stats homework

1. Explain the following concepts in your own words:

(a) What is the main limitation of the z test and what alternative exists that does not have that limitation? How does the shape of a t distribution change as the sample size increases?  Fully explain your answer.

(b) A social psychologist records the number of outbursts in a sample of different classrooms at a local school. Based on the statement below, what are the sample size, decision (retain or reject the null hypothesis), and effect size in this study? 

The number of outbursts among students at this local school (M = 3) was significantly less than that in the general population, t(39) = 4.19, p < .05 (d = 0.25).

(c) A One-Sample t test was conducted to compare a mean depression score in a sample of 40 participants to a known mean score in the population. Examine the data below, calculate Cohen’s d, and write the findings in APA format:

One-Sample Statistics

	N	Mean	Std.Dev.	Std. Error Mean
Dep_score	40	3.7225	.73709	.11654

One-Sample Test

	Test Value = 4.0
	t	df	Sig.(2-tailed)	Mean Difference	95% Confidence Interval of the Distance
					Lower	Upper
Dep_score	-2.381	39	.022	-.27750	-.5132	-.0418

2. Research Articles:  Choose one of the research scenarios below and respond to the prompt.

Hoekstra et al. (2012). Using Confidence Intervals for statistical inference. Hoekstra et al. (2012) contrasted hypothesis testing with the use of confidence intervals and explained, “When a CI is used only to determine whether the null value lies within the interval, the statistical inference is no different than determining whether the outcome of a t test is significant or not” (p. 1041). Explain what statistical inference can be made when the value of the null hypothesis “lies within the interval”.

Riopelle (2003).  Estimating the population variance.

In an article comparing the t test with the z test, Riopelle (2003) demonstrated that as the sample size increased from 10 to 200 participants, the sample variance more closely estimated the population variance.  Knowing this, how will increasing the sample size change the shape of the t distribution. Explain your answer.

Hoekstra 2012 Confidence Intervals(1).pdf

Riopelle 2003 Null Hypothesis and Tests of It(1).pdf