Question

Hedge fund directors understand there is a certain amount of irrational behavior in the stock market. One such director believes a tipping point in irrational behavior is reached when the percentage of people who believe the current market is fairly valued differs from 65%. In a sample of 100 people, 60% answered "yes" to the market being fairly valued. Has a tipping point been reached? Assume the allowed amount for a Type 1 error is 5%.

Question 25 options:

a)	No because |ztest| < |zcrit|

b)	No because |ztest| > |zcrit|

c)	Yes because |ztest| < |zcrit|

d)	Yes because |ztest| > |zcrit|

Answer 1

As we are testing here whether the proportion varies significantly from 0.65, therefore this is a case of two tailed test. For 0.05 level of significance, we have from the standard normal tables here:
P( -1.96 < Z < 1.96) = 0.95

Therefore the critical values here are given as: -1.96, 1.96

Therefore, |Zcrit | = 1.96

The test statistic here is computed as:

As the test statistic value here is -1.0483 > -1.96 and -1.0483 < 1.96, therefore it lies in the non rejection region and therefore we cannot reject the null hypothesis here.

Therefore No because |ztest| < |zcrit| is the correct answer here. Therefore A is the correct answer here.