A stress researcher is measuring how fast people hit a red button after a loud n

Question

A stress researcher is measuring how fast people hit a red button after a loud noise. He gathers data from 81 people (N=81). His participants' reaction times are normally distributed. The average reaction time was 2.0 seconds, with a standard deviation of 0.2 seconds. Using a standard normal table (Table A-1), answer the following questions (hint: you need a convert raw scores into z-scores).

a. What proportion of his participants will be between 1.6 and 2.1 seconds?

b. What proportion of his participants will be between 1.4 and 2.2?

c. What proportion of his participants will be between 2.3 and 2.7?

d. What proportions of participants will be above 2.4 seconds?

e. Of the z-scores you calcualtes above wich 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 o) 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)?

Explanation / Answer

Normal distribution params are given out here:

Mean = 2

Stdev = .2

n = 81

a. P(1.6<X<2.1) = P(1.6-2/(.2)<Z< (2.1-2)/(.2) = P(-2<Z<.5) =0.69146- 0.02275 = 0.6687

b. P(1.4<X<2.2 )= P(1.4-2 / .2 <Z< 2.2-2 / .2) = P(-3<Z<1) = 0.8413-0.00135 = 0.84

c. P(2.3<X<2.7) = P(2.3-2/.2<Z<2.7-2/.2) = P(-.5<Z<3.5) = 0.99977-0.30854 = 0.69123

d. P(X>2.4) = P(Z> 2.4-2/.2) = P(Z>2) = .025

e. Based on the above, b is most probable and d is least probable.

f. SE = .2/sqrt(81) = .2/9 = 0.0222

g. +/- 1.96 or rounded off to 2 : is the critical Z value for alpha = .05

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