Question

The Institute of Educational Sciences published the results of the Trends in International Math and Science Study. In 2011, the mathematics scores for 8th-grade students from the United States and Hong Kong were reported, and the sample statistics are summarized in the table below:

	n	x	s
United States	10	509	80
Hong Kong	12	586	70

Determine whether the math scores for the United States students are lower than the scores of the Hong Kong students. Use a level of significance of 0.01. Assume that both samples come from populations with Normal distributions.

Answer 1

Answer)

Null hypothesis Ho : u1 - u2 = 0

Alternate hypothesis Ha : u1 - u2 < 0

Test statistics is = (x1-x2)/(standard error).

Standard error = √{(s1^2/n1)+(s2^2/n2)}

X1 = 509, X2 = 586

N1 = 10, N2 = 12

S1 = 80, S2 = 70

After substitution.

Test statistics t = -2.378

As the population s.d is not given and we are using sample s.d as the best estimate, we will use t distribution table to estimate the p-value.

Degrees of freedom is = smaller of n1-1, n2-1 = 9

For 9 dof and -2.378 test statistics, P-value from t distribution is = 0.020682

As the obtained p-value is greater than the given significance 0.01.

We fail to reject the null hypothesis Ho

We do not have enough evidence to support the claim that the math scores for the United States students are lower than the scores of the Hong Kong students.