Answer :
Answer:
The test statistic for the researcher's hypothesis is 1.976
Step-by-step explanation:
The standard error (SE) is,
[tex]SE=\sqrt{\frac{S_1^2}{n_1}+\frac{S_2^2}{n_2} }[/tex]
Given that,
[tex]\bar x = 22.30,S_1=3.20\\\\\bar x=17.30,S_2=9,60\\\\n_1=16,n_2=16[/tex]
[tex]SE =\sqrt{\frac{(3.20)^2}{16} +\frac{(9.60)^2}{16} } \\\\=\sqrt{(0.64+5.76)} \\\\=2.53[/tex]
The test statistic is obtained below:
[tex]t=\frac{( \bar x_1 - \bar x_2)}{\sqrt{\frac{S_1^2}{n_1} +\frac{S_2^2}{n_2} } }[/tex]
[tex]=\frac{(22.30-17.30)}{2.53} \\\\=\frac{5}{2.53} \\\\=1.976[/tex]
Therefore, the test statistic for the researcher's hypothesis is 1.976
The test statistics for the researcher's hypothesis will be "1.976".
According to the given question,
- [tex]\bar x_1 = 22.30[/tex], [tex]\bar x = 17.30[/tex]
- [tex]S_1 = 3.20[/tex], [tex]S_2 = 9.60[/tex]
- [tex]n_1 = 16[/tex], [tex]n_2 = 16[/tex]
The standard error will be:
→ [tex]S.E = \sqrt{\frac{S_1^2}{n_1}+\frac{S_2^2}{n_2} }[/tex]
By putting the values, we get
[tex]= \sqrt{0.64+5.76}[/tex]
[tex]= 2.53[/tex]
hence,
The test statistic will be:
→ [tex]t = \frac{(\bar x_1 - \bar x_2)}{\sqrt{\frac{S_1^2}{n_1} +\frac{S_2^2}{n_2} } }[/tex]
[tex]= \frac{22.30-17.30}{2.53}[/tex]
[tex]= \frac{2}{2.53}[/tex]
[tex]= 1.976[/tex]
Thus the above answer is correct.
Learn more about psychological researcher here:
https://brainly.com/question/13100685