By Spearman-Brown Prophecy Formula,
rkk = k(r11) / [1 + (k – 1)* r11]
Given,
r11 = 0.60
rkk = 0.80
0.80 = 0.60 k / [1 + (k – 1)* 0.60]
0.8 [1 + (k – 1)* 0.60] = 0.6 k
0.8 (1 + 0.6k - 0.6) = 0.6k
0.8(0.4 + 0.6k) = 0.6k
0.32 + 0.48k = 0.6k
(0.6 - 0.48)k = 0.32
0.12k = 0.32
k = 0.32/ 0.12 = 8/3
The test need to be increased by 8/3 times in order to raise the reliability to 0.80
The number of questions to be increased by (8/3) * 30 = 80
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