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A clinical psychologist wants to test whether experiencing childhood trauma affects one's self-efficacy in adulthood. He randomly selects 231 adults who have experienced childhood trauma and finds that their mean self-efficacy score equals 148.9. The standard deviation of the sample equals 27.4. Self-efficacy scores in the general population of adults are distributed normally with a mean equal to 152.5 . Is there sufficient evidence to conclude that the self-efficacy of adults who have experienced childhood trauma differs from that in the general population of individuals

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Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 152.5

For the alternative hypothesis,

µ ≠ 152.5

This is a two tailed test.

Since no population standard deviation is given, the distribution is a student's t.

Since n = 231

Degrees of freedom, df = n - 1 = 231 - 1 = 230

t = (x - µ)/(s/√n)

Where

x = sample mean = 148.9

µ = population mean = 152.5

s = samples standard deviation = 27.4

t = (148.9 - 152.5)/(27.4/√231) = - 2

We would determine the p value using the t test calculator. It becomes

p = 0.047

Since alpha, 0.05 > thanthere sufficient evidence to conclude that the self-efficacy of adults who have experienced childhood trauma differs from that in the general population of individuals the p value, 0.047, then we would reject the null hypothesis. Therefore, At a 5% level of significance, there is sufficient evidence to conclude that the self-efficacy of adults who have experienced childhood trauma differs from that in the general population of individuals

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