Question

17 students after 6 weeks mean is 84, SD= 16 N=17. Previous mean=78. Is difference consistent

Answer 1

One sample t-test.

Null hypothesis $H_0:\;\mu=78$

Alternative hypothesis $H_a:\;\mu\neq78$

Test statistic: $t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}=\frac{84-78}{\frac{16}{\sqrt{17}}}=1.55$

Degrees of freedom: $df=n-1=17-1=16$

P-value: $p=0.1407$

Since the P-value is greater than 0.05, fail to reject the null hypothesis.

The difference is not consistent..