2 Dr X is conducting a study examining the effect of caffein

2. Dr. X is conducting a study examining the effect of caffeine on extraversion (a personality trait). A standardized measure of extraversion is normally distributed in the population with a mean of 50. Dr. X administers a large dose of caffeine to a sample of n=25 participants, then has them complete the extraversion measure. The sample has a mean on the measure of 56 with a standard deviation of 10. Test whether the caffeine increased scores on the extraversion measure. Use an alpha of .01.

a. Explain what an alpha level of .01 means. (1 pt.)

b. Write the null and alternative hypotheses. (1 pt.)

c. Find the degrees of freedom (1 pt.)

d. Specify the critical values. (1 pt.)

e. Compute the estimated standard error. (1 pt.)

f. Compute the t-statistic. (1 pt.)

g. Make your decision. (1 pt.)

h. Compute Cohen’s d. (1 pt.)

i. In words, interpret Cohen’s d. (1 pt.)

j. Identify one thing the researcher could have done to increase the statistical power of this study. (2 pts.)

k. Define the term “Type II error”. If the researcher in this example wants to decrease the probability of committing a Type II error, what should she do? (2 pts)

Solution

Set Up Hypothesis
Null, caffeine doest n\'t shows any effect H0: U<50
Alternate,caffeine increased scores on the extraversion measure H1: U>50
Test Statistic
Population Mean(U)=50
Sample X(Mean)=56
Standard Deviation(S.D)=10
Number (n)=25
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =56-50/(10/Sqrt(24))
to =3
| to | =3
Critical Value
The Value of |t | with n-1 = 24 d.f is 2.492
We got |to| =3 & | t | =2.492
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Right Tail - Ha : ( P > 3 ) = 0.0031
Hence Value of P0.01 > 0.0031,Here we Reject Ho

We have evidence to suppoet caffeine increased scores on
the extraversion measure