Question

A child psychologist believe that controlled physical outbursts of anger (like punching a pillow) may improve the mood of young boys with emotional impairment. He believes that the proportion of boys who benefit from the treatment is greater than the proportion of girls. A random sample from each population receives counseling in the treatment and is asked about their mood after an episode (x is the number of test subjects that reported an improvement in mood). The results of the study are summarized in the table below. Girls Boys ni = 200 X1 - 35 n2 = 210 X2 = 28 Blank #1: Find the two sample proportions, reporting each as a decimal, rounded to two decimal places. Do the initial (untested) findings show what the researcher expected? Enter your answer as a list of 3 items: Ô 1, 2, yes or no. Do not add any extra spaces and pay attention to rounding. For example, a valid answer may look like 52, 14 yes or 25.50, no. Untested, you compared them but you could have done that before you took stats class:) Comparing the sample proportions does not build in any uncertainty or variation into the estimates; thus we use inference procedures such as confidence intervals and significance tests to do so. Let 1 be boys and 2 be girls. To explore the suspicion above, conduct a significance test using the hypotheses: P1 = P2 P1 P2 Blank #2: Determine the correct alternative hypothesis by filling in the blank with < > or not equals. Blank #3: The test statistic of this test is z = 1.17 with corresponding p-value of p = 0.1211. If you were to draw the distribution of the sample proportions under the assumption of the null hypothesis, this p-value is the area in the tail formed by z= 1.17 (left, right or both) Blank #4: Give the test decision: (reject or do not reject) Ho Blank #5: Evidence (favors or does not favor) that the proportion of boys who benefit from the treatment is greater than the proportion of girls Blank #6: Once the uncertainty has been built in with the significance test, is the decision of the test the same as your untested answer in blank #1? lyes or no)

Answer 1

1. 0.18,0.13,yes

2. >

3. right

4. do not reject

5. does not favor

6. no

p1	p2	pc
0.18	0.13	0.1537	p (as decimal)
35/200	28/210	63/410	p (as fraction)
35.	28.	63.	X
200	210	410	n
	0.0417	difference
	0.	hypothesized difference
	0.0356	std. error
	1.17	z
	.1211	p-value (one-tailed, upper)