Seasonal affective disorder (SAD) is a type of depression during seasons with le

Question

Seasonal affective disorder (SAD) is a type of depression during seasons with less daylight (e.g., winter months). One therapy for SAD is phototherapy, which is increased exposure to light used to improve mood. A researcher tests this therapy by exposing a sample of SAD patients to different intensities of light (low, medium, high) in a light box, either in the morning or at night (these are the times thought to be most effective for light therapy). All participants rated their mood following this therapy on a scale from 1 (poor mood) to 9 (improved mood). The hypothetical results are given in the following table.

(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test. (Round your answers to two decimal places. Assume experimentwise alpha equal to 0.05.)

State the decision for the main effect of the time of day.

Retain the null hypothesis. Reject the null hypothesis.    

State the decision for the main effect of intensity.

Retain the null hypothesis. Reject the null hypothesis.    

State the decision for the interaction effect.

Retain the null hypothesis. Reject the null hypothesis.    

(b) Compute Tukey's HSD to analyze the significant main effect.

The critical value is 21 for each pairwise comparison.

Light Intensity Low Medium High Time of
Day Morning 5 5 7 6 6 8 4 4 6 6 7 9 5 9 5 6 7 8 Night 5 6 9 8 8 6 6 7 6 7 5 8 4 9 7 3 8 6

Explanation / Answer

a. H0:mu1=mu2 (there is no difference in mean mood score for participants during morning and night)

H1:there is difference in mean mood score for participants during morning and night.

p value for F(2,14)=4 is 0.0422.

Per rejection rule, based on p value, reject H0, if p value is less than 0.05. Here, p value is less than 0.05, therefore, reject H0.

H0:mu1=mu2=mu3 (there is no difference in mean mood score for participants during three different intensity of light)

H1:atleast one mean mood score is differnt from another.

p value for F(6,14)=8 is 0.0006.

Per rejection rule, based on p value, reject H0, if p value is less than 0.05. Here, p value is less than 0.05, therefore, reject H0.

H0:there is no interaction between time of day and intensity of light

H1:there is interaction between time of day and intensity of light.

p value for F(11,15)=12 is 0.0000.

Per rejection rule, based on p value, reject H0, if p value is less than 0.05. Here, p value is less than 0.05, therefore, reject H0.

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