Statistics in Human Behavior

Question

The mean of a self-worth measure in the population of adult males is 30.00. A researcher is interested in whether females report differing levels of self-worth. The researcher randomly samples 150 adult females and give them the self-worth battery. Use the 5 steps of hypothesis testing to determine whether females report differing levels of self-worth than males. Assume the researcher obtained the following statistics in the female sample: (M = 31.9; s = 10.52). Assume α = .05, two-tailed test.

 Step 1: State the hypotheses

 Step 2: Three Characteristics of the Comparison Distribution

 Step 3: Cutoff scores (1 point) Step 4: Calculate the statistic

 Step 5: Statistical decision and interpretation 

Answer 1

Theresa:

 

Step 1; Let μ_F be the population mean of self-worth measure for females.

H_o : μ_F = 30. H₁ : μ_F ≠ 30 .

 

Step 2: Since the population SD is not given (unknown) t-test is to be used Characteristic (1) Degrees of Freedom (DF) = 150 - 1 = 149 Characteristic (2) Large DF, so t-distribution can be approximated as normal. Characteristic (3): Symmetric bell shaped.

 

Step 3: Cutoff scores (1 point): α = 0.05. Cut-off scores: plus or minus 1.96 (t_α/2 = z_{α/2 (approx) = 1.96.})

 

Step 4: Calculate the statistic  t = (sample mean - (null) hypothesized μ_F) / [Sample SD / √(sample size)]

 

       t = (31.9 - 30) / [10.52/√150] = 2.21

 

Step 5: Statistical decision and interpretation

 

Since the calculated t is larger than the cut-of value, we reject the null hypothesis.  Interpretation:  The data provide sufficient evidence at 5% level of significance the the population mean of self-worth battery for adult females is different from from the corresponding mean for adult males.

 

Dr. G.