stats exam #2

a normal distribution has a mean of µ = 40 with σ = 10. what proportion of the scores in this distribution are greater than X = 55? a. 0.0668 b. 0.3085 c. 0.6915 d. 0.9332

a. 0.0668

john drives to work each morning and the trip takes an average of µ = 38 minutes. the distribution of driving times is approximately normal with a standard deviation of σ = 5 minutes. for a randomly selected morning, what is the probability that john's drive to work will take less than 35 minutes? a. 0.2743 b. 0.3446 c. 0.6554 d. 0.7257

a. 0.2743

a normal distribution has a mean of µ = 100 with σ = 20. if one score is randomly selected from this distribution, what is the probability that the score will have a value between X =75 and X =95? a. 0.2957 b. 0.1056 c. 0.5069 d. 0.4013

a. 0.2957

a population of scores has µ = 44. in this population, a score of X = 40 corresponds to z = -0.50. what is the population standard deviation? a. 8 b. 2 c. 4 d. -8

a. 8

a normal distribution has a mean of µ = 24 with σ = 3. what is the minimum score needed to be in the top 14% of the distribution? a. X = 27.24 b. X = 25.08 c. X = 24.42 d. X = 20.76

a. X = 27.24

which combination of factors will produce the smallest value for the standard error? a. a large sample and a small standard deviation b. a small sample and a large standard deviation c. a large sample and a large standard deviation d. a small sample and a small standard deviation

a. a large sample and a small standard deviation

a professor standardizes exam scores so that all exams have μ = 50 and s = 10. if the original scores from an exam have μ = 42 and s = 6, then a student with an original exam score of x =45 would receive a standardized score of x =55. a. true b. false

a. true

a score with a value less than or equal to the mean will have a z-score that is less than or equal to zero. a. true b. false

a. true

according to the central limit theorem, the standard error for a sample means becomes smaller as the sample size increases a. true b. false

a. true

all probabilities can be expressed as decimal values ranging from 0 to 1.00 a. true b. false

a. true

for a normal distribution, the z-score boundary that separates the lowest 2.5% of the scores from the rest is z = -1.96 a. true b. false

a. true

if samples are selected from a normal population, the distribution of sample means will also be normal. a. true b. false

a. true

the critical region for a hypothesis test consists of sample outcomes that are very unlikely to occur if the null hypothesis is true a. true b. false

a. true

a random sample of n = 4 scores is obtained from a population with a mean of µ = 80 and a standard deviation of σ = 10. if the sample mean is M = 90, what is the z-score for the sample mean? a. z = 2.00 b. z = 5.00 c. z = 20.00 d. z = 1.00

a. z = 2.00

for a population with what is the z-score corresponding to X = 68? a. -12.00 b. -2.00 c. -0.50 d. +2.00

b. -2.00

even if a treatment has an effect, it is still possible to obtain a sample mean that is very similar to the original population mean. what outcome is likely if this happens? a. correctly fail to reject H0 b. fail to reject H0 and make a Type II error c. correctly reject H0 d. reject H0 and make a Type 1 error

b. fail to reject H0 and make a Type II error

a two-tailed hypothesis test is being used to evaluate a treatment effect with α = .01. if the sample data produce a z-score of z = 2.24, then what is the correct decision?​ a. ​ reject the null hypothesis and conclude that the treatment has an effect. b. fail to reject the null hypothesis and conclude that the treatment has no effect. c. reject the null hypothesis and conclude that the treatment has no effect. d. ​ fail to reject the null hypothesis and conclude that the treatment has an effect.

b. fail to reject the null hypothesis and conclude that the treatment has no effect.

a significant treatment effect indicates that a large treatment effect was found a. true b. false

b. false

what term is used to identify the mean of the distribution of sample means? a. the standard error of M b. the expected value of M c. the sample mean d. the central limit mean

b. the expected value of M

under what circumstances is a score that is located 5 points above the mean a central value, relatively close to the mean? a. when the population SD is much less than 5 b. when the population SD is much greater than 5 c. when the population mean is much less than 5 d. when the population mean is much greater than 5

b. when the population SD is much greater than 5

what z-score value separates the top 70% of a normal distribution from the bottom 30%? a. z = -0.84 b. z = -0.52 c. z = 0.84 d. z = 0.52

b. z = -0.52

what is the consequence of a Type II error? a. ​concluding that a treatment has no effect when it really has no effect b.​ concluding that a treatment has no effect when it really does c. ​concluding that a treatment has an effect when it really has no effect d. concluding that a treatment has an effect when it really does

b.​ concluding that a treatment has no effect when it really does

for a normal distribution, what z-score value separates the lowest 25% of the scores from the rest of the distribution? a. 0.67 b. 0.75 c. -0.67 d. 0.25

c. -0.67

a sample of n = 16 individuals is selected from a population with μ = 60 and σ = 6 and a treatment is administered to the sample. after treatment, the smaple mean is M = 63. what is the value of Cohen's d for this sample? a. 2.00 b. 0.33 c. 0.50 d. 3.00

c. 0.50

a sample is obtained from a population with μ = 100 and σ = 20. which of the following samples would produce the most extreme z-score for the sample mean? a. a sample of n = 100 scores with M = 102 b. a sample of n = 25 scores with M = 104 c. a sample of n =25 scores with M = 102 d. a sample of n = 100 scores with M = 104

d. a sample of n = 100 scores with M = 104

what is the relationship between the alpha level , the size of the critical region, and the risk of a Type 1 error? a. as the alpha level increases, the size of the critical region increases and the risk of a Type 1 error decreases b. as the alpha level increases, the size of the critical region decreases and the risk of a Type 1 error increases c. as the alpha level increases, the size of the critical region increases and the risk of a Type 1 error increases d. as the alpha level increases, the size of the critical region decreases and the risk of a Type 1 error decreases

c. as the alpha level increases, the size of the critical region increases and the risk of a Type 1 error increases

by selecting a larger alpha level, a researcher is ______. a. attempting to make it more difficult to reject H0 b. less able to detect a treatment effect c. increasing the risk of a Type I error d. decreasing the risk of a Type I error

c. increasing the risk of a Type I error

for a normal population with a mean of µ = 80 and a standard deviation of σ = 10, what is the probability of obtaining a sample mean greater than M = 75 for a sample of n = 25 scores? a. p = 0.6915 b. p = 0.3085 c. p = 0.9938 d. p = 0.0062

c. p = 0.9938

which of the following is not a requirement of a random sample? a. the probabilities cannot change during a series of selections b. every individual has an equal chance of being selected c. there must be at least 100 observations d. there must be sampling with replacement

c. there must be at least 100 observations

a population with µ = 85 and σ = 12 is transformed into z-scores. after the transformation, what is the standard deviation for the population of z-scores? a. σ = 12 b σ = 0 c. σ = 1.00 d. σ = 4

c. σ = 1.00

if the possible random sample with n = 36 scores are selected from a normal population with µ = 80 and σ = 18, and the mean is calculated for each sample, then what is the average of all the sample means? a. 2 b. it cannot be determined without additional information c. 6 d. 80

d. 80

for a population with µ = 100 and σ = 20, what is the X value corresponding to z = -0.75? a. 95 b. 105 c. 115 d. 85

d. 85

a distribution with µ = 35 and σ = 8 is being standardizes so that the new mean and standard deviation will be µ = 50 and σ = 10. in the new, standardized distribution your score is X = 45. what was your score in the original distribution? a. X = 39 b. X = 30 c. X = 45 d. X = 31

d. X = 31

a random sample of n = 36 scores is selected from a population. which of the following distributions will definitely be normal? a. there is not enough information to answer this question b. the scores in this sample will form a normal distribution c. the scores in the population will form a normal distribution d. the distribution of sample means will form a normal distribution

d. the distribution of sample means will form a normal distribution

a population distribution has σ = 6. what position in this distribution is identified by a z-score of z = +2.00? a. twelve points below the mean b. two points below the mean c. two points above the mean d. twelve points above the mean

d. twelve points above the mean

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

d. z = +0.50

a researcher is conducting a study to evaluate a treatment that is expected to increase the scores for individuals in a population. if the researcher uses a one-tailed test with a = .01, then which of the following correctly identifies the critical region? a. z < 2.58 b. z > 2.58 c. z < 2.33 d. z > 2.33

d. z > 2.33

a researcher conducts a hypothesis test to evaluate the effect of a treatment. the hypothesis test produces a z-score of z = 2.37. assuming that the researcher is using a two-tailed test, what decision should be made? a. ​the researcher should reject the null hypothesis with either α = .05 or α = .01. b. the researcher should ignore the results c. ​the researcher should fail to reject H0 with either α = .05 or α = .01. d. ​the researcher should reject the null hypothesis with α = .05 but not with α = .01.

​d. the researcher should reject the null hypothesis with α = .05 but not with α = .01.