Question

"Calculate the observed value of the t statistic" for testing the difference between the two population means using paired data. (Round your answer to three decimal places.)d = 0.3, sd2 = 0.15, n1 = n2 = 10, Ha: (μ1 − μ2) ≠ 0

Answer 1

Answer:

$d = 0.3$ represent the sample difference

$s^2_d = 0.15$ represent the sample variance

$s_d = \sqrt{0.15} =0.387$ represent the sample deviation for the difference

$n_1= n_2 =10$ represent the sample size

The statistic on this case is given by:

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{0.3 -0}{\frac{0.387}{\sqrt{10}}}=2.449$

Step-by-step explanation:

A paired t-test is used to compare two population means where you have two samples in  which observations in one sample can be paired with observations in the other sample. For example  if we have Before-and-after observations (This problem) we can use it.  

Let put some notation  

1=test value before , 2 = test value after

The system of hypothesis for this case are:

Null hypothesis: $\mu_1- \mu_2 = 0$

Alternative hypothesis: $\mu_1 -\mu_2 \neq 0$

For this case we know the following info:

$d = 0.3$ represent the sample difference

$s^2_d = 0.15$ represent the sample variance

$s_d = \sqrt{0.15} =0.387$ represent the sample deviation for the difference

$n_1= n_2 =10$ represent the sample size

The statistic on this case is given by:

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{0.3 -0}{\frac{0.387}{\sqrt{10}}}=2.449$