Question

4. The general population (Population 2) has a mean of 30 and a standard deviation of 5, and the cutoff Z score for significance in a study involving one participant is 1.96. If the raw score obtained by the participant is 45, what decisions should be made about the null and research hypotheses?

Answer 1

The null hypothesis is rejected and research hypotheses is supported

Explanation:

From the question we are told that

The population mean is
`\mu = 30`

The standard deviation is
`\sigma = 5`

The sample size is n = 1

The cutoff Z score for significance is
`Z_(\alpha ) = 1.96`

The mean score is
`\= x = 45`

Generally the test hypothesis is mathematically represented as

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

=>
`t = (45 - 30 )/( ( 5)/(√(1) ) )`

=>
`t = 3`

From the obtained value we can see that
`t > Z_(\alpha )`

Hence the null hypothesis is rejected and research hypotheses is supported