Answer:
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
Step-by-step explanation:
From the question we are told that
The average time taken is [tex]\mu = 2.5 \ seconds[/tex]
The sample size is [tex]n = 30[/tex]
The sample mean is [tex]\= x = 2.7 \ seconds[/tex]
The standard deviation is [tex]\sigma = 1.4 \ seconds[/tex]
The null hypothesis is [tex]H_o: \mu = 2.5[/tex]
The alternative hypothesis is [tex]H_a : \mu > 2.5 \ seconds[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x - \mu }{ \frac{\sigma }{ \sqrt{n} } }[/tex]
=> [tex]z = \frac{ 2.7 -2.5 }{ \frac{1.4}{ \sqrt{30} } }[/tex]
=> [tex]z = 0.7825[/tex]
From the z table the area under the normal curve to the right corresponding to 0.7825 is
[tex]p-value = P(Z > 0.7825 ) = 0.21696[/tex]
So from the question we see that the [tex]p-value > \alpha[/tex] 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
