A psychologist develops a new inventory to measure depression.  The population of "normal" individuals has mean score on this test of µ = 55 with σ = 12.  To determine whether the test is sensitive to detecting those individuals that are severely depressed, a random sample of patients who are described as depressed by a therapist is selected and given the test.  Presumably, the higher the score on the inventory, the more depressed the patient is.  The data are as follows: 59, 60, 60, 67, 65, 90, 89, 73, 74, 81, 71, 71, 83, 83, 88, 83, 84, 86, 85, 78, 79

Use Hypothesis testing to determine if the new inventory differentiates between the patients who are described as depressed?  Use an α = .05

Step 1: State Hypothesis

The Null hypothesis

H₀: µ_{depression measure} = 55

a. State the null hypothesis in your own words

The Alternative hypothesis

H₁: µ_{depression measure}  ≠ 55

b. State the alternative hypothesis in your own words

Step 2: Set Criteria

                α = .05 with a two tails

c. Using the table in the book fill in the values for p and z critical

Step 3: Compute Sample Statistic

In this example we are not given M or n.  We are however given the sample scores, so all we have to do to get M is to find the average of the scores.  We get n by counting the frequency of scores n =21.

M = (59 + 60 + 60 + 67 + 65 + 90 + 89 + 73 + 74 + 81 + 71 + 71 + 83 + 83 + 88 + 83 + 84 + 86 + 85 + 78 + 79)/ 21 = 1609/21 = 76.62

σ_M = σ/√n                            σ_M = 12/√21 = 12/4.58 = 2.62

z = (M - μ)/ σ_M  z_obt = (76.62 - 55)/ 2.62 = 21.62/ 2.62 = 8.25

d. Use Excel to replicate the test statistic that was computed by hand.  Include the output or a copy of your excel file

Step 4: Make a decision

e. Did you reject the null/fail to reject the null

f. State your conclusions in your own words

2. A rocket scientist, Dr. Boom, is measuring the weight of a sample of 25 rockets in his latest spaceship.  He thinks they might weight less than the average rocket.  The sample has on average 102 lbs with a standard deviation of 10 lbs.  The average rocket weights 106 lbs. 

Use Hypothesis testing to determine if Dr. Boom is correct, that his sample of 25 rockets weight less than the average rocket.    Use an α = .01

Step 1: State Hypothesis

The Null hypothesis

H₀: µ_rocket ≥ 106

a. State the null hypothesis in your own words

The Alternative hypothesis

H₁: µ_rocket< 106

b. State the alternative hypothesis in your own words

Step 2: Set Criteria

α = .01 with a one tailed test

df = n - 1 = 25 - 1 = 24

c. Using the table in the book fill in the values for p and t critical

Step 3: Compute Sample Statistic

d. In this example we are not given the raw data which means we cannot use Excel to compute the test statistic; however, we are given all the necessary values to compute the test statistic by hand.  Compute the test statistic.

Step 4: Make a decision

e. Did you reject the null/fail to reject the null

f.  State your conclusions in your own words