Question

Tomorrow’s highest temperature can be lower than, higher than or the same as today’s highest temperature. After evaluating all the relevant information available, a weather forecaster has determined that the probability that tomorrow’s highest temperature will be higher than today’s is determined to be 65%. This is an example of using which of the following probability approach?

Select one:

A. Priori probability

B. Empirical probability

C. Subjective probability

D. Conditional probability

Because of the outbreak of the coronavirus, students of UM are allowed to opt for Pass/Fail grade for courses they enroll in the second semester of 2019/2020. An instructor of ISOM2002 believes that there will be more than 35% of the students in the course choosing this option. A random sample of 40 students of ISOM2002 reveals that 16 of them prefer to take the Pass/Fail option. At 5% level of significance, what would be the rejection rule if we want to test the instructor’s belief?

Select one:

A. Reject H₀ if t_STAT < –1.6849.

B. Reject H₀ if Z_STAT < –1.645.

C. Reject H₀ if Z_STAT > +1.645.

D. Reject H₀ if t_STAT > +1.6849.

Answer 1

Given:

1) Tomorrow’s highest temperature can be lower than, higher than or the same as today’s highest temperature.

After evaluating all the relevant information available, a weather forecaster has determined that the probability that tomorrow’s highest temperature will be higher than today’s is 65%.

This is an example of conditional probability.

Explanation:

The conditional probability of an event B is the probability that the event will occur given the knowledge that an event A has already occurred.

So answer is option D i.e, conditional probability.

2) An instructor of ISOM2002 believes that there will be more than 35% of the students in the course choosing this option.

So the hypothesis test is

Null hypothesis, H0 : p = 0.35

Alternative hypothesis, Ha : p > 0.35

n = 40, X = 16,  

Significance level, = 0.05

At 0.05 significance level the critical value of Z for right tailed is

Z/2 = Z0.05/2 = + 1.645

Rejection rule :

We reject null hypothesis if observed test statistics is greater than Z/2 i.e,

Zstatistics > Z/2

Reject H0 if ZSTAT > +1.645

Therefore C is the correct option.