Question

1. A study claims residents in a suburban town spend 1.8 hours per weekday commuting. A researcher wanted to see if this claim was true by sampling 101 adults. The mean and standard deviation of time spent commuting per weekday is shown below:

             X=2.1 s=0.5

1. Can you support the claim (a=.05) that the mean time spent commuting per weekday is more than 1.8 hours. Show all steps (Design, Data, Conclusion).

2. In designing the test shown in part a, the researcher was concerned about the power of the test if the actual time commuting was 1.9 hours. Under the test described in Part a, Power was calculated to be only 64%. Determine the probability of making Type II error (given Ha is true) for this design.

3. How would the following modifications to the design affect the power
   (choose one answer)?
   

   1. Change the sample size to 200: increase power or reduce power
      

   2. Change significance level to 1%: increase power or reduce power
      

   3. Change actual commuting time to 1.95 hours: increase power or reduce power

Answer 1

SInce the null hypothesis is rejected we have evidence to support the claim that the mean time spent commuting per weekday is more than 1.8 hours.

b) Power of the test = 0.64

Probability of making a type II error = 1- power of the test = 1-0.64 =0.36

c)

Power is the probability of making a correct decision which is to reject the null hypothesis when the null hypothesis is false. Power is the probability that a test of significance will pick up on an effect that is present.

1.) Change the sample size to 200 means increasing the sample size which increase power.

2.) Change significance level to 1% means that the significance level is reduced from 0.05 to 0.01 which reduce power.

If you reduce the significance level the region of acceptance gets bigger. As a result, you are less likely to reject the null hypothesis.