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What are the alpha and the confidence level for a 90 percent confidence interval?
For a 90 percent confidence interval, the alpha (α) level is 0.10, which represents the total probability of making a Type I error. This means that there is a 10% chance that the true population parameter lies outside the interval. The confidence level of 90% indicates that if the same sampling procedure were repeated multiple times, approximately 90% of the constructed intervals would contain the true parameter.
What is the confidence interval for 85 percent?
it would be with a level of significance of 0.15.
What would happen to the width of the confidence interval if the level of confidence is lowered from 95 percent to 90 percent?
decrease
What combination of factors would definitely reduce the width of a confidence interval?
To reduce the width of a confidence interval, one can increase the sample size, as larger samples tend to provide more precise estimates of the population parameter. Additionally, using a lower confidence level (e.g., 90% instead of 95%) decreases the interval's width. Finally, reducing the variability in the data, such as by controlling for extraneous factors or using a more homogenous sample, can also lead to a narrower confidence interval.
Distinguish between the significance level and the confidence level?
The significance level, often denoted as alpha (α), is the probability of rejecting the null hypothesis when it is actually true, typically set at values like 0.05 or 0.01. In contrast, the confidence level refers to the percentage of times that a confidence interval would contain the true population parameter if the same sampling procedure were repeated multiple times, commonly expressed as 90%, 95%, or 99%. Essentially, the significance level relates to hypothesis testing, while the confidence level pertains to estimation through intervals. Both concepts are fundamental in inferential statistics but serve different purposes in data analysis.
What are the alpha and the confidence level for a 90 percent confidence interval?
For a 90 percent confidence interval, the alpha (α) level is 0.10, which represents the total probability of making a Type I error. This means that there is a 10% chance that the true population parameter lies outside the interval. The confidence level of 90% indicates that if the same sampling procedure were repeated multiple times, approximately 90% of the constructed intervals would contain the true parameter.
What is the confidence interval for 85 percent?
it would be with a level of significance of 0.15.
What would happen to the width of the confidence interval if the level of confidence is lowered from 95 percent to 90 percent?
decrease
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
What combination of factors would definitely reduce the width of a confidence interval?
To reduce the width of a confidence interval, one can increase the sample size, as larger samples tend to provide more precise estimates of the population parameter. Additionally, using a lower confidence level (e.g., 90% instead of 95%) decreases the interval's width. Finally, reducing the variability in the data, such as by controlling for extraneous factors or using a more homogenous sample, can also lead to a narrower confidence interval.
Does the population mean have to fall within the confidence interval?
No. For instance, when you calculate a 95% confidence interval for a parameter this should be taken to mean that, if you were to repeat the entire procedure of sampling from the population and calculating the confidence interval many times then the collection of confidence intervals would include the given parameter 95% of the time. And sometimes the confidence intervals would not include the given parameter.
Distinguish between the significance level and the confidence level?
The significance level, often denoted as alpha (α), is the probability of rejecting the null hypothesis when it is actually true, typically set at values like 0.05 or 0.01. In contrast, the confidence level refers to the percentage of times that a confidence interval would contain the true population parameter if the same sampling procedure were repeated multiple times, commonly expressed as 90%, 95%, or 99%. Essentially, the significance level relates to hypothesis testing, while the confidence level pertains to estimation through intervals. Both concepts are fundamental in inferential statistics but serve different purposes in data analysis.
What are the advantages of a small confidence interval in statistics?
The smaller the confidence interval, the more certain you are of the answers. Remember confidence level and confidence interval (margin of error) are 2 separate things. So if you are using an industry standard confidence level of 95% and 5% margin of error in a standard statistical table, then you could say, for example, with 95% certainty that 60% of those polled would vote for John McCain. Another way of saying this is even though you did not poll everyone (if you did, it would then become a very expensive census), you can say with a high degree of certainty (95% certainty) that 55% to 65% of those polled will vote for Johnny (sadly).
What happen to confidence interval if increase sample size and population standard deviation simultanesous?
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.
Confidence level and significance level?
I have always been careless about the use of the terms "significance level" and "confidence level", in the sense of whether I say I am using a 5% significance level or a 5% confidence level in a statistical test. I would use either one in conversation to mean that if the test were repeated 100 times, my best estimate would be that the test would wrongly reject the null hypothesis 5 times even if the null hypothesis were true. (On the other hand, a 95% confidence interval would be one which we'd expect to contain the true level with probability .95.) I see, though, that web definitions always would have me say that I reject the null at the 5% significance level or with a 95% confidence level. Dismayed, I tried looking up economics articles to see if my usage was entirely idiosyncratic. I found that I was half wrong. Searching over the American Economic Review for 1980-2003 for "5-percent confidence level" and similar terms, I found: 2 cases of 95-percent significance level 27 cases of 5% significance level 4 cases of 10% confidence level 6 cases of 90% confidence level Thus, the web definition is what economists use about 97% of the time for significance level, and about 60% of the time for confidence level. Moreover, most economists use "significance level" for tests, not "confidence level".
What is confidence intervals in statistics?
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.
What is a confidence interval in statistics?
When you calculate a statistic the result is not going to be perfectly accurate because of random errors in your observations. You therefore can give the result as one value along with a confidence interval (CI) around it. There are two interpretations of a CI. One interpretation is that you can be confident, with the stated level of confidence, that the true value of your statistic lies within the CI. The other interpretation is that if you repeated your experiment then, for the stated percentage of cases, the statistic would lie within the CI.
