A developmental psychologist was studying a new program to

Question

Need help in this hypothesis Testing question:

A developmental psychologist was studying a new program to reduce anxiety among children bullied at school. Assume that it is known from previous research that the anxiety level of children in general who are bullied at school is normally distributed, with a mean of 85 and a standard deviation of 15, on a common scale used to measure anxiety. The new program is tried on one randomly selected child who is being bullied. After the program, the childs anxiety level on the scale is 52

Using the 5-step hypothesis testing to evaluate whether the anxiety of bullied children in the new program is less than children in general who are bullied. Use an alpha level of .05.

I have done what I was able to do on my own will like help on what I could not do.

step 1: Population 1: Anxiety levels of bullied children in the New Program

Population 2: Children in general who are bullied

Research Hyphothesis(H₁) Population 1 will have less anxiety scores than population 2

μ1 < μ2

Null Hypothesis (H_o) Population 1 will not have less anxiety scores than population 2

μ1 ≥ μ2

Step 2: Comparison Distribution

μ "mu"= 85

σ "sigma"=15

Shape= Normal Curve

Step3: Determine Cutoff Score

Cutoff Z(.05, one-tailed, low) -1.64

(you use a one-tailed test because the program wants to reduce(lessen) anxiety levels among bullied children at school)

Step4: Turn Comparison Distribution in to Z score

Z= X-μ/σ         z=52-85/15 Z Score= -2.2

Step5: Decide whether to reject the Null Hypothesis. Describe why?

I know the cut off score is -1.64 and the Z score fall at -2.2 bellow the cut off score. Does this mean I will reject the null? If so why or why not.