Answer:
There is significant statistical evidence to suggest there is a difference between the groups
Step-by-step explanation:
The number of adolescents in the sample that were given a pamphlet, n₁ = 10
The average score of those given a pamphlet,
= 51
s₁² = 16
The number of adolescents in the sample that were given a video, n₂ = 10
The average score of those given a video,
= 46
s₂² = 20
The alpha level of the test, α = 0.05
H₀ = No difference
Hₐ = Difference between the groups
The test statistic for the difference in mean is given as follows;
![t=\dfrac{(\bar{x}_1-\bar{x}_{2})}{\sqrt{\dfrac{s_{p}^{2} }{n_{1}}+\dfrac{s _{p}^{2}}{n_{2}}}}](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7B%28%5Cbar%7Bx%7D_1-%5Cbar%7Bx%7D_%7B2%7D%29%7D%7B%5Csqrt%7B%5Cdfrac%7Bs_%7Bp%7D%5E%7B2%7D%20%7D%7Bn_%7B1%7D%7D%2B%5Cdfrac%7Bs%20_%7Bp%7D%5E%7B2%7D%7D%7Bn_%7B2%7D%7D%7D%7D)
Plugging in the values, gives;
![t=\dfrac{(46-55)}{\sqrt{\dfrac{18 }{10}+\dfrac{18}{10}}} \approx -4.73](https://tex.z-dn.net/?f=t%3D%5Cdfrac%7B%2846-55%29%7D%7B%5Csqrt%7B%5Cdfrac%7B18%20%7D%7B10%7D%2B%5Cdfrac%7B18%7D%7B10%7D%7D%7D%20%20%5Capprox%20-4.73)
The degrees of freedom, n₁ + n₂ - 2 = 20 - 2 = 18
The critical-t = 2.101
Therefore
Given that the test statistic is larger than than the critical-t, we reject the null hypothesis that there is no difference