Question

Which of the following is a simple hypothesis?

• A. The yield of paddy in India is distributed normally with mean yield 2.5 t/ha
• B. The yield of paddy in India is distributed normally with mean yield 2.5 t/ha and variance 15.6 (t/ha)\(^2\)
• C. The yield of paddy in India is distributed normally with variance in yield as 1.56 (t/ha)\(^2\)
• D. The yield of paddy in India is distributed normally with mean yield 2.5 t/ha and variance greater than 1.56 (t/ha)\(^2\)

Hint:

Exam Tip:
A simple hypothesis completely specifies the population distribution.
A composite hypothesis does not (it leaves some parameters unspecified or specifies a range).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A simple hypothesis is one that completely specifies the distribution of the population.
This means it specifies both the form (e.g., normal) and all the parameters (mean, variance, etc.) exactly.

Step 2: Analyzing the Options:

• (A) Specifies only the mean, not the variance.
The distribution is not completely specified. So, it is a composite hypothesis.
• (B) Specifies both the mean (2.5) and the variance (15.6) exactly.
The distribution is completely specified. So, it is a simple hypothesis.
• (C) Specifies only the variance, not the mean.
The distribution is not completely specified. So, it is a composite hypothesis.
• (D) Specifies the mean (2.5) and a range for the variance (greater than 1.56).
The variance is not specified exactly. So, it is a composite hypothesis.

Step 3: Final Answer:
Therefore, option (B) is correct.