if the confidence interval is 24.4 to 38.0 than the average is the exact middle:
31.2, and the margin of error is 6.8
Increasing the sample size decreases the width of the confidence interval. This occurs because a larger sample provides more information about the population, leading to a more accurate estimate of the parameter. As the sample size increases, the standard error decreases, which results in a narrower interval around the sample estimate. Consequently, the confidence interval becomes more precise.
The confidence interval becomes smaller.
The width of the confidence interval increases.
When the sample size is doubled from 100 to 200, the width of the confidence interval generally decreases. This occurs because a larger sample size reduces the standard error, which is the variability of the sample mean. As the standard error decreases, the margin of error for the confidence interval also decreases, resulting in a narrower interval. Thus, a larger sample size leads to more precise estimates of the population parameter.
To decrease the width of a confidence interval without sacrificing the level of confidence, you can increase the sample size. A larger sample provides more information about the population, which reduces the standard error and narrows the interval. Additionally, using a more precise measurement technique can also help achieve a narrower interval. However, it's important to note that increasing the sample size is the most effective method for maintaining the desired confidence level while reducing width.
Never!
A confidence interval of x% is an interval such that there is an x% probability that the true population mean lies within the interval.
1.0966
It becomes narrower.
The Confidence Interval is a particular type of measurement that estimates a population's parameter. Usually, a confidence interval correlates with a percentage. The certain percentage represents how many of the same type of sample will include the true mean. Therefore, we would be a certain percent confident that the interval contains the true mean.
The confidence interval becomes smaller.
The mean plus or minus 2.576 (4/sqr.rt. 36)= 1.72 So take your average plus or minus 1.72 to get your confidence interval
No.
The width of the confidence interval increases.
The increase in sample size will reduce the confidence interval. The increase in standard deviation will increase the confidence interval. The confidence interval is not based on a linear function so the overall effect will require some calculations based on the levels before and after these changes. It would depend on the relative rates at which the change in sample size and change in standard deviation occurred. If the sample size increased more quickly than then standard deviation, in some sense, then the size of the confidence interval would decrease. Conversely, if the standard deviation increased more quickly than the sample size, in some sense, then the size of the confidence interval would increase.
In general, the confidence interval (CI) is reduced as the sample size is increased. See related link.
1) What conditions are required to form a valid large-sample confidence interval for µ?