CAS Exam MAS-I Spring 2018, Question 20

Study guide: Exam MAS-I

You are given the following information:

• A random variable X follows a gamma distribution with parameters \alpha = 0.6 and unknown \theta.
• Null hypothesis is H_0: \theta = 2000
• Alternative hypothesis is H_1: \theta > 2000
• n values of X will be observed and the null hypothesis is rejected if:

\frac{1}{n}\sum_{i=1}^{n} X_i > 1500

Calculate the minimum value of n which will result in a probability of Type I error of less than 2.5%, using the normal approximation.

• A) Less than 100
• B) At least 100, but less than 105
• C) At least 105, but less than 110
• D) At least 110, but less than 115
• E) At least 115

Answer this question and see the worked solution

Concepts tested

• Type I Error
• Hypothesis Testing
• Gamma
• Central Limit Theorem

More questions from this set

• CAS Exam MAS-I Spring 2018, Question 19
• CAS Exam MAS-I Spring 2018, Question 21