A sample of n=9 individuals is selected from a population with a mean of μ=10. A researcher suspects that after the individuals have gone through a specific type of treatment, their performances on a standardized examination will be different from the general population. After the treatment, the sample has a M=13 and s2=9.

The Null and alternative hypotheses are as follows: H0: μ = 10. H1: μ ≠ 10. Since sample size is…

Answered: A sample of n=9 individuals is selected…

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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A sample of n=9 individuals is selected from a population with a mean of μ=10. A researcher suspects that after the individuals have gone through a specific type of treatment, their performances on a standardized examination will be different from the general population. After the treatment, the sample has a M=13 and s²=9.

Expert Solution

Step 1

The Null and alternative hypotheses are as follows:

H₀: μ = 10.

H₁: μ ≠ 10.

Since sample size is small and population standard deviation is unknown, t-test is appropriate in this situation.

Test statistic:

Here, the sample mean, x-bar is 13.

Population mean, µ is 10.

Sample standard deviation, s = 3

Sample size, n is 9.

The test statistic for hypothesis test for mean is given by:

t =(x-bar –μ)/(s/√n)

= (13-10)/(3/√9)

= 3

The test statistic is 3.

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