Question

A nonprofit company concerned with the school dropout rates has designed a tutoring program aimed at students between 16 to 18 years old. A national center for educational statistics reported that the high school dropout rate for the year 2000 was 9.5​%. One school​ district, who adopted the use of the​ nonprofit's tutoring program and whose dropout rate has always been very close to the national​ average, reported in 2004 that 157 of their 1754 students dropped out. Is their experience evidence that the tutoring program has been​ effective?

A. Compute the test statistic.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.095

H_a : p 0.095

n = 1754

x = 157

= x / n = 157 / 1754 = 0.0895

P₀ = 0.095

1 - P₀ = 1 - 0.095 = 0.905

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.0895 - 0.905 / [(0.095 * 0.905) / 1754]

= -0.784

Test statistic = -0.784

P(z < -0.784) = 0.2165

P-value = 2 * 0.2165 = 0.433

= 0.05

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that  the tutoring program has been​ effective .