Question

Assume that I am conducting an experiment that involves a task that is very difficult for

subjects. My graduate assistants tell me that overall, they have to throw out 25% of the subjects

they run because the subjects never complete the task (call this the status quo or null hypothesis).

Now ...a new assistant just ran 10 subjects and had to throw out 7 of the 10. Test the hypothesis

that this assistant is from the group from which the average "throw out rate" was 25%, against

the alternative hypothesis that this assistant's throw out rate was significantly greater than 25%.

Answer 1

H0: Null Hypothesis: P = 0.05

HA: Alternative Hypothesis: P > 0.25

n = Sample Size =10

p = Sample Proportion = 7/10 = 0.7

P = Population Proportion = 0.25

Q = 1 - p = 0.75

SE=$\sqrt{PQ/n}=\sqrt{0.25\times 0.75/10}=0.1369$

Test statistic is given by:

Z = (0.7 - 0.25)/0.1369

= 3.2871

Take $\alpha$ = 0.05

One Tail - Right Side Test

From Table, critical value of Z = 1.645

Since calculated value of Z = 3.2871 is greater than critical value of Z = 1.645, the difference is significant. Reject null hypothesis.

Conclusion:
The data support that claim that this assistant's throw out rate was significantly greater than 25%.