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

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  $\mu = 2.5 \ seconds$

      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

                $z = \frac{\= x - \mu }{ \frac{\sigma }{ \sqrt{n} } }$

=>              $z = \frac{ 2.7 -2.5 }{ \frac{1.4}{ \sqrt{30} } }$

=>              $z = 0.7825$

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