Question

7.

You wish to test the following at a significance level of α=0.05α=0.05.

      H0:p=0.85H0:p=0.85
      H1:p>0.85H1:p>0.85

You obtain a sample of size n=250n=250 in which there are 225 successful observations.

For this test, we use the normal distribution as an approximation for the binomial distribution.

For this sample...

1. The test statistic (zz) for the data =  (Please show your answer to three decimal places.)
2. The p-value for the sample =  (Please show your answer to four decimal places.)
3. The p-value is...
   • greater than αα
   • less than (or equal to) αα
4. Base on this, we should...
   • fail to reject the null hypothesis
   • accept the null hypothesis
   • reject the null hypothesis
5. As such, the final conclusion is that...
   • The sample data suggest that the population proportion is significantly greater than 0.85 at the significant level of αα = 0.05.
   • The sample data suggest that the population proportion is not significantly greater than 0.85 at the significant level of αα = 0.05

10.

In a certain school district, it was observed that 24% of the students in the element schools were classified as only children (no siblings). However, in the special program for talented and gifted children, 72 out of 236 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.)

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:

(A)	(B)	(C)
H0:p=0.24H0:p=0.24 Ha:p<0.24Ha:p<0.24	H0:p=0.24H0:p=0.24 Ha:p≠0.24Ha:p≠0.24	H0:p=0.24H0:p=0.24 Ha:p>0.24Ha:p>0.24
(D)	(E)	(F)
H0:p=0.305H0:p=0.305 Ha:p<0.305Ha:p<0.305	H0:p=0.305H0:p=0.305 Ha:p≠0.305Ha:p≠0.305	H0:p=0.305H0:p=0.305 Ha:p>0.305Ha:p>0.305

(A)

(B)

(C)

(D)

(E)

(F)

Using the normal approximation for the binomial distribution (without the continuity correction), what is the test statistic (z-score) 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.)

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

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

As such, the final conclusion is that...

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

Answer 1