Hypothesis Test for a Population Proportion

In a certain school district, it was observed that 34% of the students in the element schools were classified as only children (no siblings). However, in the special program for talented and gifted children, 158 out of 415 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=0.010.01level 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.)

Based on the statement of this problem, how many tails would this hypothesis test have?

• one-tailed test
• two-tailed test

Choose the correct pair of hypotheses for this situation:

H0:p=0.34H0p0.34 Ha:p<0.34Hap0.34	H0:p=0.34H0p0.34 Ha:p0.34Hap0.34	H0:p=0.34H0p0.34 Ha:p>0.34Hap0.34
H0:p=0.381H0p0.381 Ha:p<0.381Hap0.381	H0:p=0.381H0p0.381 Ha:p0.381Hap0.381	H0:p=0.381H0p0.381 Ha:p>0.381Hap0.381

(A)

(B)

(C)

(D)

(E)

(F)

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.)

What is the P-value for this test?

P-value =

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

This P-value (and test statistic) leads to a decision to...

• reject the null hypothesis
• accept the null hypothesis
• fail to reject the null hypothesis
• reject the alternative hypothesis

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the assertion that there is a different proportion of only children in the G&T program.
• 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.
• The sample data support the assertion that there is a different proportion of only children in the G&T program.
• There is not sufficient evidence to support the assertion that there is a different proportion of only children in the G&T program.