Question

The sizes and means of two independent random samples are 400, 225; 3.5 and 3.0 respectively. can we conclude that the samples are drawn from the same population with standard deviations 1.5 ?​

Answer 1

Answer:

Sample size is greater than 30, hence use Z Test for two independent samples

Step-by-step explanation:

Given

n1 = 400 n2 = 225

x̄1 = 3.5 x̄2 = 3.0

Standard Deviation = 1.5

$z \: = \: x̄1 - x̄2 \div s \sqrt{n1n2 \div n1 + n2}$

Z = 3.5 - 3.0 / 1.5 √(400)(225) ÷ 400 + 225

Z = 0.5 / 1.5 × √90000/625

Z = 0.3333 × 12

Z = 3.9996

Table Value @ 5% level of significance = 1.96

Calculated Value > Table Value

H0 or Null Hypothesis is rejected