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2 years ago

Question 1:

Mathematics

1 answer:

Anni [7]2 years ago

7 0

When I took this quiz mine was H

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. An independent-measures research study was used to compare two treatment conditions with n=12 participants for each treatment.

Andru [333]

Answer:

Decision rule is

Fail to reject the null hypothesis

The conclusion is

There is sufficient evidence that indicate that there is a significant difference between the two treatments

Step-by-step explanation:

From the question we are told that

The sample size is n = 12

The first mean is $M_1 = 55$

The variance is $s^2_1 = 8$

The second mean is $M_2 = 52$

The second variance is $s^2_2 = 4$

Let the level of significance be $\alpha = 0.05$

The null hypothesis is $H_o : M_1 = M_2$

The alternative hypothesis is $H_a : M_1 \ne M_2$

Generally the test statistics is mathematically

$t = \frac{M_1 - M_2 }{ \sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2}} }$

=> $t = \frac{55 - 52 }{ \sqrt{\frac{8}{12} +\frac{4}{12 }} }$

=> $t = 1.1619$

Generally the degree of freedom is mathematically represented as

$df = 12 -1$

=> $df = 11$

Generally from the t- distriibution table the critical value of $\alpha$ at a degree of freedom of $df = 11$ is

$t_{0.05 , 11} = 2.20098516$

Here given that the critical value is greater than the t statistics value the

Decision rule is

Fail to reject the null hypothesis

The conclusion is

There is sufficient evidence that indicate that there is a significant difference between the two treatments

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