Researchers studying sleep loss followed the length of sleep, in hours, of 10 in

Question

Researchers studying sleep loss followed the length of sleep, in hours, of 10 individuals with insomnia before and after cognitive behavioral therapy (CBT). Assume a 5% significance level to test the claim that there is a difference between the length of sleep of individuals before and after CBT. Also, assume the samples are simple random samples and the pairs of values are from a population having a distribution that is approximately normal. 1) To answer the research question, what is the best test to carry out? 2) Identify the null hypothesis and alternative hypothesis. 3) Based on the following R outputs, please state a conclusion about the null hypothesis at 5% level. Why? t = -7.8558, df = 9, p-value = 2.559e-05 alternative hypothesis: true difference in means is not equal to percent confidence interval: -3.0911 -1.7089 sample estimates: mean of the differences -2.4

Explanation / Answer

1)

A t-test is used when you're looking at a numerical variable - for example, height - and then comparing the averages of two separate populations or groups (e.g., males and females).

Requirements

2) Null Hypothesis

H0: u1 = u2 , where u1 is the mean of first population and u2 the mean of the second.

H1: u1 u2

3) A small p-value (typically 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

Here, p value is less than alpha thus null is rejected.

So, there is a difference before and after CBT treatment.

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.