Math

Which of the following is not a characteristic of the distribution of sample means? a. The sample means should pile up around the population mean. b. The pile of sample means should tend to form a normal-shaped distribution. c. The sample means should have standard deviations similar to the population standard deviation. d. The larger the sample size, the closer the sample means should be to the population mean.

c

Check My Work Which of the following is equal to p(z > 2.00) in a normal distribution?I. p(z < -2.00)II. 1 - p(z < 2.00)III. p(z > 1.00)

1 2

What is the probability of a z-score falling within 1 standard deviation of the mean in a normal distribution?

68.26

A score that is 10 points above the mean corresponds to a z-score of z = +1.20. What is the standard deviation?

8.33

•Membership of MENSA requires a score of 130 on the Stanford-Binet 5 IQ test, which has μ = 100 and σ = 15. What proportion of the population qualifies for MENSA? A.p = 0.0228 B.p = 0.9772 C.p = 0.4772 p = 0.0456

A

•A score of X = 59 comes from a distribution with μ = 63 and σ = 8. This distribution is standardized to a new distribution with μ = 50 and σ = 10. What is the new value of the original score? A.59 B.45 C.46 55

B

•A z-score of z = +1.00 indicates a position in a distribution _____. A.above the mean by 1 point B.above the mean by a distance equal to 1 standard deviation C.below the mean by 1 point D.below the mean by a distance equal to 1 standard deviation

B

•For a population with μ = 50 and σ = 10, what is the X value corresponding to z = 0.4? A.50.4 B.10 C.54 10.4

C

•Last week Andy had exams in chemistry and in Spanish. On the chemistry exam, the mean was µ = 30 with σ = 5, and Andy had a score of X = 45. On the Spanish exam, the mean was µ = 60 with σ = 6, and Andy had a score of X = 65. For which class should Andy expect the better grade? A.chemistry B.Spanish C.There is not enough information to know.

Chemistry

•Find the proportion of the normal curve that corresponds to z > 1.50. A.p = 0.9332 B.p = 0.5000 C.p = 0.4332 D.p = 0.0668

D. p=0.0668

selection process wherein the probability of being selected stays constant from one selection to next

Independent random sampling

result from relabeling data into new table with positive, whole-number predetermined mean and standard deviation

Standardized Score

composition of data used to make dissimilar distributions comparable

Standardized distribution

equation used to transform z-scores back into X values, for a population

X= poupulation mean + z0 LOOK OVER

equation used to transform z-scores back into X values, for a sample

X= sample mean + ZS LOOK OVER

specification of the precise location of each X value within a distribution

Z-Score

relabeling of X values in a population into precise X-value locations within a distribution

Z-score Transformation

formula used to transform X values into z-scores, for a sample

Z= X minus sample mean/ sample LOOK OVER

Check My Work When is the distribution of sample means identical to the population distribution? a. when n = 1 b. when the standard error equals the population standard deviation c. when n is a very large number

a b

Check My Work Which combination of factors will produce the largest value for the standard error?

a. a small sample and a large standard deviation

ll of the possible random samples of size 5 are selected from a population, and the variance among these sample means is 16. If all possible random samples of size 10 are selected from the same population, what can we say about the variance of this new set of sample means? a. It will be exactly 16. b. It will be less than 16. c. It will be greater than 16. d. It will be exactly 32.

b

•A population has μ = 60 with σ = 5; the distribution of sample means for samples of size n = 4 selected from this population would have an expected value of _____. A.5 B.60 C.30 d.15

b.60

mathematical proposition which serves as a cornerstone for much of inferential statistics

central limit theorem

Which of the following accurately describes the proportions in the tails of a normal distribution when z = -0.50? a. Proportions in the right-hand tail are greater than 0.50, and proportions in the left-hand tail are less than 0.50. b. Proportions in the right-hand tail are less than 0.3085, and proportions in the left-hand tail are greater than 0.3085. c. Proportions in both tails are 0.50. d. Proportions in both tails are less than 0.3085.

d

hat happens to the standard error of M as sample size increases? a. It stays constant. b. It increases. c. The standard error does not change in a predictable manner when sample size increases. d. It decreases.

d

collection for all the possible random data sets of a particular size

distribution of sample means

data set obtained using selection process wherein the probability of being selected stays constant

independent random sampling

What happens to the standard distance between the sample mean and the population mean when the sample size is multiplied by 4?

divided by two

mean of the distribution of sample means which is always equal to the population mean

expected value of M

rule that larger sample size increases probability that sample and population means will be close

law of large numbers

The standard error for a particular sample is 3.6. A researcher needs the standard error to be 1.2. What should the researcher do to the sample size?

multiply the sample size by 9

What is the benefit of converting raw scores from a sample into z-scores?

new scores are easier to compare

If the standard error among sample means is small, which of the following is true?I. All the possible sample means are clustered close together.II. A researcher can be confident that any individual sample mean will provide a reliable measure of the population.III. A researcher must be concerned that a different sample could produce a different conclusion.

one and 2

•A deck of 52 cards contains 12 royalty cards. If you randomly select a card from the deck, what is the probability of obtaining a royalty card? A.p = 1/52 B.p = 12/52 C.p = 3/52 p = 4/52

p = 12/52

score referred to by its portion of scores less than/equal to the specific score

percentile

portion of individuals in a distribution with scores less than/equal to the specific score

percentile rate

fraction or proportion of all the possible outcomes

probability

selection process wherein each individual in the population has an equal chance of being selected

random sampling

original, unchanged datum that is the direct result of measurement

raw score

group of statistics obtained by selecting all possible samples of a specific size

sampling distribution

statistics obtained by selecting all possible samples of a specific size from a population

sampling distribution

natural discrepancy between a statistic and its corresponding population parameter

sampling error

selection process that returns individuals to the population in order to keep probabilities from changing

sampling with replacement

selection process that does not require constant probabilities

sampling without replacement

data set obtained using selection process wherein each individual has equal chance of being selected

simple random sampling

Which quantity decreases as the sample size increases?

standard error

measure of distance expected between sample mean and population mean

standard error of M

list of proportions of the normal distribution for a full range of possible z-score values

unit normal table

formula used to transform X values into z-scores, for a population

z= X minus population mean/ 0 LOOK OVER

•A random sample of n = 16 scores is obtained from a population with µ = 50 and σ = 16. If the sample mean is M = 58, the z-score corresponding to the sample mean is _____? A.z = 1.00 B.z = 2.00 C.z = 4.00 cannot determine

z=2.00

•T/F -A sample mean with z = 3.00 is a fairly typical, representative sample.

•False -A z-score of 3.00 is an extreme, or unlikely, z-score

•T/F -For any negative z-score, the tail will be on the right-hand side.

•False -For negative z-scores the tail will always be on the left side

•T/F -If you know a z-score, you can find the probability of obtaining that z-score in a distribution of any shape.

•False -If a distribution is skewed, the probability shown in the unit normal table will not be accurate

•T/F -If μ = 40 and 50 corresponds to z = +2.00, then σ = 10 points.

•False -If z = +2, then 2σ = 10, so σ = 5

•T/F If σ = 20, a score above the mean by 10 points will have z = 1.00

•False -If σ = 20, then z = 10/20 = 0.5

•T/F -The mean of the sample is always equal to the population mean.

•False -Individual samples will vary from the population mean

•T/F Choosing random individuals who walk by you yields a random sample.

•False -Not all individuals walk by, so not all have an equal chance of being selected for the sample

•T/F -A score close to the mean has a z-score close to 1.00

•False -Scores quite close to the mean have z-scores close to 0.00

•T/F -If a sample of n = 10 scores is transformed into z-scores, there will be five positive z-scores and five negative z-scores.

•False -The number of z-scores above/below the mean will be exactly the same as the number of original scores above/below the mean

•T/F -Probability predicts what kind of population is likely to be obtained.

•False -The population is given; probability predicts what a sample is likely to be like

•T/F -The shape of a distribution of sample means is always normal.

•False -The shape is normal only if the population is normal or n ≥ 30

•T/F -It is possible to find the X score corresponding to a percentile rank in a normal distribution.

•True -Find the z-score for the percentile rank, then transform it to X

•T/F -If you know the probability, you can find the corresponding z-score.

•True -First find the proportion in the appropriate column, then read the z-score from the left column

•T/F -As sample size increases, the value of the standard error decreases.

•True -Sample size is in the denominator of the equation so as n grows larger, standard error decreases

•T/F Transforming an entire distribution of scores into z-scores will not change the shape of the distribution

•True -The location of each score relative to all other scores is unchanged, so the shape of the distribution is unchanged

•T/F -A negative z-score always indicates a location below the mean

•True -The sign indicates that score is below the mean