Question

In: Statistics and Probability

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

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.

Expert Solution

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.

orchestra answered 1 year ago

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