Question

Hi, can you help me answer this question please, thank you!

Answer 1

Assuming that you have to calculate the test statistic for the difference between the population means, μ₁, μ₂. To calculate the statistic you have to subtract the population parameter from the point estimate and divide it by the standard deviation.

The population parameter is (μ₁ - μ₂)

The point estimator is (x-bar₁ - x-bar₂)

The standard deviation is [(S₁/√n₁) +(S₂/√n₂)]

Let's say, for example, that the test is two-tailed, then:

`\begin{gathered} H_0\colon\mu_1-\mu_2=0 \\ H_1\colon\mu_1-\mu_2\\e0 \end{gathered}`

The test statistic can be calculated as:

`\frac{(\bar{x}_1-\bar{x_2})-(\mu_1-\mu_2)}{(\frac{S_1}{\sqrt[]{n_1}}+\frac{S_2}{\sqrt[]{n_1}})}`

n₁= 50

x-bar₁= 2.31

S₁= 0.89

n₂=30

x-bar₂= 2.02

S₂= 0.61

For the difference between the population means you have to use the value under the null hypothesis, in this case, μ₁ - μ₂ = 0

`\frac{(2.31-2.02)-0}{(\frac{0.89}{\sqrt[]{50}}+\frac{0.61}{\sqrt[]{30}})}=(0.29)/(0.237)=1.22`

The value of the statistic is 1.22