Question

1. An investigator uses children’s WISC IQ scores as part of her study of how children respond to different teaching methods. She obtains a random sample of four children from a 5^th grade class and obtains their WISC IQ scores. Their scores are shown below. Her null hypothesis is that her sample does not differ from the general population of 5^th graders, whose IQ scores are assumed to have a m of 100 and a s of 15. She decides to use the known m and s, adopts an a of .05, and uses a non-directional (i.e., 2-sided) alternative hypothesis.

IQ scores: 112, 110, 123, 115

Assume the investigator does not know m and wishes to construct a confidence interval using her sample mean, s, and sample size. Construct a 95% confidence interval for the mean (2-sided). Show your work. State your confidence interval and briefly explain what it means.

Answer 1

From the given data, the following statistics are calculated:

n = 4

= 460/4 = 115

s = 5.7155

SE = s/

= 5.7155/ =2.8578

= 0.05

ndf = n - 1 = 4 - 1 = 3

From Table, critical values of t = 3.1824

Confidence Interval:

115 (3.1824 X 2.8578)

= 115 9.0945

= (105.9055 124.0945)

So,

Confidence Interval:

105.9055 < < 124.0945

EXPLANATION:

The 95% Confidence interval: (105.9055 124.0945) is a range of values that likely to contain unknown population mean. If repeated samples are taken and the 95% confidence interval is computed for each sample, 95% of the intervals will contain the population mean.