Answer to Question #120067 in Statistics and Probability for Kamarul

Question

A random sample of stipends of teaching assistants in economic is listed. Is there sufficient evidence at the alpha = 0.05 to conclude that the average stipend differs from 15,000. The stipends (in dollars) listed in the figure are for the academic year
14,000 18,000 12,900 14,356 13,185
13,419 14,000 11,981 17,604 12,283
16,338 15,000

Answer 1

Н₀: μ=15000,

H_alt: μ≠15000

μ=(14000+18000+12900+14356+13185+13419+14000+11981+17604+12283+16338+15000)/12=14422

$\sigma=2200$

t=(14422-15000)/(2200/$\sqrt{12}$ )=-1.1

d.f.=12-1=11

using table for t-test with t - 1.1 and d.f. 11- P-value>0.2

alpha = 0.05

0.2>0.05 - don't reject H_{0 -} we do not have sufficient evidence to conclude that the average stipend differs from 15,000