Name
Chapter 4 Practice Problems
11. List the five steps of hypothesis testing, and explain the procedure and logic of
each.
The five stages of theory testing are:
1.) Say again the query as a research theory and a null theory regarding the
populations. This stage is necessary to explain the theory and recognize the
populations which will be worked with all through the study.
2.) Find out the features of the comparison distribution. In instances where the null
theory is correct the comparison distribution is compared to the score depending
on the sample’s outcomes.
3.) Find out the sample cutoff score. This stage is significant since it provides the
examiner a position at which the null theory will be turned down. An instance of a
cutoff score that could be utilized in a survey is 5%, or p < .05.
4.) Find out the sample’s score on the comparison distribution. Once the sample
outcomes are the Z score can be computed as under: is z = (x - μ) / σ.
5.) Make a decision whether to discard the null theory. To do this the Z score must
be compared to the cutoff sample score which was found out in step 3.
14. Based on the information given for each of the following studies, decide whether to
reject the null theory. For each, give (a) the Z-score cutoff (or cutoffs) on the
comparison distribution at which the null theory should be turned down, (b) the Z score
on the comparison distribution for the sample score, and (c) your conclusion. Assume
that all populations are normally distributed.
Study A:
z –score = (7 – 5)/1 = 2
At 0.05 significance level, the z-score is + 1.64
z-score cut-off value = +1.64
As 2 > 1.64
The null theory is turned down.
Study B:
z –score = (7 – 5)/1 = 2
At 0.05 significance level for two-tailed test, the z-score is ±1.96.
z-score cut-off value = ±1.96
Because 2 > +1.96
The null theory is turned down.
Study C:
z –score = (7 – 5)/1 = 2
At 0.01 significance level, the z-score is +2.33
z-score cut-off value = +2.33
As 2 < 2.33
Could not turn down the null theory.
Study D:
z –score = (7 – 5)/1 = 2
At 0.01 significance level for two-tailed test, the z-score is ±2.58.
z-score cut-off value = ±2.58
Because58<2<2.58
Could not turn down the null theory.
18. An examiner forecasts that listening to music while solving math problems will make
a particular brain area more active. To test this, a research participant has her brain
scanned while listening to music and solving math problems, and the brain area of
interest has a percentage signal change of 58. From many previous studies with this
same math problems procedure (but not listening to music), it is known that the signal
change in this brain area is normally distributed with a mean of 35 and a standard
deviation of 10. (a) Using the .01 level, what should the researcher conclude? Solve this
problem explicitly using all five steps of theory testing, and illustrate your answer with a
sketch showing the comparison distribution, the cutoff (or cutoffs), and the score of the
sample on this distribution. (b) Then explain your answer to someone who has never
had a course in statistics (but who is familiar with mean, standard deviation, and Z
scores).
Null Theory: H0: μ = 35
Alternate Theory: H1: μ ≠ 35
Significance level: α = 0.01
Critical value = ±2.58
Test statistic:
Z = (xbar-μ)/(σ) = (58-35)/(10) = 2.3
Conclusion:
Because 2.3 < 2.58
When we see at the demonstration above, the Z score of 2.3 doesn’t lie in the refusal
area; therefore we could not turn down the Null Theory.