# A foundation that provides fun

A foundation that provides funding to the Metro City TeenPregnancy Prevention Coalitions (TPPC) has asked the organizationto start collecting program outcomes data. Specifically, thefoundation would like to know if the pregnancy rate for teen girlswho participate in the educational programing at TPPC issignificantly lower than the citywide average (currently 21%). Thedirector of TPPC collects data for a random sample of girls whocompleted the Coalitions programming and finds that 8 out of 65clients contacted went on to become pregnant. Should the directorbe concerned about presenting their findings to the foundation?

Solution:

Given: the foundation would like to know if the pregnancy ratefor teen girls who participate in the educational programing atTPPC is significantly lower than the citywide average (currently21%).

That is we have to test if proportion the pregnancy rate forteen girls who participate in the educational programing at TPPC issignificantly 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 andcontacted 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 ofsignificance =

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

Area 0.0500 is in between 0.0495 and 0.0505 and both the areaare 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 Zcritical = -1.645

Step 4) Decision rule:

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

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

Step 5) Conclusion:

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

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

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