Question

At Rio Salado College, it was observed that 26% of the students were still classified as dependents on their parents. However, in the honors program for students, 70 out of 222 students are dependents. The administrators want to know if the proportion of dependent students in the honors program is significantly different from the proportion for the school district. Test at the α=.05 level of significance.

What is the hypothesized population proportion for this test?
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=0.26

Ha:p<0.26
   H0:p=0.26

Ha:p≠0.26
   H0:p=0.26

Ha:p>0.26

(D)   (E)   (F)
H0:p=0.315

Ha:p<0.315
   H0:p=0.315

Ha:p≠0.315
   H0:p=0.315

Ha:p>0.315
(A)
(B)
(C)
(D)
(E)
(F)

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?
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...

There is sufficient evidence to warrant rejection of the assertion that there is a different proportion of dependent students in the honors program.
There is not sufficient evidence to warrant rejection of the assertion that there is a different proportion of dependent sudents in the honors program.
The sample data support the assertion that there is a different proportion of dependent sudents in the honors program.
There is not sufficient sample evidence to support the assertion that there is a different proportion of dependent sudents in the honors program.

Answer 1

hypothesized population proportion for this test,p =0.26

Ho :   p =    0.26                  
H1 :   p ╪   0.26      

(Two tail test)          

----------------

                          
Level of Significance,   α =    0.05                  
Number of Items of Interest,   x =   70                  
Sample Size,   n =    222                  
                          
Sample Proportion ,    p̂ = x/n =    0.3153                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0294                  
Z Test Statistic = ( p̂-p)/SE = (   0.3153   -   0.26   ) /   0.0294   =   1.879

                          
  
p-Value   =   0.0602 [excel formula =2*NORMSDIST(z)]              
Decision:   p value>α ,fail to reject the null

There is not sufficient sample evidence to support the assertion that there is a different proportion of dependent sudents in the honors program.