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A child psychologist believes that controlled physical outbursts of anger (like punching a pillow) may not improve the mood of young girls with emotional impairment. He believes that the proportion of girls who benefit from the treatment is less than the proportion of boys. A random sample from each population receives counseling in the treatment and is asked about their mood after an episode (Xis the number of test subjects that reported an improvement in mood). The results of the study are summarized in the table below. 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: i'l , p2 , yes 01' 110. 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 classz) 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 girls be population 1 and boys be population 2. To explore the suspicion above, conduct a significance test using the hypotheses: Hozpl = p2 Ha: 131192 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 = -1.86 with corresponding p-value of p = 0.0317. 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= -1.86 (left, right or both) Blank #4: Give the test decision: (reject or do not reject) H 0 Blank #5: Evidence _______________ (favors or does not favor) that the proportion of girls who benefit from the treatment is less than the proportion of boys 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? (yes or no)