Question

A stress researcher is measuring how fast parents respond to a crying infant. He gathers data from 64 people (N = 64). His participants' reaction times are normally distributed. The average reaction time was 3.0 seconds, with a standard deviation of 0.2 seconds. Using a standard normal table (Table A-1), answer the following questions (hint: you need to convert raw scores into z-scores).

a. What proportion of his participants will be between 2.6 and 3.1 seconds?
b.      What proportion of his participants will be between 2.4 and 3.2?
c. What proportion of his participants will be between 3.3 and 3.7?
d. What proportions of participants will be above 3.4 seconds?
e. Of the z-scores you calculated above which is the most probable? Which is the least probable? Explain your answers.
f. What would the standard error of the mean be for the sampling distribution from which this sample of reaction times was drawn, if we assume the population SD (sigma, σ) is also 0.2?
g. If we are using an alpha = .05, what would the critical values be in raw units (hint: you don't need the z-table for this)?

Answer 1

(a)

(b)

(c)

(d)

(e)

z-score 3.5 corresponding to X = 3.7 is least probable while the z-score 0.5 corresponding to X= 3.1 is most probable.

(f)

The standard error will be

(g)

The critical values are -1.96 and 1.96.