STATS 2381 Ch. 2,3,4,6,7,8 All True/False Quizzes
The population mean is an example of an estimator.
F pop mean is a parameter
The population mean, population median, and population mode are all the same value.
F
A normal distribution always has an expected value of zero.
F A standard normal distribution always has an expected value of zero.
The Central Limit Theorem is important because, provided the sample size is sufficiently large, it can be applied for determining the sampling distribution of the sampling median without assuming the distribution of the population of interest is known.
F CLT determines distribution of sample mean, not median
Every estimator is a statistic.
T
The area to the right of 0 in a standard normal distribution is a. equal to .5 minus the area to the left of 0 b. .5 c. equal to the area to the right of 0 in any normal distribution d. undetermined unless μ and σ are known e. 1
b. .5
Suppose for a sample size of 75, we have a mean of 13 and a standard deviation of 2. Then a 96% confidence interval for the mean of the sampled population would have left and right end-points 13-(2.06)(2/Sqrt(75)) and 13+(2.06)(2/Sqrt(75)) respectively. If we constructed such a confidence interval for 100 samples, we could expect about _____ of them to contain the mean population. a. 4 b. 2 c. 96 d. 2.58 e. 75
c. 96 96% = 96/100
The standard normal distribution a. is skewed b. is a discrete probability distribution c. always has a mean equal to 0 and a standard deviation equal to 1 d. has a mean (μ) equal to 1 and a variance (σ2) equal to 0 e. is symmetric about σ2
c. always has a mean equal to 0 and a standard deviation equal to 1
The areas under a probability density function of a continuous random variable correspond to probabilities for the random variable X. This implies that a. X is a discrete random variable b. X is a normal random variable. c. the total area under the probability density function equals 1 d. the probability distribution is always mound shaped e. all of the above
c. the total area under the probability density function equals 1
Any function of the sample data is an estimator.
F is a statistic
Consider a population with mean μ and population standard deviation σ. The Central Limit Theorem states that for a sufficiently large sample size, the sampling distribution of the sample mean (X bar) is approximately a normal distribution with expected value (mean) μ and standard error (standard deviation) σ.
F for (X bar), standard deviation is σ/Sqrt (n)
A disadvantage of using a 99% confidence level rather than a 95% confidence level for a parameter estimation is that larger samples must be taken for establishing higher levels of confidence.
F Confidence level is independent of sample size.
Increasing the confidence level decreases the width of the interval estimate for the population mean μ, given that the sample data remains the same.
F Increasing confidence level increases the width
The Central Limit Theorem lays a key role in developing a confidence interval for the population mean μ provided the sample size is not too large.
F The sample size must be sufficiently large to apply the Central Limit Theorem.
A 95% confidence interval has a probability of .95 that the parameter μ will be contained in the confidence interval.
F There is no probability associated with μ.
There is only one symmetric bell shaped density function that has mean 0 and standard deviation 1.
F There is only one standard normal, but there are many with mean 0 and standard deviation 1.
Every estimator has a sampling distribution having parameters that are totally unrelated to the population of interest from which the data was sampled.
F They are often related
The Central Limit Theorem is not applicable to samples taken from non-normally distributed samples.
F applies to all with sufficiently large sample size
According to the Central Limit Theorem, the standard error of (X bar) decreases as the population variance increases.
F as population variance decreases
An estimator is said to be consistent if the estimator gets closer to the parameter it is estimating as the population variance increases.
F as population variance decreases
According to the Central Limit Theorem, the sampling distribution of the sample mean for sufficiently large sample sizes will be very similar to the probability density function of the population of interest.
F distribution is always approx. normal
A point estimate is preferred over an interval estimate from a statistical point of view.
F interval estimate accounts for sampling error
The Central Limit Theorem yields the approximate sampling distribution of the population mean provided the sample size is sufficiently large.
F population mean is a parameter, and parameters have no distributions.
According to the Central Limit Theorem, the sampling distribution of the sample mean for sufficiently large sample sizes will be identical to the distribution of the sampled (parent) population.
F regardless of population of interest, distribution of (X bar) will be approximately normal.
All student's t based confidence intervals for a population mean μ will be of equal width provided the level of confidence is the same for each interval.
F sample size, level of confidence, and standard deviation must be the same for each interval.
The sample mean is identical to the population mean.
F sampling error
Every random sample is a representative sample.
F sampling error is likely
Parameters are used to estimate statistics.
F statistics are used to estimate parameters
Confidence intervals give no information regarding the precision of an estimator.
F the smaller the interval, the more precise the estimator
Statistical inference occurs when a population population parameters are used to infer the values of statistics.
F use estimators to infer the values of parameters
The Central Limit Theorem states that for a sufficiently large sample size, the sampling distribution of the sample mean (X bar) is N(μ,σ) where μ is the mean of the population of interest, σ is the standard deviation of the population, and n is the sample size.
F σ/Sqrt(n)
An estimator is said to be unbiased if the expected value of the estimator is exactly the parameter which the estimator.
T
Every estimator of a population parameter is a random variable which has its own density function.
T
Parameters describe some characteristic of the population of interest.
T
Sampling error is a source of error for every estimator.
T
Statistical inference permits us to draw conclusions concerning a population and its population parameters based on sample data.
T
The Central Limit Theorem applies to populations which are modeled as discrete random variables.
T
The Central Limit Theorem can be applied without regard to the shape of the population density function provided the sample size is sufficiently large enough
T
The Central Limit Theorem is important because it can always be applied without assuming the of the population of interest, provided the sample size is sufficiently large and the population variance is finite.
T
The expected value of the sample mean (X bar) is the same as the population mean of the sampled population.
T
The expected value of the sample mean is identical to the population mean.
T
The standard error of the sample mean (X bar) does not depend on the expected value of the population of interest that is being sampled.
T
The terms "random variable" and "population of interest" are often interchanged in statistical analysis.
T
The width of a confidence interval for the population mean μ is dependent on the sample standard deviation.
T
The width of a confidence interval for μ decreases as the sample size increases for a fixed confidence level, provided the sample standard deviation remains constant.
T
The width of a confidence interval for μ depends only on the parameter value it is attempting to estimate.
T