Question

A study compared substance use, delinquency, psychological well-being, and social support among various family types, for a sample of urban African-American adolescent males. The sample contained 108 subjects from single-mother households and 44 from households with both biological parents. The youths responded to a battery of questions that provides a measure of perceived parental support. This measure had sample means of 46 (s = 9) for the single-mother households and 42 (s = 10) for the households with both biological parents. Consider the conclusion, "The mean parental support was 4 units higher for the single-mother households. If the true means were equal, a difference of this size could be expected only 2% of the time. For samples of this size, 95% of the time one would expect this difference to be within 3.4 of the true value."

a. Explain how this conclusion refers to the results of (i) a confidence interval, (ii) a hypothesis test. From the information provided, replicate (i.e. show the calculations yourself for) the confidence interval and hypothesis test.

b. Explain the results of the study to someone who has not studied inferential statistics.

Answer 1

a

Hypotheses are:

(i)

Here we have

The 95% confidence interval is

Since confidence interval does not contain zero so we cannot conclude that populations means are equal.

(ii)

The p-value is 0.02

Since p-value is less than 0.05 so we reject the null hypothesis.

(b)

The results suggest that the mean parental support for groups single-mother households and both biological parents.