TESTING A CLAIM ABOUT A MEAN - INSOMNIA Be sure to include the null and alternative, significance level, critical value(s), the test statistic with calculations shown, the properly drawn graph, decision criteria, decision and one of the four possible conclusions. Don't forget to answer the question at the end of the problem. **Insomnia Treatment**A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment with the drug, 18 subjects had a mean wake time of 97.3 min. After treatment, the 18 subjects had a mean wake time of 68.4 minutes and a standard deviation of 26.4 minutes. Assume that the samples are from a normally distributed population and are randomly selected. At the 0.1 significance level test the claim that after treatment with the drug subjects have a mean wake time of less than 97.3 minutes. Does it appear that the drug is effective?

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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TESTING A CLAIM ABOUT A MEAN - INSOMNIA

Be sure to include the null and alternative, significance level, critical value(s), the test statistic with calculations shown, the properly drawn graph, decision criteria, decision and one of the four possible conclusions. Don't forget to answer the question at the end of the problem.

**Insomnia Treatment**

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment with the drug, 18 subjects had a mean wake time of 97.3 min. After treatment, the 18 subjects had a mean wake time of 68.4 minutes and a standard deviation of 26.4 minutes. Assume that the samples are from a normally distributed population and are randomly selected. At the 0.1 significance level test the claim that after treatment with the drug subjects have a mean wake time of less than 97.3 minutes. Does it appear that the drug is effective?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

Given information-

Population mean, μ = 97.3 minutes

Sample size, n = 18

Sample mean, x-bar = 68.4 minutes

Population standard deviation, s = 26.4 minutes

Hypothesis Formulation-

Null Hypothesis, H₀: μ = 97.3

Alternate Hypothesis, H_a: μ < 97.3

Since here population standard deviation is unknown and sample size is <30, so using t-test statistics.

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