotheses? Be sure to define all the terms and symbols you use. b) Are the assumptions necessary for inference met? c) Perform the appropriate test, indicating the formula you used, the calculated value of the test statistic, the df, and the P-value. d) State your conclusion.

An experiment was performed to see whether sensory deprivation over an extended period of time has any effect on the alpha-wave patterns produced by the brain. To determine this, 20 subjects, inmates in a Canadian prison, were randomly split into two groups.
Members of one group were placed in solitary confinement. Those in the other group were allowed to remain in their own cells. Seven days later, alpha-wave frequencies were measured for all subjects, as shown in the following table. (P. Gendreau et al., “Changes in EEG Alpha Frequency and Evoked Response Latency During Solitary Confinement,” Journal of Abnormal Psychology 79 [1972]: 54–59)
(TABLE CAN'T COPY)
a) What are the null and alternative hypotheses? Be sure to define all the terms and symbols you use.
b) Are the assumptions necessary for inference met?
c) Perform the appropriate test, indicating the formula you used, the calculated value of the test statistic, the df, and the P-value.
d) State your conclusion.

Key Concepts

P-Value and Decision Making

The p-value is a key component in hypothesis testing, representing the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed if the null hypothesis were true. If the p-value is smaller than a predetermined significance level (commonly 0.05), the null hypothesis is rejected in favor of the alternative hypothesis. This process supports the decision making in determining whether the data provide sufficient evidence of an effect.

Assumptions for Inference

For the two-sample t-test to yield valid results, several assumptions must be met. These include the independence of observations in each group, the assumption that the data in each group are approximately normally distributed, and, in the case of a pooled variance approach, the assumption of equal variances between groups. Verifying these assumptions is critical to ensure that the conclusions drawn from the test are reliable.

Two-Sample t-Test

The two-sample t-test is used when comparing the means of two independent groups, especially when the sample sizes are small and the population standard deviations are unknown. This test calculates a t-statistic based on the difference between the sample means, the variability within each group, and the sample sizes. The t-statistic is then compared against a theoretical t-distribution with a corresponding degrees of freedom to evaluate the significance of the observed difference.

Hypothesis Testing

Hypothesis testing is a structured process that involves making an initial claim called the null hypothesis (typically stating that there is no effect or difference) and an alternative hypothesis (indicating the presence of an effect or difference). In this framework, symbols such as ?1 and ?2 might represent the population means of different groups. The purpose of the test is to determine whether there is sufficient evidence in the sample data to reject the null hypothesis in favor of the alternative hypothesis.

Transcript

00:01 All right.

00:02 In this problem, what we're given is the results of an experiment where there were 20 people, 10 of them put in a non -confined environment.

00:11 So they're with other people, 10 put in a confined environment where they are alone for a while.

00:17 And they wanted to see if the alpha brainwaves would increase or decrease or be different for those who were confined.

00:25 So we're given those data.

00:27 What we want is the hypothesis.

00:29 So the null and the alternative.

00:30 We want to see if the condition.

00:32 Are met, and we want to test, actually end up testing it and writing our conclusion.

00:39 So let's start with our null and alternative hypothesis.

00:45 For our null hypothesis, that would mean that our mean of the alpha waves for non -confined is equal to the mean of the confined, meaning there's no difference.

00:55 So we're going to put mu, because that means our mean, let's say mu of one, one being non -confined, is equal to mu of 2.

01:06 That is our null hypothesis.

01:08 Our alternative hypothesis is that they are not equal.

01:11 There is some sort of difference that happens from someone being confined, right? let's check if our conditions are met.

01:20 So it's not a paired t test because we're not pairing up people, right? it's different people, 10 different people on this side, 10 on this side.

01:28 They're not related in any way.

01:30 It's two independent samples.

01:32 So we don't need to see if they're paired.

01:34 Again, they are.

01:34 Independent.

01:35 They're also independent from each other.

01:37 One person's alpha waves does not change or alter the other person's alpha waves.

01:41 Those are all independent measurements.

01:44 So we're good to go on that.

01:46 Random.

01:47 It said that these 20 people were chosen at random.

01:50 So we're good.