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

Answer:

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

Alternate Hypothesis, $H_A$ : $\mu_A-\mu_B\neq$ 2.0 units  or  $\mu_D\neq$ 2.0 units

Step-by-step 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, $H_A$ : $\mu_A-\mu_B\neq$ 2.0 units  or  $\mu_D\neq$ 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.