Question

Question 03) Suppose you wish to test the effect of Prozac on the well-being of depressed individuals, using a standardized "well-being scale" that sums Likert-type items to obtain a score that could range from 0 to 20. Higher scores indicate greater well-being (that is, Prozac is having a positive effect). | 7 Patient ID 1 MoodPre 3 MoodPost 5 4 7 17 5 4 10 6 3 9 8 9 14 11 8 17 Has Prozac been effective? a) Write down your hypothesis.

Answer 1

The R output is:

Project: (None) - + Run + - Source - List - C . ® RStudio File Edit Code View Plots Session Build Debug Profile Tools Help OR H B O Go to file/function - Addins Untitled1* * a Source on Save 97 0 1 MoodPre <- C(3,0,6,7,4,3,2,1,4) MoodPost <- c(5,1,5,7,10,9,7,11,8) 3 t.test(Moodpre, MoodPost, paired = TRUE, alternative = "two. sided") 4 delta <- -3.666667 5 sigma <- 3.5 6 d <- delta/sigma 7 power.t.test(n = 9, d=d, sig. level = 0.05, type = 'paired') 8 power. t.test(d=d, sig. level = 0.05, power = 0.85, type = 'paired') Environment History Connections A Import Dataset Global Environment values -1.04761914285714 delta -3.666667 MoodPost num (1:9] 5 1 5 7 10 9 7 11 8 Moodpre num (1:9] 3 0 6 7 4 3 2 1 4 sigma 3.5 Files Plots Viewer Packages Help Zoom Export 9:1 (Top Level) R Script Console Terminal Jobs power = 0.7856895 alternative = two.sided NOTE: n is number of *pairs*, sd is std. dev. of *differences within pairs > power. t.test(d=d, sig. level = 0.05, power = 0.85, type = 'paired') Paired t test power calculation n = 10.27718 delta = 1.047619 sd = 1 sig. level = 0.05 power = 0.85 alternative = two.sided NOTE: nis number of *pairs*, sd is std.dev. of *differences within pairs

The R code is:

MoodPre <- c(3,0,6,7,4,3,2,1,4)
MoodPost <- c(5,1,5,7,10,9,7,11,8)
t.test(MoodPre, MoodPost, paired = TRUE, alternative = "two.sided")
delta <- -3.666667
sigma <- 3.5
d <- delta/sigma
power.t.test(n = 9, d=d, sig.level = 0.05, type = 'paired')
power.t.test(d=d, sig.level = 0.05, power = 0.85, type = 'paired')

(a) The hypothesis being tested is:

H₀: µ_d = 0

H_a: µ_d ≠ 0

(b) The paired t-test statistic is -3.1429.

(c) Reject H₀ if t > 1.859548.

(d) The p-value is 0.01375.

(e) Since the p-value (0.01375) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that Prozac is effective.

(f) Power = 0.7856895

(g) Sample size = 10.27718 = 11

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