A researcher believes that children who grow up as an only child develop vocabulary skills at a faster rate than children with siblings. To test this, a random sample of n = 10 four-year-old only children are tested on a standardized vocabulary test (μ = 60, σ = 10). Can the researcher conclude that children from one-child families have greater vocabulary skills than the norm? Test at the 0.05 level. Use the data below to conduct the analysis: 53, 55, 59, 60, 62, 65, 68, 72, 73, 77.
Step 1: Develop Hypotheses:
a. Independent Variable = Scale: Categorical/Quantitative
b. Dependent Variable = Scale: Categorical/Quantitative
c. Circle: One-tailed/Two-tailed
d. Alternative hypothesis in sentence form.
e. Null hypothesis in sentence form.
f. Write the alternative and null hypotheses using correct notation. H1: μ > 60, H0: μ ≤ 60
Step 2: Establish significance criteria
g. α = 0.05
Step 3: Calculate test statistic, effect size, confidence interval
h. z_calculated = Level of significance (p) =
i. Decision: reject null or fail to reject null
j. Calculate effect size
k. Determine the 95% confidence interval
Step 4: Draw conclusion
l. Write your conclusion in sentence form including appropriate results notation.