Question

30 schizophrenics score a mean of 12, with a standard deviation of 3.5 on a short-term memory test. If the mean for the general population is 13.7, what is the two-tailed p correspondng to the one-sample t value comparing the 30 schizophrenics to the general population? PLEASE EXPLAIN YOUR ANSWER AND SHOW ALL WORK!

a) > /05

b) between .05 and .02

c) between .02 and .01

d) <.01

Answer 1

Solution,

Given that,

The null and alternative hypothesis is ,

H₀ :   = 13.7

H_a :    13.7

= 12

s = 3.5

n = 30

degrees of freedom = n - 1 = 30 - 1 = 29

Test statistic = t =

= ( - ) / s / n

= (12 - 13.7) / 3.5 / 30

Test statistic = t = -2.66

P( t < -2.66)

= 0.0063

This is the two tailed test .

P-value = 2 * P( t < -2.66)

P-value = 2 * 0.0063

P-value = 0.0126

correct option is = c) between .02 and .01