Chapter 4, Practice Problem: #11

Chapter 4, Practice Problem: #11

#11. List the five steps of hypothesis testing, and explain the procedure and logic ofeach.

Hypothesis Testing
The 5 steps in hypothesis testing are:
Step – 1 (Formulate and State the Hypothesis)
Step – 2 (Decide on the Significance Level and the Type of Test)
Step – 3 (State the Decision Rule)
Step – 4 (Calculate the Test Statistic)
Step – 5 (Calculate the p- value and State the Conclusion)
What happens in each step is best understood with the help of an example. Here is one:
Problem -The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire can be driven before the tread wears out is 60,000 miles. The standard deviation of the mileage is 5,000 miles. The Crosset Truck Company bought 48 tires and found that the mean mileage for their trucks is 59,500 miles.
Research Question: Is Crosset’s experience different from that claimed by the manufacturer at the .05 significance level?
Step – 1 (Formulate and State the Hypothesis)
Null hypothesis, Ho: The mean mileage is 60000 miles, that is  = 60000
Alternative hypothesis, Ha: The mean mileage is different from 60000 miles, that is  ≠ 60000
Step – 2 (Decide on the Significance Level and the Type of Test)
 = 0.05, Since the population standard deviation is known, we conduct a two-tailed z- test
Step – 3 (State the Decision Rule)
Decision Rule: Reject Ho if the test p- value < 0.05
Step – 4 (Calculate the Test Statistic)
SE = s/n = 5000/48 = 721.69
z = (x-bar – )/SE = (59500 – 60000)/721.69 = -0.693
Step – 5 (Calculate the p- value and State the Conclusion)
p- value corresponding to z = -0.693 is 0.488
Since 0.488 > 0.05, we fail to reject Ho
Conclusion: There is no sufficient evidence that the mean mileage is different from 60000 miles.

#14. Based on the information given for each of the following studies, decidewhether to reject the null hypothesis. For each, give (a) the Z-score cutoff (or

cutoffs) on the comparison distribution at which the null hypothesis should be

rejected, (b) the Z score on the comparison distribution for the sample score, and

Population

Study _ _ Sample Score p Tails of Test

A 5 1 7 .05 1 (high predicted)

B 5 1 7 .05 2

C 5 1 7 .01 1 (high predicted)

D 5 1 7 .01 2

(A) (a) 1.645 (b) 2 (c) Reject Ho
(B) (a) 1.96 (b) 2 (c) Reject Ho
(C) (a) 2.3263 (b) 2 (c) Fail to reject Ho
(D) (a) 2.576 (b) 2 (c) Fail to reject Ho

#18. A researcher predicts that listening to music while solving math problems willmake a particular brain area more active. To test this, a research participant hasher 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 hypothesistesting, and illustrate your answer with a sketch showing the comparisondistribution, 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).

(a) H0: Music has no effect on Math problem solving skills, that is, m ≤ 35
Ha: Music increases the Math problem solving skills, that is, m > 35
(b) Upper-tailed z- test for a mean
Critical z- score for a = 0.01 is z = 2.3263
The rejection region is shown in the figure below:

Decision rule: Reject H0 if the test z- score > 2.3263.
(c) z = (x - m)/s = (58 - 35)/10 = 2.30
(d) Since 2.30 < 2.3263, we fail to reject H0
(e) Conclusion: There is no sufficient statistical evidence that music increases the Math problem solving skills.