Question

It is known that a particular laboratory task takes the average person 2.5 seconds. A researcher was interested in whether older people are slower (take longer) on this task. The researcher tested 30 randomly selected 80-year-olds. Their meantime was 2.7 seconds, with an estimated population standard deviation of 1.4 seconds. What should the researcher conclude (use the .05 level)?

Answer 1

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is no sufficient evidence to conclude that older people are slower

Explanation:

From the question we are told that

The average time taken is
`\mu = 2.5 \ seconds`

The sample size is
`n = 30`

The sample mean is
`\= x = 2.7 \ seconds`

The standard deviation is
`\sigma = 1.4 \ seconds`

The null hypothesis is
`H_o: \mu = 2.5`

The alternative hypothesis is
`H_a : \mu > 2.5 \ seconds`

Generally the test statistics is mathematically represented as

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

=>
`z = ( 2.7 -2.5 )/( (1.4)/( √(30) ) )`

=>
`z = 0.7825`

From the z table the area under the normal curve to the right corresponding to 0.7825 is

`p-value = P(Z > 0.7825 ) = 0.21696`

So from the question we see that the
`p-value > \alpha` hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is no sufficient evidence to conclude that older people are slower