6. What eect does increasing the sample size have on the size of a confidence interval? Explain. (1 point)
Increasing the sample size decreases the size of the confidence interval. Increasing the sample size means
multiplying by a smaller z-score when calculating the margin of error. This reduces the margin of error,
which decreases the size of the confidence interval.
Increasing the sample size increases the size of the confidence interval. Increasing the sample size means
dividing by a smaller number when calculating the margin of error. This increases the margin of error,
which increases the size of the confidence interval.
Increasing the sample size increases the size of the confidence interval. Increasing the sample size means
multiplying by a larger z-score when calculating the margin of error. This increases the margin of error,
which increases the size of the confidence interval.
Increasing the sample size decreases the size of the confidence interval. Increasing the sample size means
dividing by a larger number when calculating the margin of error. This reduces the margin of error, which
decreases the size of the confidence interval.
Increasing the sample size decreases the size of the confidence interval. This is because a larger sample size reduces the variability in the data and provides a more accurate estimate of the population parameter. As a result, there is less uncertainty in the estimate and a smaller margin of error is needed to construct the confidence interval. Therefore, the confidence interval becomes narrower and more precise as the sample size increases.
Increasing the sample size decreases the size of the confidence interval. Increasing the sample size means multiplying by a smaller z-score when calculating the margin of error. This reduces the margin of error, which decreases the size of the confidence interval.
Increasing the sample size decreases the size of the confidence interval. This is because a larger sample size provides more data and thus reduces the uncertainty in estimating the population parameter.
To understand why increasing the sample size reduces the size of the confidence interval, we need to consider the formula for calculating the margin of error. The margin of error is the range within which we estimate the population parameter to fall.
In general, the formula for calculating the margin of error is given by:
Margin of Error = z-score * (standard deviation / square root of sample size)
The z-score is determined by the desired level of confidence, and it represents the number of standard deviations away from the mean the z-value lies.
When we increase the sample size, the denominator in the formula for the margin of error (square root of sample size) increases. Since division by a larger number reduces the overall value, the margin of error decreases. Therefore, the range of the confidence interval becomes smaller, resulting in a smaller confidence interval.
To summarize, increasing the sample size decreases the size of the confidence interval because it reduces the margin of error, which is determined by dividing by the square root of the sample size.