A stress researcher is measuring how fast parents respond to a crying infant. He gathers data from 49 people (N = 49). His participants' reaction times are normally distributed. The average reaction time was 4.0 seconds, with a standard deviation of 0.2 seconds. Using a standard normal table (Table A-1 in the Appendix of the textbook), answer the following questions (hint: you need to convert raw scores into z-scores)

What proportion of his participants will be between 3.9 and 4.6 seconds?

Step 1:

z = (3.9 - 4.0)/0.2 = (-0.1)/0.2 = -0.5

z = (4.6 - 4.0)/0.2 = (0.6)/0.2 = 3

Step 2:

Use table A-1 mean to z for z = -0.5 is 19.15%

Use table A-1 mean to z for z = 3 is 49.87%

Step 3: Convert to proportions 0.1915 and 0.4987

Step 4: p = 0.1915 + 0.4987 = 0.6902

What proportion of his participants will be between 3.4 and 4.2?

Step 1:

z = (3.4- 4.0)/0.2 = (-0.6)/0.2 = -3

z = (4.2-4.0)/0.2 = (0.2)/0.2 = 1

Step 2:

Use table A-1 mean to z for z = -3 is 49.87%

Use table A-1 mean to z for z = 1 is 34.13%

Step 3: Convert to proportions 0.4987 and 0.3413

Step 4: p = 0.4987 + 0.3413 = 0.84

What proportion of his participants will be between 4.3 and 4.7?

Step 1:

z = (4.3- 4.0)/0.2 = (0.3)/0.2 = 1.5

z = (4.7- 4.0)/0.2 = (0.7)/0.2 = 3.5

Step 2:

Use table A-1 mean to z for z = 1.5 is 43.32%

Use table A-1 mean to z for z = 3.5 is 49.98%

Step 3: Convert to proportions 0.4332 and 0.4998

Step 4: p = 0.4332 + 0.4998 = 0.933

What proportion of participants will be above 4.4 seconds?

Step 1: z = (4.4- 4.0)/0.2 = (0.4)/0.2 = 2

Step 2: Use table A-1 percent in tail for z = 2 is 2.28%

Step 3: Convert to proportions 0.0228

Question:

Of the z-scores you calculated above which is the most probable? Which is the least probable? Explain your answers.

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)?