Question

A foundation that provides funding to the Metro City Teen Pregnancy Prevention Coalitions (TPPC) has asked the organization to start collecting program outcomes data. Specifically, the foundation would like to know if the pregnancy rate for teen girls who participate in the educational programing at TPPC is significantly lower than the citywide average (currently 21%). The director of TPPC collects data for a random sample of girls who completed the Coalitions programming and finds that 8 out of 65 clients contacted went on to become pregnant. Should the director be concerned about presenting their findings to the foundation?

Answer 1

Solution:

Given: the foundation would like to know if the pregnancy rate for teen girls who participate in the educational programing at TPPC is significantly lower than the citywide average (currently 21%).

That is we have to test if proportion the pregnancy rate for teen girls who participate in the educational programing at TPPC is significantly lower than the citywide average (currently 21%).

That is: p < 0.21

Sample size = n = 65

x = number of girls who completed the Coalitions programming and contacted went on to become pregnant = 8

Thus sample proportion:

Thus we use following steps:

Step 1) State H0 and H1:

H0: p = 0.21           Vs       H1: p < 0.21

Step 2) Find test statistic

We use z test statistic for proportion.

Step 3) z test statistic value:

Since level of significance is not given, we use level of significance =

Thus look in z table for Area = 0.0500 or its closest area and find z value

Area 0.0500 is in between 0.0495 and 0.0505 and both the area are at same distance from 0.0500

Thus we look for both area and find both z values

Thus Area 0.0495 corresponds to -1.65 and 0.0505 corresponds to -1.64

Thus average of both z values is : ( -1.64+ - 1.65) / 2 = -1.645

Thus Z_critical = -1.645

Step 4) Decision rule:

Reject H0, if z test statistic value < Z_critical = -1.645, otherwise we fail to reject H0.

Since z test statistic value = -1.72 < Z_critical = -1.645, we reject H0.

Step 5) Conclusion:

Since we have rejected H0, we conclude that: the pregnancy rate for teen girls who participate in the educational programing at TPPC is significantly lower than the citywide average ( that is: p < 21%).

Since the director has proved that the pregnancy rate for teen girls who participate in the educational programing at TPPC is significantly lower than the citywide average ( that is: p < 21%), the director should not be concerned about presenting their findings to the foundation.