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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.
When the population is normally distributed population standard deviation s is unknown and the sample size is n equals 15 the confidence interval for the population mean s is based on the?
The Z test.
What does a 95 percent confidence interval tell you about the population proportion?
There is a 95% probability that the true population proportion lies within the confidence interval.
If the standard deviation is doubled what will be the effect on the confidence interval?
The confidence intervals will increase. How much it will increase depends on whether the underlying probability model is additive or multiplicative.
When comparing the 95 percent confidence and prediction intervals for a given regression analysis what is the relation between confidence and prediction interval?
Confidence interval considers the entire data series to fix the band width with mean and standard deviation considers the present data where as prediction interval is for independent value and for future values.
What effect increasing only the population standard deviation will have on the width of the confidence interval?
It will make it wider.
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.
When the sample size and sample standard deviation remain the same a 99 percent confidence interval for a population mean will be narrower than the 95 percent confidence interval for the mean?
Never!
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.
When population distribution is right skewed is the interval still valid?
You probably mean the confidence interval. When you construct a confidence interval it has a percentage coverage that is based on assumptions about the population distribution. If the population distribution is skewed there is reason to believe that (a) the statistics upon which the interval are based (namely the mean and standard deviation) might well be biased, and (b) the confidence interval will not accurately cover the population value as accurately or symmetrically as expected.
Is it true that the larger the standard deviation the wider the confidence interval?
no
How do you calculate Margin of error of a confidence interval?
The margin of error (MOE) for a confidence interval is calculated using the formula: MOE = z * (σ/√n), where z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size. If the population standard deviation is unknown, the sample standard deviation (s) can be used instead. The resulting MOE indicates the range within which the true population parameter is likely to fall, based on the sample data.
When the population is normally distributed population standard deviation s is unknown and the sample size is n equals 15 the confidence interval for the population mean s is based on the?
The Z test.
What happens to the confidence interval as the standard deviation of a distribution decreases?
It goes up.
When to t test z test t interval z interval etc?
Use a t-test when comparing the means of two groups, especially when the sample size is small (n < 30) and the population standard deviation is unknown. A z-test is appropriate for large sample sizes (n ≥ 30) or when the population standard deviation is known. For confidence intervals, use a t-interval for smaller samples with unknown population standard deviation, and a z-interval for larger samples or known population standard deviation. Always check if the data meets the assumptions for each test before proceeding.
What does a confidence interval for a population mean constructed from sample data show?
A confidence interval of x% is an interval such that there is an x% probability that the true population mean lies within the interval.
What does a 95 percent confidence interval tell you about the population proportion?
There is a 95% probability that the true population proportion lies within the confidence interval.
