Answer to Question #91130 in Statistics and Probability for john paul

Question

17 students in a class are assigned to a new method of teaching science. after 6 hours in the classroom, they are given a test assessing their knowledge of basic science concepts to see if their teaching has been effective. the results is mean =84, standard deviation=16 and N=17.previously the students in that class had a mean of 78 on this exam(N=78). is the difference after 6 weeks of instruction consistent with what is likely under conditions of chance above or does it likely reflect a difference?

Answer 1

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

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

Test statistic: $t=\frac{84-78}{\frac{16}{\sqrt{17}}}=1.55.$

P-value: $p=0.1407.$

Since the P-value is greater than 0.05, fail to reject the null hypothesis. The difference after 6 weeks of instruction is consistent with what is likely under conditions of chance above.