stats final

4. For the standard normal probability distribution, what z-value, z0, corresponds to P(Z >z0) =.95? a. 1.96 b. 1.65 c. -1.65 d. -1.96

a. 1.96

8. Suppose a sample mean is distributed Normally. If the sample size increases, what happens to the shape of the sampling distribution of the sample mean? a. Distribution becomes wider and flatter. b. Distribution becomes narrower and taller. c. Distribution remains the same. d. Distribution turns upside down and inside out.

b. Distribution becomes narrower and taller.

7. Suppose a sample mean of 30 is based on a simple random sample of 100 individuals taken from a population of 1000 individuals with distribution known to be Normal with mean of 35 and a standard deviation of 10. Then the distribution of the sample mean is also Normally distributed with the following parameters ... a. mean=30 and standard error =1. b. mean =30 and standard error=0.95. c. mean = 35 and standard error=0.95. d. mean =35 and standard error =1.

a. mean=30 and standard error =1.

9. One benefit of knowing the sampling distribution of the sample mean is that ... a. the sampling distribution can be used to provide probability information about how close the estimator is to the population mean. b. one can calculate the probability that the sample mean is less than the population mean minus twice its standard error. c. one can get two cheese burgers for the price of one at McDonalds. d. there is no benefit.

a. the sampling distribution can be used to provide probability information about how close the estimator is to the population mean.

3. The value added to and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the a. confidence coefficient. b. margin of error. c. parameter estimate. d. planning value.

b. margin of error.

7. If we change a 99% confidence interval estimate to a 95% confidence interval estimate, we can expect ... a. width of the confidence interval to increase. b. width of the confidence interval to decrease. c. width of the confidence interval to remain the same. d. a bunch of people whining about the change over social media.

b. width of the confidence interval to decrease.

2. A sampling "frame" is... a. used exclusively to display pictures of samples. b. a random sample from a finite population. c. a list of elements/individuals that make up a finite population and from which a random sample can be taken. d. a manipulation or creation of evidence in which an innocent person is made to look guilty.

c. a list of elements/individuals that make up a finite population and from which a random sample can be taken.

1. The margin of error for a sample mean equals ... a. twice the length of an interval estimate or confidence interval b. an acceptable level of confidence c. half the length confidence interval d. a low calorie substitute for butter

c. half the length confidence interval

12. Let the sample mean, 𝒙, be based on a simple random sample (SRS) of n individuals from a Normal population with unknown mean μ and known standard deviation σ. Then there is a probability equal to 0.95 that the interval given by 𝒙 ± 𝟏. 𝟗𝟔 𝝈 𝒏 contains the unknown population mean, μ .

true

12.The probability distribution of the sample mean is the same as the sampling distribution of the sample mean.

true

13. The sample mean is unbiased for the population mean.

true

1. An interval estimate gives the lower and upper bounds of the parameter value.

true

1.A sample mean based on a simple random sample of individuals coming from a normal distribution must be also normally distributed.

true

10. Because different sample selections provide different numerical sample mean estimates, the sample mean estimator is considered a random variable.

true

11. Point estimation is an example of statistical inference because point estimates are calculated using sample data that are obtained via (simple) random sampling for the purpose of estimating a characteristic of the population

true

13. Let the sample mean, 𝒙, be based on a simple random sample (SRS) of n individuals from a Normal population with unknown mean μ and known standard deviation σ. Then there is a probability equal to 0.95 that sample mean, 𝒙 will be contained in the interval given by 𝝁 ± 𝟏. 𝟗𝟔 𝝈 𝒏 .

true

14. Suppose the sample mean is based on a sample of n individuals from Normal population with known standard deviation of σ. Then there is a 0.95 probability that the value of a sample mean will provide a margin of error less than or equal to 1.96 𝝈 𝒏 .

true

15. As the degrees of freedom increase the t-distribution looks more and more like the standard normal probability distribution.

true

16. As sample size decreases, so do the degrees of freedom for the t-value used in computing the margin of errors.

true

2.The Central Limit Theorem says that the sample mean is approximately normally distributed for large samples regardless of the initial distribution (of the individuals).

true

3. As the sample size increases, the distribution of the sample mean looks more and more like a normal distribution, even if the original sample was taken from a non-normal distribution.

true

3.Sampling frames are useful when sampling from a finite population

true

4. A 95% interval estimate for the mean is equivalent to a 95% confidence interval for the mean.

true

4.In simple random sampling (SRS) all samples of the same size have the same probability of being selected

true

5. As the sample size increases, the magnitude of the margin of error decreases.

true

6. According to the Central Limit Theorem, as the sample size increases the distribution of the sample mean looks more and more like a normal distribution, regardless of the distribution of the individuals from the population.

true

7. As the sample size increases, the standard error gets closer to 0.

true

8. As the sample size increases, the standard deviation gets smaller.

true

8. The standard error is another name of the standard deviation of the sample mean.

true

6. Suppose a random variable, X is normally distributed with mean=500 and STD=50. For a sample of 100 individuals, what is the standard error (or the STD of the sample mean)? a. 5 b. 50 c. 10 d. 0.5

A.5

2. A correct interpretation for a 95% confidence interval for the population mean is "there is a 0.95 probability that the point estimate (calculated from a random sample of the population) equals the population parameter value."

False

5. Reasons for sampling "randomly" (as opposed to a convenience) include... a. Random sampling protects estimates (and yourself) from accusations of sampling bias. b. Convenience sampling has the added disadvantage of having to use your brain to determine whether or not a given individual's inclusion into a sample is "really" convenient for you. c. In Las Vegas, you have much better odds using estimates based on random sampling than you have using estimates based on what is "convenient" for the "House." d. There is no difference.

a. Random sampling protects estimates (and yourself) from accusations of sampling bias.

9. The Central Limit Theorem claims that the distribution of the sample mean of size n resulting from a simple random sample of a population... a. can be approximated by a normal distribution as n becomes larger, even if the distribution of individuals that made up the sample is non-normal. b. can be approximated by a normal distribution as n becomes smaller, even if the distribution of individuals that made up the sample is non-normal. c. can be approximated by a normal distribution regardless sample size, ONLY if the original distribution of individuals is non-normal. d. all the above.

a. can be approximated by a normal distribution as n becomes larger, even if the distribution of individuals that made up the sample is non-normal.

6. Increasing the confidence level for estimating the population proportion, results in the corresponding confidence interval of the population proportion a. becoming narrower. b. becoming wider. c. becoming really arrogant.. d. remaining the same.

b. becoming wider.

1. An entity on which data are measured is called ... a. sample b. element or individual c. variable d. Dave

b. element or individual

4. A confidence interval estimate of a population mean based on a random sample of size 100 from a moderately skewed population where the standard deviation is known relies on a. t-value with 100 degrees of freedom b. z-value from standard normal distribution c. t-value with 9 degrees of freedom d. a u-value from a uniform distribution

b. z-value from standard normal distribution

5. Suppose population's proportion is estimated from a sample of size 100 yielding a sample proportion = 0.5. At 95% confidence, the margin of error (round to the nearest 0.01) is a. 15.00 b. 2.00 c. 0.10 d. 4.25

c. 0.10

10. When is it appropriate to use the finite population correction when estimating standard error? a. Never. b. Whenever the population is finite. c. When the sample size is less than 5% of the population size d. When the sample size is greater than 5% of the population size.

d. When the sample size is greater than 5% of the population size.

2. In order to construct an interval estimate of a population mean based on a random sample of size 100 from a normal population having known standard deviation, the margin of error must be computed using ... a. the sample standard deviation divided by 99. b. the sample standard deviation divided by 99. c. population standard deviation divided by 100. d. population standard deviation divided by 10.

d. population standard deviation divided by 10.

3. Which of the following is NOT an example of sampling frames? a. list of student ID numbers b. credit card numbers c. driver's licenses d. the grains of sand on Manhattan Beach

d. the grains of sand on Manhattan Beach

8. The probability that sample mean +/- Margin of error includes the true value of the parameter mean, the observed sample mean will provide a margin of error equal to 1.96𝜎! is a. 0.05 b. 0.95 c. 95% d. 0.

d.0

10. As the sample size increases so does the width of the confidence interval.

false

11. The purpose of width of the interval estimate is to provide information about how close the point estimator is to the parameter it is estimating.

false

17. As the sample size increases, the shape of the t-distribution gets wider and flatter.

false

18. As the sample size increases, the shape of the t-distribution gets wider and flatter.

false

5.The Central Limit Theorem maintains that a normal distribution can be used to approximate the distribution of a sample mean based on a simple random sample (SRS) of individuals coming from a moderately skewed population, regardless of how many individuals make up the sample

false

6. A parameter value is a numerical summary measure for a characteristic of a random sample

false

7.The Central Limit Theorem allows the use of the normal probability distribution to approximate the sampling distribution of the sample mean x regardless of the size of the sample or the population distribution of the individuals from which the sample was drawn

false

9. As the sample size increases, the shape of the standard normal distribution gets wider and flatter.

false

9. Assuming the standard deviation of individuals that makes up the sample mean remains the same, increasing the sample size decreases the standard error

false