Question

In: Statistics and Probability

In an experiment to determine the effectiveness of sleep-inducing drugs, 18 insomniacs were randomly assigned to...

In an experiment to determine the effectiveness of sleep-inducing drugs, 18 insomniacs were randomly assigned to three treatments:

                1. Placebo (no drug)

                2. Standard drug

                3. New experimental drug

The data shown is the average number of sleep per night for a week. Use α = 0.05 (use excel)

  1. Write the statistical effects model completely specify each component. State the necessary assumptions for the analysis.
  2. Perform the appropriate analysis, identify what hypotheses are being tested, the test statistic, critical value and p-value. State your conclusions and make any specific recommendations for use of these drugs.

c. Use Dunnett’s method and perform comparisons to the placebo. Fully explain your conclusions.

Treatments
1 2 3
5.6 8.4 10.6
5.7 8.2 6.6
5.1 8.8 8
3.8 7.1 8
4.6 7.2 6.8
5.1 8 6.6

Solutions

Expert Solution

(a) The model is:

Sleep per night = 4.983 + 0.0 Treatments_1 + 2.967 Treatments_2 + 2.783 Treatments_3

(b) The hypothesis being tested is:

Null hypothesis All means are equal
Alternative hypothesis Not all means are equal
Significance level α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
Treatments 3 1, 2, 3

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Treatments 2 33.16 16.582 15.04 0.000
Error 15 16.54 1.102
Total 17 49.70

Since the p-value (0.000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that Not all means are equal.

(c) Using the Dunnett Method and 95% Confidence

Treatments N Mean Grouping
3 (control) 6 7.767 A
2 6 7.950 A
1 6 4.983

Means not labelled with the letter A are significantly different from the control level mean.

orchestra answered 1 year ago
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