Stats 190 test 2

probability of same event occurring twice in a row

(p)(p)

z score formula

(x-mean)/standard deviation

higher # of subjects = more normal distribution

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the probability of being selected stays constant from one selection to the next when more than one individual is selected.

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things that are truly random will produce a normal distribution

.

What is the value of the z- score if X is the same as the mean?

0

What are three characteristics of z-score transformations?

1. same shape as OG distribution 2. mean of Z-score distribution always 0 3. Standard deviation always 1

t distribution

A distribution specified by degrees of freedom; shape changes when n changes

sigmaM

Standard error of mean

Value of Z score increases when...

Standard error of mean decreases and sample size increases

How do you transform a regular population of scores to a population of z-scores?

Subtract the mean and divide by the standard deviation

Low SD means?

The data point is close to the mean!

High SD means?

The data point is far away from the mean!

What is the variability of the sampling error measured by?

The standard error of the mean

What is a percentile rank?

a percent of individuals in a distribution who have scores less than or equal to a specific score; AKA cumulative percent

If a population with m = 60 and s = 8 is transformed into z-scores, then the resulting distribution of z-scores will have a mean of ____ and a standard deviation of ____. a. 0 and 1 b. 60 and 1 c. 0 and 8 d. 60 and 8 (unchanged)

a. 0 and 1

A sample of n = 25 individuals is selected from a population with m = 60 and s = 10 and a treatment is administered to the sample. After treatment, the sample mean is M = 63. What is the value of Cohen's d for this sample? a. 0.30 b. 1.50 c. 10.0 d. cannot answer without additional information

a. 0.30

What proportion of a normal distribution is located in the tail beyond a z-score of z = -0.50? a. 0.3085 b. 0.6915 c. -0.3085 d. -0.6915

a. 0.3085

For a normal distribution with m = 100 and s = 10, what proportion of the scores have values less than X = 85? a. 6.68% b. 43.32% c. 93.32% d. -6.68%

a. 6.68%

What level of measurement is probability?

continuous(scalar)

A researcher conducts a hypothesis test to evaluate the effect of a treatment. The hypothesis test produces a z-score of z = -3.60. Assuming that the researcher is using a two-tailed test, what is the correct statistical decision? a. Reject the null hypothesis with a = .05 but not with a = .01. b. Reject the null hypothesis with either a = .05 or a = .01. c. Fail to reject the null hypothesis with either a = .05 or a = .01. d. cannot answer without additional information

b. Reject the null hypothesis with either a = .05 or a = .01.

Which alpha level provides the smallest chance of committing a Type I error? a. a = .01 b. a = .05 c. a = .10 d. a = .025

a. a = .01

In N = 25 games last season, the college basketball team averaged m = 78 points with a standard deviation of s = 12. In their final game of the season, the team scored 89 points. Based on this information, the number of points scored in the final game was ____. a. a little above average b. far above average c. above average, but it is impossible to describe how much above average d. There is not enough information to compare last year with the average.

a. a little above average

A researcher risks a Type I error ____. a. anytime H0 is rejected b. anytime H1 is rejected c. anytime the decision is "fail to reject H0" d. All of the other options are correct.

a. anytime H0 is rejected

In general, increasing the alpha level (for example from .01 to .05) will ____. a. increase the likelihood of rejecting the null hypothesis b. decrease the likelihood of rejecting the null hypothesis c. increase the standard error d. decrease the standard error

a. increase the likelihood of rejecting the null hypothesis

Suppose you earned a score of X = 54 on an exam. Which set of parameters would give you the highest grade? a. m = 50 and s = 2 b. m = 50 and s = 8 c. m = 52 and s = 2 d. m = 52 and s = 8

a. m = 50 and s = 2

The critical region for a hypothesis test consists of ____. a. outcomes that have a very low probability if the null hypothesis is true b. outcomes that have a high probability if the null hypothesis is true c. outcomes that have a very low probability whether or not the null hypothesis is true d. outcomes that have a high probability whether or not the null hypothesis is true

a. outcomes that have a very low probability if the null hypothesis is true

If the sample data produce a test statistic (z-score) that is in the critical region, then which of the following is the appropriate conclusion for the test? a. reject H0 b. reject H1 c. fail to reject H0 d. fail to reject H1

a. reject H0

Even if a treatment has no effect, it is still possible to obtain an extreme sample mean that is very different from this population mean. If this happens, you are likely to ____. a. reject H0 and make a Type I error b. correctly reject H0 c. fail to reject H0 and make a Type II error d. correctly fail to reject H0

a. reject H0 and make a Type I error

For a distribution of scores, which of the following z-score values represents the location closest to the mean? a. z = +0.50 b. z = +1.00 c. z = -1.00 d. z = -2.00

a. z = +0.50

In a normal distribution, what z-score value separates the highest 20% of the scores from the rest of the distribution? a. z = 0.84 b. z = -0.84 c. z = 2.05 d. z = 0.20

a. z = 0.84

For a population with m = 100 and s = 20, what is the X value corresponding to z = -0.50? a. -10 b. 80 c. 90 d. 99.5

c. 90

For a population with m = 80 and s = 12, what is the z-score corresponding to X = 71? a. -0.50 b. -0.75 c. -1.00 d. -1.50

b. -0.75

What is the probability of randomly selecting a z-score less than z = -0.80 from a normal distribution? a. 0.7881 b. 0.2119 c. -0.7881 d. -0.2119

b. 0.2119

A vertical line is drawn through a normal distribution at z = 1.00. What proportion of the distribution is located between the mean and the line? a. 0.1587 b. 0.3413 c. 0.6826 d. 0.8413

b. 0.3413

A sample of n = 4 scores has a standard error of 12. What is the standard deviation of the population from which the sample was obtained? a. 48 b. 24 c. 6 d. 3

b. 24

A population of scores has m = 44. In this population, a score of X = 40 corresponds to z = -1.00. What is the population standard deviation? a. 2 b. 4 c. -2 d. -4

b. 4

A set of scores has a mean of m = 63 and a standard deviation of s = 8. If these scores are standardized so that the new distribution has m = 50 and s = 10, what new value would be obtained for a score of X = 59 from the original distribution? a. The score would still be X = 59. b. 45 c. 46 d. 55

b. 45

For a particular population, a sample of n = 4 scores has a standard error of 10. For the same population, a sample of n = 16 scores would have a standard error of ____. a. 2.5 b. 5 c. 10 d. 20

b. 5

A researcher uses a hypothesis test to evaluate H0 m = 80. Which combination of mean and standard deviation is most likely to result in rejecting the null hypothesis? a. M = 85 and s = 10 b. M = 85 and s = 20 c. M = 90 and s = 10 d. M = 90 and s = 20

c. M = 90 and s = 10

For the past 20 years, the high temperature on April 15th has averaged m = 62 degrees with a standard deviation of s = 4. Last year, the high temperature was 72 degrees. Based on this information, last year's temperature on April 15th was ____. a. a little above average b. far above average c. above average, but it is impossible to describe how much above average d. There is not enough information to compare last year with the average.

b. far above average

If a treatment has a very small effect, then a hypothesis test evaluating the treatment effect is likely to ____. a. result in a Type I error b. result in a Type II error c. correctly reject the null hypothesis d. correctly fail to reject the null hypothesis

b. result in a Type II error

The numerator of the z-score test statistic measures ____. a. the average distance between M and m that would be expected if H0 was true b. the actual distance between M and m c. the position of the sample mean relative to the critical region d. whether or not there is a significant difference between M and m

b. the actual distance between M and m

A random sample of n = 9 scores is obtained from a population with m = 50 and s = 9. If the sample mean is M = 59, what is the z-score corresponding to the sample mean? a. z = 1.00 b. z = 3.00 c. z = 9.00 d. cannot determine without additional information

b. z = 3.00

example of sampling without replacement

blackjack

A random sample of n = 4 scores is selected from a population with m = 80 and s = 20. On average, how much difference would you expect between the sample mean and the population mean? a. 0 points (the sample mean should be the same as the population mean) b. 5 points c. 10 points d. 80 points

c. 10 points

An introductory psychology class has 9 freshman males, 15 freshman females, 8 sophomore males, and 12 sophomore females. If one student is randomly selected from this class, what is the probability of getting a sophomore? a. 8/24 b. 20/24 c. 20/44 d. 14/44

c. 20/44

In a population with m = 60, a score of X = 58 corresponds to a z-score of z = -0.50. What is the population standard deviation? a. 1 b. 2 c. 4 d. cannot be determined without additional information

c. 4

If random samples, each with n = 9 scores, are selected from a normal population with m = 80 and s = 18, and the mean is calculated for each sample, then the average of all the sample means would be ____. a. 2 b. 6 c. 80 d. cannot be determined without additional information

c. 80

A treatment is administered to a sample selected from a population with a mean of m = 80 and a standard deviation of s = 10. After treatment, the effect size is measured by computing Cohen's d, and a value of d = 0.60 is obtained. Based on this information, the mean for the treated sample is M = ____. a. 6 b. 60 c. 86 d. cannot be determined without additional information

c. 86

A random sample of n = 36 scores is selected from a population. Which of the following distributions definitely will be normal? a. The scores in the sample will form a normal distribution. b. The scores in the population will form a normal distribution. c. The distribution of sample means will form a normal distribution. d. Neither the sample, the population, nor the distribution of sample means will definitely be normal.

c. The distribution of sample means will form a normal distribution.

Last week Sarah had exams in Math and in Spanish. On the math exam, the mean was m = 40 with s = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was m = 60 with s = 8 and Sarah had a score of X = 68. For which class should Sara expect the better grade? a. Math b. Spanish c. The grades should be the same because the two exam scores are in the same location. d. There is not enough information to determine which is the better grade.

c. The grades should be the same because the two exam scores are in the same location.

A sample has M = 72 and s = 4. In this sample, what is the X value corresponding to z = -2.00? a. X = 70 b. X = 68 c. X = 64 d. X = 60

c. X = 64

A Type II error means that a researcher has ____. a. concluded that a treatment has an effect when it really does b. concluded that a treatment has no effect when it really has no effect c. concluded that a treatment has no effect when it really does d. concluded that a treatment has an effect when it really has no effect

c. concluded that a treatment has no effect when it really does

A z-score of z = +3.00 indicates a location that is ____. a. near the center of the distribution b. slightly above the mean c. far above the mean in the extreme right-hand tail of the distribution d. The location depends on the mean and standard deviation for the distribution.

c. far above the mean in the extreme right-hand tail of the distribution

The probability of committing a Type I error ____. a. is determined solely by the size of the treatment effect b. cannot be controlled by the experimenter c. is determined by the level of significance (a) that one chooses d. is determined by the value for beta (b) that one selects

c. is determined by the level of significance (a) that one chooses

Which of the following samples would have the smallest standard error? a. n = 25 scores from a population with s = 10 b. n = 25 scores from a population with s = 20 c. n = 100 scores from a population with s = 10 d. n = 100 scores from a population with s = 20

c. n = 100 scores from a population with s = 10

Using z-scores, a population with m = 37 and s = 6 is standardized so that the new mean is m = 50 and s = 10. How does an individual's z-score in the new distribution compare with his/her z-score in the original population? a. new z = old z + 13 b. new z = (10/6)(old z) c. new z = old z d. cannot be determined with the information given

c. new z = old z

In general, the standard error of M gets smaller as ____. a. sample size and standard deviation both increase b. sample size and standard deviation both decrease c. sample size increases and standard deviation decreases d. sample size decreases and standard deviation increases

c. sample size increases and standard deviation decreases

For a regular two-tailed test with a = .01, the boundaries for the critical region would be defined by z-scores of ____. a. z = ±1.96 b. z = ±2.33 c. z = ±2.58 d. z = ±3.30

c. z = ±2.58

example of sampling with replacement

coin flip

For a population with m = 80 and s = 12, the z-score corresponding to X = 74 is z = ____. a. 6 b. -6 c. 0.50 d. -0.50

d. -0.50

A population has m = 50 and s = 10. If these scores are transformed into z-scores, the population of z-scores will have a mean of ____ and a standard deviation of ____. a. 50, 10 b. 50, 1 c. 0, 10 d. 0, 1

d. 0, 1

A random sample of n = 4 scores is obtained from a normal population with m = 40 and s = 6. What is the probability of obtaining a mean greater than M = 46 for this sample? a. 0.3085 b. 0.1587 c. 0.0668 d. 0.0228

d. 0.0228

A population distribution has m = 80 and s = 6. In this distribution, a z-score of z = +2.00 identifies a location ____. a. 2 points above the mean b. 2 points below the mean c. 12 points above the mean d. 12 points below the mean

d. 12 points below the mean

What proportion of a normal distribution is located between z = +0.50 and z = -0.50? a. 0.6915 b. 2(0.3085) = 0.6170 c. 0.1915 d. 2(0.1915) = 0.3930

d. 2(0.1915) = 0.3930

Probability values are always ____. a. greater than or equal to 0 b. less than or equal to 1 c. positive numbers d. All of the other choices are correct.

d. All of the other choices are correct.

A researcher uses a hypothesis test to evaluate H0 m= 80. Which combination of sample mean and alpha level (a) is most likely to result in rejecting the null hypothesis? a. M = 85 and a = .01 b. M = 85 and a = .05 c. M = 90 and a = .01 d. M = 90 and a = .05

d. M = 90 and a = .05

A sample is obtained from a population with m = 50 and s = 8. Which of the following samples would produce the most extreme z-score (farthest from zero)? a. a sample of n = 4 scores with M = 52 b. a sample of n = 16 scores with M = 52 c. a sample of n = 4 scores with M = 54 d. a sample of n = 16 scores with M = 54

d. a sample of n = 16 scores with M = 54

A z-score of z = -2.00 indicates a position in a distribution ____. a. above the mean by 2 points b. above the mean by a distance equal to 2 standard deviations c. below the mean by 2 points d. below the mean by a distance equal to 2 standard deviations

d. below the mean by a distance equal to 2 standard deviations

The median for any distribution corresponds to a z score of ____. a. 0 b. 1 c. N d. cannot be determined from the information given

d. cannot be determined from the information given

A Type I error means that a researcher has ____. a. concluded that a treatment has an effect when it really does b. concluded that a treatment has no effect when it really has no effect c. concluded that a treatment has no effect when it really does d. concluded that a treatment has an effect when it really has no effect

d. concluded that a treatment has an effect when it really has no effect

The z-score boundaries for the critical region are determined when the experimenter decides ____. a. the number of subjects b. the difficulty of the question c. the size of the standard error d. the alpha level

d. the alpha level

In hypothesis tests, standard error measures ____. a. the size of the treatment effect b. variability among population means c. the size of the critical region d. the amount of difference between M and m that is reasonable to expect if H0 is true

d. the amount of difference between M and m that is reasonable to expect if H0 is true

In a typical hypothesis testing situation, the null hypothesis makes a statement about ____. a. the population before treatment b. the population after treatment c. the sample before treatment d. the sample after treatment

d. the sample after treatment

Under what circumstances would a score that is located 5 points above the mean be considered relatively close to the mean? a. when the population mean is much less than 5 b. when the population mean is much greater than 5 c. when the population standard deviation is much less than 5 d. when the population standard deviation is much greater than 5

d. when the population standard deviation is much greater than 5

In a normal distribution, what z-score value separates the lowest 20% of the distribution from the highest 80%? a. z = 0.20 b. z = 0.80 c. z = 0.84 d. z = -0.84

d. z = -0.84

Standard error of mean

difference between sample mean and population mean

A sample obtained from a population with s = 10 has a standard error of 2 points. The sample size is ____. n = 5 n = 10 n = 20 n = 25

n = 25

p value > .05 then...o?

not statistically significant; fail to reject null hypothesis

What is a z-score?

number of standard deviations away from the mean

probability of single event occurring

p

alpha level

probability that the test will lead to a type 1 error; 5% of the time

probabilities are ALWAYS...

proportions

What is probability based on?

randomness

What does the unit normal table list?

relationships between z-score locations and proportions in a normal distribution

Type II error

researcher fails to reject the null hypothesis that is actually false and has failed to detect a real treatment affect

Type I error (alpha)

researcher rejects null hypothesis that is actually true and concludes treatment has affect when it really doesn't

p value < .05 then... ?

statistically significant; reject the null hypothesis

Law of Large Numbers

the larger the sample size, the more probable it is that the sample mean will be close to the population mean

Sampling error

the natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter

Alternative Hypothesis (Ha)

the sample is different from the population; z score falls at the high or low end of distribution; ind. variable has an effect on dep. variable

Null Hypothesis (H0)

the sample is not different from the population; z score falls in the middle part of the normal distribution; ind. variable has no effect on dep. variable

population variance

the smaller the variance in the population, the more probable it is that the sample mean will be close to the population mean