stat exam 3 (confidence intervals)
A 100% confidence interval is more accurate than a 90% confidence interval and is therefore more preferable
false
A benefit of point estimates is that they provide information about their accuracy
false
A sample proportion equal to 0.50 will require the smallest sample size to achieve a particular margin of error for a confidence interval for the proportion
false
A wider the margin of error will result in a more precise confidence interval
false
All else being equal, a 90% confidence interval will be wider than a 95% confidence interval
false
Five random samples, each of size 40, are selected from a population of interest. A 90% confidence interval using a z-score is calculated for each sample. The margin of error for each confidence interval need not be the same
false
Given that a 95% confidence interval is (6.5, 12.5), we can state that there is a 95% probability that the true population mean is between 6.5 and 12.5.
false
The binomial distribution can be approximated by the Student's t-distribution when the following conditions are met: and .
false
The confidence interval for the mean is symmetrical around the population mean
false
When the sample size is more than 30 and sigma is known, the population must be normally distributed to calculate a confidence interval
false
The confidence interval for the proportion is a point estimate around the sample proportion that provides us with a value for the true population proportion
false
The degrees of freedom are used to determine the critical z-score for the normal distribution when calculating a confidence interval
false
The finite population correction factor for adjusting the confidence interval when sampling from a finite population is used when .
false
The margin of error can be reduced by reducing the size of the sample
false
The margin of error for a sample is dependent on the sample mean
false
The necessary sample size to determine the confidence interval for the mean will double when the required margin of error is reduced by half
false
The shape of the t-distribution becomes similar to the binomial distribution as the sample size increases
false
When determining the sample size required for a 95% confidence interval for the population mean, the sample mean needs to be known
false
A ________ is a single value that best describes the population of interest. A) confidence interval B) point estimate C) confidence level D) margin of error
point estimate
A 99% confidence interval has a greater chance of "catching" the true population mean when compared to a 90% confidence interval
true
If a pilot sample is not available, it is recommended to set the sample proportion equal to 0.50 to calculate the required sample size for a confidence interval for the proportion
true
Increasing the sample size will reduce the margin of error for a given confidence level
true
The confidence level is a complement to the significance level
true
The definition of a 90% confidence interval is that we expect that close to 90% of a large number of sample means drawn from a population will produce confidence intervals that include that population's mean
true
The degrees of freedom are the number of values that are free to vary given that certain information, such as the sample mean, is known
true
The point estimate for the population mean will always be found within the limits of the confidence interval for the mean.
true
The point estimate may not equal the true population mean because of the presence of sampling error.
true
The purpose of generating a confidence interval for the mean is to provide an estimate for the value of the population mean
true
The standard error of the proportion measures the average variation around the mean of the sample proportions taken from the population
true
The variation in sample means is measured by the standard error of the mean.
true
There is no guarantee that every confidence interval taken from a population will include the population mean
true
We can approximate the standard error of the proportion by substituting the sample proportion, p, for the population proportion, p.
true
When substituting the sample standard deviation for the population standard deviation, we can no longer rely on the normal distribution to provide the critical z-score for the confidence interval.
true
When the population standard deviation is unknown, we substitute the sample standard deviation in its place to calculate confidence intervals
true
When we use the t-distribution to calculate a confidence interval, we need to assume that the population of interest follows the normal probability distribution
true
Without the finite population correction factor, the standard error is overestimated when calculating a confidence interval for a finite population
true
The critical z-score for a 98% confidence level is ________. A) 1.28 B) 1.96 C) 2.33 D) 2.575
2.33
A ________ for the mean is an interval estimate around a sample mean that provides us with a range of where the true population mean lies A) margin of error B) significance level C) confidence level D) confidence interval
confidence interval
A ________ is defined as the probability that the interval estimate will include the population parameter of interest, such as a mean or a proportion. A) margin of error B) confidence level C) significance level D) confidence interval
confidence level