Question

The group of 25 victims scored an average of 25.3 with a sample standard deviation of 9 on the depression scale. The group of 23 bully-victims scored an average of 20.5 with a sample standard deviation of 8 on the same scale. You do not have any presupposed assumptions about whether victims or bully-victims will be more depressed, so you formulate the null and alternative hypotheses as:

Answer 1

Complete Question

The group of 25 victims scored an average of 25.3 with a sample standard deviation of 9 on the depression scale. The group of 23 bully-victims scored an average of 20.5 with a sample standard deviation of 8 on the same scale. You do not have any presupposed assumptions about whether victims or bully-victims will be more depressed, so you formulate the null and alternative hypotheses as:

$H_o: \ \ \mu_{victims} - \mu_{bully-victims} = 0H1: \ \ \mu _{victims} - \mu_{bully-victims} \ne 0$

You conduct an independent-measures t test. Given your null and alternative hypotheses,

this is a ________ [ Select ]                       ["two-tailed", "one-tailed"]         test.

The degree of freedom is __________   [ Select ]       ["46", "48", "24", "22"]    

and for an alpha of .01, the critical t is +/-    _________ [ Select ]                       ["2.704", "2.021", "1.684"]    

In order to calculate the t statistic, you first need to calculate the standard error under the assumption that the null hypothesis is true. In order to calculate the standard error, you first need to calculate the pooled variance. The pooled variance is   ________ [ Select ]                       ["72.8696", "145", "0.3756", "71.3201"] .

The standard error is   ___________ [ Select ]             ["2.4664", "2.5572", "1.9543", "72.8712"]         .

The t-statistic is _________ [ Select ]                       ["1.95", "2.55", "-1.70", "-2.25"]

Answer:

First Question

 The correct option is  "two-tailed"

Second Question

    The correct option is "46"

Third Question

     The correct option is  "2.704"

Fourth Question

     The correct option is "72.8696"

Five  Question

     The correct option is "2.4664"

Sixth  Question

     The correct option is "1.95"

Step-by-step explanation:

From the question we are told that

   The number of victims is  $n_1 = 25$

   The sample mean is  $\= x_1 = 25.3$

   The standard deviation is  $s_1 = 9$

   The  number of bully victims is  $n_2 = 23$

   The sample mean is  $\= x_2 = 20.5$

    The standard deviation is  $s_2 = 8$

Generally this is a two -tailed test because  from the null and the alternative hypothesis we see that the test is know whether the mean number of victims is significantly more depressed than bully -victims  or significantly  less depressed than bully -victims

   

Generally the degree of freedom is mathematically represented as  

      $df = n_1 + n_2 -2$

=>   $df = 25 + 23 -2$

=>   $df = 46$

Generally from t distribution table the critical value of  $\alpha = 0.01$ for  a two-tailed test at a degree of freedom of  $df = 46$ is  

      $t_{0.01 , 46} = \pm 2.704$

Generally the pooled variance is mathematically represented as

     $s^2 = \frac{(n_1 - 1) s_1^2 + (n_2 - 1)s_2^2}{df}$

=>    $s^2 = \frac{(25 - 1) 9^2 + (23 - 1)8^2}{46}$

=>    $s^2 = 72.8696$

Generally the standard error is mathematically represented as

     $SE = s \sqrt{\frac{1}{n_1} + \frac{1}{n_2} }$

    $SE = \sqrt{s^2} * \sqrt{\frac{1}{n_1} + \frac{1}{n_2} }$

=>   $SE = \sqrt{72.8696} * \sqrt{\frac{1}{25} + \frac{1}{23} }$

=>    $SE = 2.4664$

Generally the  test statistics is mathematically represented as

     $t = \frac{\= x_ 1 - \= x_2}{SE }$

=>   $t = \frac{25.3 - 20.5}{ 2.4664 }$

=>   $t =1.95$

Answer 2

To test if bully-victims are more depressed, we have that:

• The null hypothesis is $H_0: \mu_B - \mu_{NB} = 0$
• The alternative hypothesis is: $\mu_M - \mu_{NB} < 0$

For our test, we consider that:

• The mean score of bully victims is given by: $\mu_B$.
• The mean score of non-bully victims is given by: $\mu_{NB}$

At the null hypothesis, we test that they have the same scores, that is:

$H_0: \mu_B = \mu_{NB}$

Which can also be written as:

$H_0: \mu_B - \mu_{NB} = 0$

At the alternative hypothesis, we test if the score of bully victims is less than the score of non-bully victims, that is:

$H_1: \mu_B < \mu_{NB}$

$H_1: \mu_B - \mu_{NB} < 0$

A similar problem is given at https://brainly.com/question/16252312