A variable of a population has a normal distribution. Suppose that you want to find a confidence interval for the population mean. a. If you know the population standard deviation, which procedure would you use? b. If you do not know the population standard deviation, which procedure would you use?
Lokubovumn
Answered question
2022-08-09
a. If you know the population standard deviation, which procedure would you use?
b. If you do not know the population standard deviation, which procedure would you use?
Answer & Explanation
Ayla Coffey
Beginner2022-08-10Added 8 answers
Requirements for a large sample confidence interval about mean:
The sample must be drawn using simple random sampling.
The population standard deviation must be known.
Either the population must be approximately normal or the sample size must be greater than 30.
Thus, the requirements must be satisfied for the confidence interval about mean using standard normal distribution to be valid.
Here, the population standard deviation is known.
Thus, the one-mean z-interval procedure can be used to construct confidence interval about mean in case of known population standard deviation.
b. Following assumptions are required for the small sample confidence interval about mean to be valid.
Requirements for a small sample confidence interval about mean:
The sample must be drawn using simple random sampling.
The population standard deviation must be unknown.
Either the population must be approximately normal or the sample size must be greater than 30.
Thus, the requirements must be satisfied for the confidence interval about mean using t-distribution to be valid.
Here, the population standard deviation is unknown.
Thus, the one-mean t-interval procedure can be used to construct confidence interval about mean in case of unknown population standard deviation.
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