Let u denote the average score on a standardized test for al

Let u denote the average score on a standardized test for all children in a certain region of the United States. The average score for all children in the United States is 100. Regional education authorities are interested in testing to see if children in the region score higher on average on this standardized test than children in general in the US. A sample of 2500 children in the region resulted in a sample mean of 101.0 with standard deviation 15.0.

(a) State the most appropriate null and alternative hypotheses for this test.

(b) Use Minitab to compute the test statistic and p-value associated with the test

(c) State the conclusion of the test.

(d) Discuss the practical significance of a sample mean of 101 as an indicator that the children in the region score better on this test than children in general in the US.

Solution

a) Test of mu = 100 vs > 100

b) N Mean StDev SE Mean 95% CI T P
2500 101.000 15.000 0.300 (100.412, 101.588) 3.33 0.001

c) as p-value < 0.05 so we rejects H0

d) the mean of population should be lager than 100