In a certain school district, it was observed that 31% of the students in the element schools were classified as only children (no siblings). However, in the special program for talented and gifted...

In a certain school district, it was observed that 31% of the students in the element schools were classified as only children (no siblings).  However, in the special program for talented and gifted children, 142 out of 412 students are only children.  The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. Test at the α=0.02α=0.02 level of significance.


What is the hypothesized population proportion for this test?
p=p=

(Report answer as a decimal accurate to 2 decimal places.  Do not report using the percent symbol.)



Using the normal approximation for the binomial distribution (without the continuity correction), what is the test statistic for this sample based on the sample proportion?
z=z=

(Report answer as a decimal accurate to 3 decimal places.)



You are now ready to calculate the P-value for this sample.
P-value =

(Report answer as a decimal accurate to 4 decimal places.)