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A bank wishing to estimate the mean balances owed by their MasterCard customers within 75 miles with a 98 percent confidence can use the following formula to calculate the required sample size:
- Sample size = (Z-score)2 * population standard deviation / (margin of error)2
- Where Z-score = 2.326 for 98 percent confidence
- Population standard deviation = 300
- Margin of error = desired confidence interval
Substituting the values into the formula the required sample size is: 2.3262 * 300 / (Confidence Interval)2 = 553.7
Therefore the bank would need to have a sample size of 554 to estimate the mean balances owed by their MasterCard customers within 75 miles with a 98 percent confidence.
What else can I help you with?
The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown?
It can be.
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!
Is it true that the larger the standard deviation the wider the confidence interval?
no
The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown?
It can be.
What effect increasing only the population standard deviation will have on the width of the confidence interval?
It will make it 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 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 does the sample standard deviation best estimate?
The standard deviation of the population. the standard deviation of the population.
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.
What is the sampling distribution when the standard deviation is known?
When the standard deviation of a population is known, the sampling distribution of the sample mean will be normally distributed, regardless of the shape of the population distribution, due to the Central Limit Theorem. The mean of this sampling distribution will be equal to the population mean, while the standard deviation (known as the standard error) will be the population standard deviation divided by the square root of the sample size. This allows for the construction of confidence intervals and hypothesis testing using z-scores.
What is the standard deviation of the sample mean called?
The standard deviation of the sample mean is called the standard error. It quantifies the variability of sample means around the population mean and is calculated by dividing the standard deviation of the population by the square root of the sample size. The standard error is crucial in inferential statistics for constructing confidence intervals and conducting hypothesis tests.
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.
Is it true that the larger the standard deviation the wider the confidence interval?
no
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.
