Question

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, 82 out of 207 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 a = 0.05 level of significance. What is the hypothesized population proportion for this test? р (Report answer as a decimal accurate to 2 decimal places. Do not report using the percent symbol.)

Answer 1

0 Test of hypothesis Ho. The proportion of student is 31% it. Ho: P=0.31 versus may H: The proportion of student is not 31-). it. Hi P70.31 @ The test statistics used is z = P-Po NCOID for large Teodo, ② where p = proportion of certain type of items in population n = sample size 207 x = number of iterns of a certain type in a sample of sizen P Proportion of certain type of items in sample. - 82/207 0.3981=ouso Po = specified Value of P=0.31 82 h P-po 0.40-0.31 Pogo 16.318 0.69 207 o.og = 40.gogo 0.0022 Z table=2207,0.05 Decision Rule: If Ecal 72 table then reject Ho at at Lo.s. Zcal = 40.90 > Ztable =0 herie reject Ho at 511-os. conclusion: The proportion of student may not be 31% 3

4 p-value = p [ z < 40.90] =0 Decision: If P-value <a=bios then reject Ho out 2-1. L-o's. Here, p-value =022=0.05 , hence we reject Ho at 5.1.2.0.5' conclusion - The proportion of student may not be 0-31