Complete Question
It is known that a particular laboratory task takes the average person 2.5 seconds (the variance is not known). 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 mean time was 2.7 seconds, with an estimated population standard deviation of 1.4 seconds. What should the researcher conclude? (Use the .05 significance level and use the five steps of hypothesis testing.)
Answer:
The researchers conclusion is
There is no sufficient evidence to show that older people are slower at the laboratory task
Step-by-step explanation:
From the question we are told that
The mean time is 
The sample size is n = 30
The sample mean is 
The standard deviation is 
The level of significance is 
The null hypothesis is 
The alternative hypothesis is 
Generally the test statistics is mathematically represented as

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

From the value obtained we see that the p-value > 
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is no sufficient evidence to show that the older people are slower at the laboratory task