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Construct an 80 percent confidence interval for the true population mean given that the standard deviation of the population is 6 and the sample mean is 18?
Wiki User
∙ 10y ago
THe answer will depend on whether the confidence interval is central or one-sided. If central, then
-1.28 < z < 1.28
-1.28 < (m - 18)/6 < 1.28
-7.68 < m - 18 < 7.68
10.3 < m < 25.7
Wiki User
∙ 10y ago
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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.
What happens to the confidence interval as the standard deviation of a distribution decreases?
It goes up.
What percentage of time will the population proportion not be found within the confidence interval?
What percentage of times will the mean (population proportion) not be found within the confidence interval?
How do you calculate confidence interval?
Confidence intervals may be calculated for any statistics, but the most common statistics for which CI's are computed are mean, proportion and standard deviation. I have include a link, which contains a worked out example for the confidence interval of a mean.
How do you calculate the parameter to a 99.9 confidence interval using mean and standard deviation?
Did you mean, "How do you calculate the 99.9 % confidence interval to a parameter using the mean and the standard deviation?" ? The parameter is the population mean μ. Let xbar and s denote the sample mean and the sample standard deviation. The formula for a 99.9% confidence limit for μ is xbar - 3.08 s / √n and xbar + 3.08 s / √n where xbar is the sample mean, n the sample size and s the sample standard deviation. 3.08 comes from a Normal probability table.
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.
What effect increasing only the population standard deviation will have on the width of the confidence interval?
It will make it wider.
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 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.
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.
Is it true that the larger the standard deviation the wider the confidence interval?
no
When to use t-test?
You use the t-test when the population standard deviation is not known and estimated by the sample standard deviation. (1) To test hypothesis about the population mean (2) To test whether the means of two independent samples are different. (3) To test whether the means of two dependent samples are different. (4) To construct a confidence interval for the population mean.
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.
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.
What percentage of time will the population proportion not be found within the confidence interval?
What percentage of times will the mean (population proportion) not be found within the confidence interval?
