Question

To evaluate the effect of a treatment, a sample of n = 9 is obtained from a population with a mean of μ = 40, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 33. If the sample has a standard deviation of s = 9, do we reject or accept the null hypothesis using a two-tailed test with alpha = .05?

Answer 1

Yes we reject the null hypothesis

Explanation:

From the question we are told that

The sample size is
`n = 9`

The population mean is
`\mu = 40`

The sample mean is
`\= x = 33`

The standard deviation is
`\sigma = 9`

The level of significance is
`\alpha = 0.05`

For a two-tailed test

The null hypothesis is
`H_o : \mu = 40`

The alternative hypothesis is
`H_a : \mu \\e 40`

Generally the test statistics is mathematically represented as

`t = (\= x - \mu )/( (\sigma)/(√(n) ) )`

=>
`t = ( 33 - 40 )/( (9)/(√(9) ) )`

=>
`t = -2.33`

The p-value for the two-tailed test is mathematically represented as

`p-value = 2 P(z > |-2.33|)`

From the z-table

`P(z > |-2.33|) = 0.01`

`p-value = 2 * 0.01`

`p-value = 0.02`

Given that
`p-value < \alpha` Then we reject the null hypothesis