Help me please with 3 and 4
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Answer:
No, there is not any sufficient evidence to conclude that individuals who have experienced childhood trauma have lower self-efficacy in adulthood.
Step-by-step explanation:
We are given that a clinical psychologist wants to test whether experiencing childhood trauma reduces one's self-efficacy in adulthood.
He randomly selects 22 adults who have experienced childhood trauma and finds that their mean self-efficacy score equals 118.1.
Self-efficacy scores in the general population of adults are distributed normally with a mean equal to 118.5 and a standard deviation equal to 18.8 .
<em>Let </em><em> = mean self-efficacy score.</em>
So, Null Hypothesis, :
118.5 {means that the individuals who have experienced childhood trauma have higher or same self-efficacy in adulthood}
Alternate Hypothesis, :
< 118.5 {means that the individuals who have experienced childhood trauma have lower self-efficacy in adulthood}
The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean self-efficacy score = 118.1
= population standard deviation = 18.8
n = sample of adults who have experienced childhood trauma = 22
So, <u><em>test statistics</em></u> =
= -0.0998
The value of z test statistics is -0.0998.
Since, in the question we are not given with the level of significance so we assume it to be 5%. <u>Now, at 5% significance level the z table gives critical value of -1.645 for left-tailed test.</u>
Since our test statistic is more than the critical value of z as -0.0998 > -1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.
Therefore, we conclude that the individuals who have experienced childhood trauma have higher or same self-efficacy in adulthood.