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Is it true that the wider the confidence interval the less precise is the estimate?
All things being equal, a wider confidence interval (CI) implies a higher confidence. The higher confidence you want, the wider the CI gets. The lower confidence you want, the narrower the CI gets The point estimate will be the same, just the margin of error value changes based on the confidence you want. The formula for the CI is your point estimate +/- E or margin of error. The "E" formula contains a value for the confidence and the higher the confidence, the larger the value hence the wider the spread. In talking about the width of the CI, it is not correct to say more or less precise. You would state something like I am 95% confident that the CI contains the true value of the mean.
What else can I help you with?
What difference wider confidence interval and narrow confidence interval?
A wider confidence interval indicates greater uncertainty about the estimate, suggesting that the true parameter value could lie within a broader range. This often occurs with smaller sample sizes or higher variability in the data. In contrast, a narrow confidence interval reflects greater precision and confidence in the estimate, indicating that the true parameter is likely to be closer to the estimated value. Thus, the width of the confidence interval provides insight into the reliability of the estimate.
What relationship is Sample size and the confidence level width have a?
Sample size and confidence level width are inversely related. As the sample size increases, the width of the confidence interval decreases, resulting in a more precise estimate of the population parameter. Conversely, a smaller sample size leads to a wider confidence interval, reflecting greater uncertainty about the estimate. This relationship emphasizes the importance of an adequate sample size in achieving reliable statistical conclusions.
In the construction of confidence interval if all other quantities are unchanged an increase in the sample size will lead to a wider interval is this statement is true or false?
True
Is it true that the wider the interval in grouping scores the more information is lost?
yes
What is the difference in using mean and median for confidence intervals?
The mean is sensitive to outliers and skewed data, which can distort the confidence interval, making it wider or narrower than it should be. In contrast, the median is a robust measure of central tendency that is less affected by extreme values, providing a more reliable confidence interval in skewed distributions. Therefore, using the median can yield a more accurate representation of the data's central tendency when the dataset contains outliers. Choosing between mean and median depends on the data's distribution characteristics and the specific analysis requirements.
What happens to the confidence interval if you increase the confidence level?
The confidence interval becomes wider.
Is a 95 percent confidence interval for a mean wider than a 99 percent confidence interval?
No, it is not. A 99% confidence interval would be wider. Best regards, NS
When the confidence interval is wider than a prediction interval?
That, my friend, is not a question.
Is it true that the larger the standard deviation the wider the confidence interval?
no
Will The finite population correction factor lead to a wider confidence interval?
No since it is used to reduce the variance of an estimate in the case that the population is finite and we use a simple random sample.
What effect increasing only the population standard deviation will have on the width of the confidence interval?
It will make it wider.
What happens to the confidence interval as the standard deviation of a distribution increases?
The standard deviation is used in the numerator of the margin of error calculation. As the standard deviation increases, the margin of error increases; therefore the confidence interval width increases. So, the confidence interval gets wider.
In the construction of confidence interval if all other quantities are unchanged an increase in the sample size will lead to a wider interval is this statement is true or false?
True
In a poll of 100 adults 45 percent reported they believe in faith healing If the poll was based on 5000 adults would the confidence interval be wider or narrower?
The formula for margin of error is (Z*)*(Standard Deviation))/(sqrt(N)), so as N increases, the margin of error decreases. Here N went from 100 to 5000, so N has increased by 4900. This means the margin of error decreases. Since the confidence interval is the mean plus or minus the margin of error, a smaller margin of error means that the confidence interval is narrower.
Is it true that the wider the interval in grouping scores the more information is lost?
yes
What is the estimate population of Liverpool?
Liverpool has a population of 435,500, and lies at the centre of the wider Liverpool Urban Area, which has a population of 816,216.
What is a rule of thumb?
A rule of thumb is a broadly applicable guideline or principle based on practical experience rather than exact calculation. It is meant to provide a quick and easy way to estimate or make decisions without needing precise measurements or data.
