Question

Talk to me ~ Fear of public speaking is a common experience across many human cultures. To help people overcome this fear, researchers developed an internet-based telepsychology program for the treatment of this common social phobia. They recruit 44 people who meet a particular social phobia criterion to participate in a study and randomly assign them to either participate in the telepsychology program or to an in-person program with a therapist. At the end of the program, participants are evaluated and are considered "improved" if they no longer meet the social phobia criterion. Results from one iteration of the study are shown in the table below.

	Improved	Did Not Improve	Total
Program 1: Telepsychology	14	11	25
Program 2: In-person	12	7	19
Total	26	18	44

Round all numeric answers to four decimal places.

1. Calculate the observed difference in the proportion of participants in the telepsychology program and the in-person program that showed improvement, p^1−p^2p^1−p^2

2. Researchers want to determine if there is a difference in results between the two programs, that is, is the telepsychology program better than the in-person program or vice versa? Or, are the two programs roughly the same? Choose the null and alternative hypotheses that are appropriate to test this research question.
A.
H0H0: There is no difference in the two treatment programs. The observed difference in p^1−p^2p^1−p^2 is due to chance.
HAHA: There is a difference in the two treatment programs. The observed difference in p^1−p^2p^1−p^2 is not due to chance.
B.
H0H0: There is no difference in the two treatment programs. The observed difference in p^1−p^2p^1−p^2 is not due to chance.
HAHA: There is a difference in the two treatment programs. The observed difference in p^1−p^2p^1−p^2 is due to chance.
C.
H0H0: There is a difference in the two treatment programs. The observed difference in p^1−p^2p^1−p^2 is not due to chance.
HAHA: There is no difference in the two treatment programs. The observed difference in p^1−p^2p^1−p^2 is due to chance.
D.
H0H0: There is a difference in the two treatment programs. The observed difference in p^1−p^2p^1−p^2 is due to chance.
HAHA: There is no difference in the two treatment programs. The observed difference in p^1−p^2p^1−p^2 is not due to chance.

3. The paragraph below describes the set up for a randomization technique, if we were to do it without using statistical software. Select an answer by choosing an option from the pull down list or by filling in an answer in each blank in the paragraph below:

To setup a simulation for this situation, we let each person be represented with a card. We write Telepsychology on __________ cards and In-person on ________ cards. Then, we shuffle these cards and split them into two groups: one group of size _________ representing those who improved, and another group of size ________representing those who did not improve. We calculate the difference in the proportion of participants in the telepsychology program and the in-person program, p^1,sim−p^2,simp^1,sim−p^2,sim. We repeat this many times to build a distribution centered at the expected difference of ___________ .
Lastly, we calculate the fraction of simulations where the simulated differences in proportions are (lessthan/greater/beyond) ? less than greater than beyond  the observed difference.

Answer 1

1.Calculate the observed difference in the proportion of participants in the telepsychology program and the in-person program that showed improvement, p^1−p^2 IS -0.0716

2.

H0: There is a difference in the two treatment programs. The observed difference in p^1−p^2 is due to chance.
HAHA: There is no difference in the two treatment programs. The observed difference in p^1−p^2 is not due to chance.

OPTION D

3.

To setup a simulation for this situation, we let each person be represented with a card. We write Telepsychology on ___25_______ cards and In-person on ____19____ cards. Then, we shuffle these cards and split them into two groups: one group of size ____28_____ representing those who improved, and another group of size ___18_____representing those who did not improve. We calculate the difference in the proportion of participants in the telepsychology program and the in-person program, p^1,sim−p^2,simp^1,sim−p^2,sim. We repeat this many times to build a distribution centered at the expected difference of ____-0.0716_______ .
Lastly, we calculate the fraction of simulations where the simulated differences in proportions are beyond  the observed difference.