Question

In: Statistics and Probability

Suppose you are interested in the basic question of, “Is there an effect of mental health...

Suppose you are interested in the basic question of, “Is there an effect of mental health on amount of sleep?” You recruit 8 healthy individuals, 8 depressed individuals, and 8 anxious individuals and measure the amount they sleep. Given that   SSb = 1902 and    SSw = 3386 fill in a source table and find the obtained value of the appropriate statistic.

a.17

b 5.90

c. 24.00

d. 4.45

  1. Given your obtained value in the sleep study, what is the correct decision?

    Significant. Reject the Ho. Mental health did not have a significant effect on amount slept.

    Significant. Reject the Ho. Mental health had a significant effect on amount slept.

    Not significant. Fail to reject the Ho. Mental health did not have a significant effect on amount slept.

    Not significant. Fail to reject the Ho. Mental health had a significant effect on amount slept.

1

Solutions

Expert Solution

The Hypothesis:

H0: Mental health does not have a significant effect on amount slept. (There is no relationship between them)

Ha: Mental health has a significant effect on amount slept. (There is a relationship between them)

______________________________________________

Number of groups, k = 3

Total Observations N = 24

df b = k - 1 = 2

df w = N - k = 24 - 3 = 21

MS b = SSb / df b = 1902 / 2 = 951

MS w = SSw / df w = 3386 / 21 = 161.238

Therefore F test = MS b / MS w = 951 / 161.238 = 5.90 (Option b)

The ANOVA table is as below

Source SS DF Mean Square F p Fc
Between 1902.00 2 951.00 5.90 0.0093 3.467
Within/Error 3386.00 21 161.24
Total 5288.00 23

The p value is calculated for F = 5.9, df1 = 2, df2 = 21

The F critical value is calculated at Alpha = 0.05 (default) df1 = 2, df2 = 21

___________________________________________________________

Since F test is > Fcritical (3.467) and also p value is < 0.05, We reject the null hypothesis.

Option 2: Significant Reject the H0. Mental health had a significant effect on the amount slept.

____________________________________________________________


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