Question

State the null and alternative hypotheses to test if the population represented by Sample 1 has a mean that is 2.0 units higher than the population represented by Sample 2. Let µd be the population mean of​ matched-pair differences for Sample 1 - Sample 2. State the null and alternative hypotheses.

Pair 1 2 3 4 5 6 7
Sample1 5 6 10 3 6 7 8
Sample2 4 4 3 5 5 5 3

Answer 1

Null Hypothesis,
`H_0` :
`\mu_A-\mu_B` = 2.0 units or
`\mu_D` = 2.0 units

Alternate Hypothesis,
`H_A` :
`\mu_A-\mu_B\\eq` 2.0 units or
`\mu_D\\eq` 2.0 units

Explanation:

We are given the following data below and we have test if the population represented by Sample 1 has a mean that is 2.0 units higher than the population represented by Sample 2;

Pair : 1 2 3 4 5 6 7

Sample1 : 5 6 10 3 6 7 8

Sample2 : 4 4 3 5 5 5 3

Let
`\mu_A` = population mean represented by Sample 1

`\mu_B` = population mean represented by Sample 2

`\mu_D` = population mean matched-pair differences for Sample 1 - Sample 2

So, Null Hypothesis,
`H_0` :
`\mu_A-\mu_B` = 2.0 units or
`\mu_D` = 2.0 units

Alternate Hypothesis,
`H_A` :
`\mu_A-\mu_B\\eq` 2.0 units or
`\mu_D\\eq` 2.0 units

Here null hypothesis states that the population represented by Sample 1 has a mean that is 2.0 units higher than the population represented by Sample 2.

On the other hand, alternate hypothesis states that the population represented by Sample 1 has a mean that is not 2.0 units higher than the population represented by Sample 2.