Answer to Question #295105 in Statistics and Probability for hash cake

Question

An achievement research was conducted to the Grade 10 students of Scott National High School. The researcher randomly selected twenty (20) Grade 10 students to take a diagnostic exam in Mathematics at the start of the school year. The same students took the achievement exam in Mathematics at the end of the school year. The scores of each exam where calculated and the mean differences of the two exams is 2.05 with a standard deviation of 2.84. Find the t-value.

Answer 1

We are given,

$\bar x_d=2.05\\s=2.84\\n=20$

The hypotheses tested are,

$H_0:\mu_d=0\\vs\\H_1:\mu_d\not=0$

The standard error is,

$SE={s\over\sqrt{n}}={2.84\over\sqrt{20}}=0.6350$

The t-value is given as,

$t_c={\bar x_d\over SE}={2.05\over0.6350}=3.2281$  

The table value is,

$t_{{0.05\over2},n-1}=t_{0.025,19}= 2.093024$

The null hypothesis is rejected if, $t_c\gt t_{0.025,19}$

$t_c=3.2281\gt t_{0.025,19}=2.093024$ hence we reject the null hypothesis and conclude that the difference in means for the two exams is significantly different at 5% level of significance.

The desired t-value is, $t_c=3.2281$