stats test #2

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

c. 0.50

Alpha Level

-value of p that will be used to reject the null hypothesis - if the value of p is lower than alpha level, reject the null hypothesis -if p is higher than alpha level, fail to reject the null hypothesis -

For a population with m= 80 and o= 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

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= 0.05 but not with a=0.01 b. reject the null hypothesis with either a=0.05 or a=0.01 c. fail to reject the null hypothesis with either a=0.05 or a=0.01 d. cannot answer without additional information

a z-score of 3.6 is off the charts b. reject the null hypothesis with either a=0.05 or a=0.01

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 info

a. 0.30

Which alpha level provides the smallest chance of committing a Type 1 error? a. a=0.01 b. a= 0.05 c. a=0.10 d. a=0.025

a. a=0.01

For a regular two-tailed test with a=0.01, the boundaries for the critical region would be defined by the z-scores of _____. a. z= +/- 1.96 b. z= +/- 2.33 c. z= +/- 2. 58 d. z= +/- 3.30

c. z= +/- 2.58

A population has m= 50 and o= 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 o=6. What is the probability 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

For the past 20 yrs, the high temp on April 15 has averaged m= 62 degrees with a SD of o=4. Last year, the high temperature was 72 degrees. Based on this information, last year's temperature on April 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 info to compare last yr with the average

z = (X-m)/SD = (72-72)/4 = 10/4 = 2.5 b. far above average

A population distribution has m= 80 o=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

z= (X-m)/SD 2= (X-80)/6 X= 92 92-80= 12 c. 12 points above the mean

A random sample of n=4 scores is obtained from a normal population with m=40 and o=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

z= 46-40/(s/sqrt(n)) z= 6/ (6/sqrt(4)) z= 6/3= +2 d. 0.0228

If the population with m= 60 and o=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

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 o= 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%

In N= 25 games last season, the college basketball team averaged m= 78 points with a standard deviation of o= 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 the average d. there is not enough information to compare last year with the average

a. a little above average

A researcher risks a Type 1 error _____. a. anytime H0 is rejected b. anytime H1 is rejected c. anytime the decision is "fail to rejected H0" d. all of the other options are correct

a. anytime H0 is rejected

In general, increasing the alpha (for example from 0.01 to 0.05) 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 earn a score of X= 54 on an exam. Which set of parameters would give you the highest grade? a. m= 50 and o=2 b. m=50 and o=8 c. m=52 and o=2 d. m=52 and o=8

a. m=50 and o=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 1 error b. correctly reject H0 c. fail to reject H0 and make a Type 2 error d. correctly fail to reject H0

a. reject H0 and make a Type 1 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

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 score has a mean of m= 63 and a standard deviation of o= 8. If these scores are standardized so that the new distribution has m=50 and o=10, what new value would be obtained for a score of X= 59 from the original distribution? a. the score would be 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

For the past 20 years, the high temperature on April 15th has average m= 62 degrees with a standard deviation of o= 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

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= 0.05 but not with a= 0.01 b. reject the null hypothesis with either a= 0.05 or a= 0.01 c. fail to reject the null hypothesis with either a= 0.05 or a= 0.01 d. cannot answer without additional information

b. reject the null hypothesis with either a=0.05 or a=0.01

If a treatment has a very small effect, then a hypothesis test evaluating the treatment effect is likely to ____. a. results in a Type 1 error b. results in a Type 2 error c. correctly reject the null hypothesis d. correctly fail to reject the null hypothesis

b. results in a Type 2 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

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

b. the population after treatment

A random sample of n=9 scores is obtained from a population with m=50 and o=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

A random sample of n=9 scores is obtained from a population with m=50 and o=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

A random sample of n=4 scores is selected from a population with m= 80 and o=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

A random sample of n=4 scores is selected from a population with m= 80 and o=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

A population distribution has m= 80 and o=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

c. 12 points above the mean

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 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

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

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

c. 90

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

c. M=90 and o=10

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 2 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 1 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 the population with o=10 b. n=25 scores from a population with o=20 c. n=100 scores from a population with o=10 d. n=100 scores from a population with o=20

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

Using z-scores, a population with m=37 and o=6 is standardized so that the new mean is m=50 and o=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

Using z-scores, a population with m= 37 and o=6 is standardized so that the new mean is m=50 and o=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 info given

c. new z = old z Meet the new z score, same as old z score. That's how we can compare scores on different distributions

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

A random sample of n=36 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

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 forms 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

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

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= 0.01 b. M=85 and a= 0.05 c. M=90 and a= 0.01 d. M= 90 and a=0.05

d. M=90 and a=0.05

A researcher uses 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=0.01 b. M=85 and a=0.05 c. M=90 and a=0.01 d. M=90 and a=0.05

d. M=90 and a=0.05

A sample is obtained from a population with m=50 and o=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 scored with M= 54

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

A sample is obtained from a population with m=50 and o=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

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 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 the 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 info given

d. cannot be determined from the info given A z-score of 0 corresponds to the mean. This may or may not be the median. We would need a perfectly normal distribution for this to be true

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

If random samples, each with n=9 scores, are selected from a normal population with m=80 and o=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

d. cannot be determined without additional information

A Type 1 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

A sample obtained from a population with o=10 has a standard error of 2 points. The sample size is_____. a. n=5 b. n=10 c. n=20 d. n= 25

d. n=25

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 amount 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

Under what circumstances would a score that is located 5 points above the mean be considers 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

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 It can't be positive, because then the higher scores would be less than 50%.

sampling error

discrepancy between a sample mean and the true population mean the variability of this error is measures by the standard error of M

Standard error of M

the standard deviation of the distribution of sample means -provides measure of how much distance is expected on average between M and m - the larger n is the smaller Om is