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, 78 out of 215 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=0.01α=0.01 level of significance.
What is the hypothesized population proportion for this test?
(Report answer as a decimal accurate to 2 decimal places. Do not report using the percent symbol.)
Based on the statement of this problem, how many tails would this hypothesis test have?
Choose the correct pair of hypotheses for this situation:
Using the normal approximation for the binomial distribution (without the continuity correction), was is the test statistic for this sample based on the sample proportion?
(Report answer as a decimal accurate to 3 decimal places.)
You are now ready to calculate the P-value for this sample.
(Report answer as a decimal accurate to 4 decimal places.)
This P-value (and test statistic) leads to a decision to...
As such, the final conclusion is that...
PLEASE SHOW WORK! THANK YOU!!
This is the two tailed test .
The null and alternative hypothesis is
H0 : p = 0.31
Ha : p 0.31
n = 215
x = 78
= x / n = 78 /215 = 0.36
P0 = 0.31
1 - P0 = 1 - 0.31 =0.69
Test statistic = z
= - P0 / [P0 * (1 - P0 ) / n]
= 0.36 - 0.31/ [0.31 *0.69 / 215 ]
Test statistic = z = 1.674
P-value = 0.0942
0.0942 ≥ 0.01
Fail to reject the null hypothesis .
There is not sufficient evidence to warrant rejection of the assertion that there is a different proportion of only children in the G&T program
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