In year 2009 1311 of a random sample of 1900 eighthgraders f

In year 2009, 1311 of a random sample of 1900 eighth-graders from Houston performed at or above the basic level in mathematics. In year 2011, 1440 of a random sample of 2000 eighth-graders from Houston performed at or above the basic level. Are there changes in the proportion of eighth-graders who performed at or above the basic level in mathematics from 2009 to 2011? Compute the pc. the pooled (or say, combined) proportion. Perform hypothesis testing regarding the problem.

Solution

A) Pooled sample proportion. Since the null hypothesis states that P₁=P₂, we use a pooled sample proportion (p) to compute the standard error of the sampling distribution.

p = (p₁ * n₁ + p₂ * n₂) / (n₁ + n₂)

so after computing we get 0.70564

B)

Sample X N Sample p
1 1311 1900 0.690000
2 1441 2000 0.720500

Difference = p (1) - p (2)
Estimate for difference: -0.0305
95% CI for difference: (-0.0591228, -0.00187722)
Test for difference = 0 (vs not = 0): Z = -2.09 P-Value = 0.037