Which of the following will decrease the width of a confidence interval
Increase the sample sizeOften, the most practical way to decrease the margin of error is to increase the sample size. Usually, the more observations that you have, the narrower the interval around the sample statistic is. Thus, you can often collect more data to obtain a more precise estimate of a population parameter. Show
You should weigh the benefits of increased precision with the additional time and resources required to collect a larger sample. For example, a confidence interval that is narrow enough to contain only the population parameter requires that you measure every subject in the population. Obviously, such a strategy would usually be highly impractical. Reduce variabilityThe less that your data varies, the more precisely you can estimate a population parameter. That's because reducing the variability of your data decreases the standard deviation and, thus, the margin of error for the estimate. Although it can be difficult to reduce variability in your data, you can sometimes do so by adjusting how you collect data. For example, you can use a paired design to compare two groups. You may also be able to reduce variability by improving the process so that the process is more consistent or by measuring more precisely. Use a one-sided confidence intervalA one-sided confidence interval has a smaller margin of error than a two-sided confidence interval. However, a one-sided interval indicates only whether a parameter is either less than or greater than a cut-off value. A one-sided interval does not provide any information about the parameter in the opposite direction. Thus, use a one-sided confidence interval to increase the precision of an estimate only when you are worried about the estimate being either greater or less than a cut-off value, but not both. For example, a beverage company wants to determine that the amount of dissolved solids in their drinking water. The fewer dissolved solids they have, the better. When they calculate a two-sided confidence interval, the upper side of the interval is 18.4. However, because the company only cares about the upper bound, they can calculate a one-sided confidence interval instead. The one-sided confidence interval shows that the upper bound for the amount of dissolved solids is even lower, 17.8 mg/L. Lower the confidence levelThe advantage of a lower confidence level is that you get a narrower, more precise confidence interval. The disadvantage is that you have less confidence that the confidence interval contains the population parameter you are interested in. So lower the confidence level only if, in your situation, the advantage of more precision is greater than the disadvantage of less confidence. For example, if it's too expensive to increase the sample size in your study, lowering the confidence level will shorten the length of the interval at the expense of losing some confidence. Remember that there is variability associated with your outcomes and statistics. When you calculate a statistic based on your sample data, how do you know if the statistic truly represents your population? Even if you've selected a random sample, your sample will not completely reflect your population. Each sample you take will give you a different result. Let's Look at an Example:Suppose that you want to compare the mean age for those with and without an IV in the prehospital setting. You review the ambulance runs for the past two weeks and calculate a mean age of 10.4 years for those with an IV and 8.5 years for those without an IV. The difference between the two means is 1.9 years. From this, you might conclude that those receiving an IV were older on average. Suddenly, it's not clear that there's an important difference in age between these two groups. Now suppose you collect the same data over the next six weeks. This time the average age for those with an IV is 9.2 years and the average age for those without an IV is 8.9 years, for a difference of 0.3 years. Suddenly, it's not clear that there's an important difference in age between these two groups. Why did your different samples yield different results? Is one sample more correct than the other? Remember that there is variability in your outcomes and statistics. The more individual variation you see in your outcome, the less confidence you have in your statistics. In addition, the smaller your sample size, the less comfortable you can be asserting that the statistics you calculate are representative of your population. Providing a Range of ValuesA confidence interval provides a range of values that will capture the true population value a certain percentage of the time. You determine the level of confidence, but it is generally set at 90%, 95%, or 99%. Confidence intervals use the variability of your data to assess the precision or accuracy of your estimated statistics. You can use confidence intervals to describe a single group or to compare two groups. We will not cover the statistical equations for a confidence interval here, but we will discuss several examples. Example The confidence interval in the above example could be described at 94 to 108 bpm (beats per minute) or 101 bpm ± 7 bpm. Here the number 7 is your margin of error. For confidence intervals around the mean, the margin of error is just half of your total confidence interval width. Sample Size and VariabilityThe precision of your statistics depends on your sample size and variability. A larger sample size or lower variability will result in a tighter confidence interval with a smaller margin of error. A smaller sample size or a higher variability will result in a wider confidence interval with a larger margin of error. The level of confidence also affects the interval width. If you want a higher level of confidence, that interval will not be as tight. A tight interval at 95% or higher confidence is ideal. Examples: rev. 04-Aug-2022 What would decrease the width of the interval?As we increase the sample size, the width of the interval decreases.
What factors affect the width of a confidence interval?There are three factors that determine the size of the confidence interval for a given confidence level. These are: sample size, percentage and population size. The larger your sample, the more sure you can be that their answers truly reflect the population.
Which of the following will decrease the width of a confidence interval for a population proportion P?You can decrease the width of a confidence interval by a. lowering the confidence level or increasing the sample size. The width of the confidence interval is decided by the margin of error.
Which of the following would increase the width of the confidence interval?The width increases as the standard deviation increases. The width increases as the confidence level increases (0.5 towards 0.99999 - stronger). The width increases as the significance level decreases (0.5 towards 0.00000... 01 - stronger).
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