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?

Answer 1

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  $\mu = 2.5 \ seconds$

    The sample size is  n  =  30

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

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

      The level of significance is  $\alpha = 0.05$

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

The alternative hypothesis is  $H_a : \mu > 2.5$

Generally the test statistics is mathematically represented as

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

=>  $z = \frac{2.7 - 3 }{ \frac{1.4}{\sqrt{30} } }$

=>  $z =0.78$

From the z table  the area under the normal curve to the right  corresponding to  $z =0.78$   is  

        $p-value = P(Z > 0.78) = 0.2177$

From the value obtained we see that the p-value  > $\alpha$

   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