# Thread: need help with a sign test problem

1. ## need help with a sign test problem

Use a sign test to test this claim.
A researcher wishes to study whether music has any effect on the ability to memorize information. 83 randomly selected adults are given a memory test in a quiet room. They are then given a second memory while listening to classical music. 66 people received a higher score on the second test, 16 a lower score, and 1 received the same score. At the 0.05 significance level , test the claim that the music has no effect on memorization skills.

2. Originally Posted by tennisair
Use a sign test to test this claim.
A researcher wishes to study whether music has any effect on the ability to memorize information. 83 randomly selected adults are given a memory test in a quiet room. They are then given a second memory while listening to classical music. 66 people received a higher score on the second test, 16 a lower score, and 1 received the same score. At the 0.05 significance level , test the claim that the music has no effect on memorization skills.
Outline:

+ if $X_i > Y_i$,
0 if $X_i = Y_i$,
- if $X_i < Y_i$.

H0: Pr(X > Y) = Pr(X < Y), that is, H0: Pr(+) = Pr(-).

H1: $\Pr(X > Y) \neq \Pr(X < Y)$, that is, H1: $\Pr(+) \neq \Pr(-)$ (why?)

The test is based on the test statistic Z = freq(+). Under H0, Z ~ Binomial(n = n*, 0.5) where n* is the number of observations of + or - signs.

Calculate $P = 2 \Pr(Z \geq 66)$ where Z ~ Binomial(n = 82, p = 0.5).