Respuesta :
The true statement is option (a) If the sample size is bigger, the interval is narrower.
Given:
for a given confidence level and population or sample standard deviation the following is true in the interval estimation of the population mean.
In a confidence interval, to find the standard error we divide the standard deviation by the sample size. When the sample size is large the value of standard error decreases. When the value of standard error decreases the width of the confidence interval also decreases. Therefore we can say If the sample size is bigger, the interval is narrower.
that is,
error α standard deviation / sample size
Here when sample size is large the error decreases because both are inversely proportional when error decreases the standard deviation or confidence intervals decrease because both are directly proportional.'
Therefore The true statement is option(a) If the sample size is bigger, the interval is narrower.
Learn more about the population mean here:
https://brainly.com/question/19538277
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Full question:
For a given confidence level and population standard deviation, which of the following is true in the interval estimation of the population mean?
(a) If the sample size is bigger, the interval is narrower.
(b) If the sample size is smaller, the interval is narrower.
(c) If the population size is bigger, the interval is narrower.
(d) If the population size is smaller, the interval is narrower.
