Statistics

Last week Tom had exams in Statistics and in English. He scored 10 points above the mean on both exams. From this information, what can you conclude about the z-scores for Tom's two scores? Select one: a.Tom will have a higher z-score for the exam with the lower mean. b.Both of Tom's z-scores are positive. c.None of the other choices is correct. d.Tom has identical z-scores for the two exams.

Both of Tom's z-scores are positive.

A sample with M = 85 and s = 12 is transformed into z-scores. After the transformation, what are the values for the mean and standard deviation for the sample of z-scores? Select one: a.M = 0 and s = 12 b.M = 85 and s = 1 c.M = 0 and s = 1 d.M = 85 and s = 12

M = 0 and s = 1

For a normal population with µ = 40 and σ = 10 which of the following samples has the highest probability of being obtained? Select one: a.M ≤ 44 for a sample of n = 4 b.M ≤ 42 for a sample of n = 4 c.M ≤ 42 for a sample of n = 100 d.M ≤ 44 for a sample of n = 100

M ≤ 42 for a sample of n = 4

Samples of size n = 4 are selected from a population with μ = 80 with σ = 8. What is the standard error for the distribution of sample means? Select one: a.4 b.2 c.80 d.8

a.4

For a population with µ = 40 and σ = 8, what is the z‑score corresponding to X = 46? Select one: a.+1.00 b.+0.75 c.+0.50 d.+1.50

b.+0.75

A normal distribution has a mean of µ = 70 with σ = 12. If one score is randomly selected from this distribution, what is the probability that the score will be less than X = 76? Select one: a.0.3830 b.0.6915 c.0.3085 d.0.1915

b.0.6915

A sample of n = 20 scores is transformed into z-scores. What is the mean for the set of 20 z-scores? Select one: a.1 b.cannot be determined without more information c.0 d.10

c.0

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 between 36 and 40 minutes? Select one: a.0.0793 b.0.1526 c.0.1554 d.0.3108

d.0.3108

For a sample with M = 80, a score of X = 88 corresponds to z = 2.00. What is the sample standard deviation? Select one: a.2 b.16 c.8 d.4

d.4

Which of the following accurately describes a hypothesis test? Select one: a. an inferential technique that uses the data from a sample to draw inferences about a population b. a descriptive technique that allows researchers to describe a sample c. a descriptive technique that allows researchers to describe a population d. an inferential technique that uses information about a population to make predictions about a sample

a. an inferential technique that uses the data from a sample to draw inferences about a population

Which of the following correctly describes the effect of increasing the alpha level (for example from .01 to .05)? Select one: a. increase the likelihood of rejecting H0 and increase the risk of a Type I error b. decrease the likelihood of rejecting H0 and decrease the risk of a Type I error c. increase the likelihood of rejecting H0 and decrease the risk of a Type I error d. decrease the likelihood of rejecting H0 and increase the risk of a Type I error

a. increase the likelihood of rejecting H0 and increase the risk of a Type I error

By definition, a Type I error is ______. Select one: a. rejecting a true H0 b. rejecting a false H0 c. rejecting a false H1 d. rejecting a true H1

a. rejecting a true H0

A researcher administers a treatment to a sample of participants selected from a population with µ = 80. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis? Select one: a. a sample mean much different than 80 with α = .05 b. a sample mean near 80 with α = .01 c. a sample mean near 80 with α = .05 d. a sample mean much different than 80 with α = .01

a. a sample mean much different than 80 with α = .05

A jar contains 10 red marbles and 30 blue marbles. A random sample of n = 3 marbles is selected from the jar with replacement. If the first two marbles are both blue, what is the probability that the third marble will be red? Select one: a.10/40 b.10/37 c.8/38 d.10/38

a.10/40

Samples of size n = 4 are selected from a population with μ = 80 with σ = 8. What is the expected value for the distribution of sample means? Select one: a.80 b.8 c.20 d.40

a.80

What happens to the standard error of M as sample size increases? Select one: a.It decreases b.It stays constant c.It also increases

a.It decreases

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

a.z = +0.50

If a sample of n = 4 scores is obtained from a population with μ = 70 and σ = 12, then what is the z-score corresponding to a sample mean of M = 76? Select one: a.z = 1.00 b.z = 0.50 c.z = 0.25 d.z = 2.00

a.z = 1.00

What z-score value separates the top 10% of a normal distribution from the bottom 90%? Select one: a.z = 1.28 b.z = -1.28 c.z = 0.25 d.z = -0.25

a.z = 1.28

Which combination of factors produces the smallest risk of a Type I error? Select one: a. α = .05 with n = 100 and σ = 10 b. The three other options all have the same risk. c. α = .05 with n = 20 and σ = 20 d. α = .05 with n = 20 and σ = 10

b. The three other options all have the same risk.

What is the consequence of a Type II error? Select one: a. concluding that a treatment has an 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 no 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

Which of the following accurately describes the critical region? Select one: a. outcomes with a very low probability whether or not the null hypothesis is true b. outcomes with a very low probability if the null hypothesis is true c. outcomes with a high probability if the null hypothesis is true d. outcomes with a high probability whether or not the null hypothesis is true

b. outcomes with a very low probability if the null hypothesis is true

If all the possible random samples 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? Select one: a.6 b.80 c.cannot be determined without addtional information d.2

b.80

A normal distribution has a mean of µ = 80 with σ = 20. What score separates the lowest 30% of the distribution from the rest of the scores? Select one: a.X = 90.4 b.X = 69.6 c.X = 50 d.X = 110

b.X = 69.6

A researcher administers a treatment to a sample of n = 25 participants and uses a hypothesis test to evaluate the effect of the 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? Select one: a. Cannot answer without additional information b. The researcher should fail to reject H0 with either α = .05 or α = .01. c. The researcher should reject the null hypothesis with α = .05 but not with α = .01. d. The researcher should reject the null hypothesis with either α = .05 or α = .01.

c. The researcher should reject the null hypothesis with α = .05 but not with α = .01.

The z-score boundaries for the critical region are determined by ______. Select one: a. the size of the standard error b. the sample data c. the alpha level d. the null hypothesis

c. the alpha level

What proportion of a normal distribution is located between the mean and z = -0.40? Select one: a.0.3446 b.0.6554 c.0.1554 d.0.3108

c.0.1554

A population of scores has µ = 80. In this population, a score of X = 86 corresponds to z = +2.00.What is the population standard deviation? Select one: a.2 b.6 c.3 d.12

c.3

What happens to the expected value of M as sample size increases? Select one: a.It decreases b.It also increases c.It stays constant

c.It stays constant

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

c.the expected value of M

On an exam with μ = 52, you have a score of X = 56. Which value for the standard deviation would give you the highest position in the class distribution? Select one: a.cannot determine from the information given b.σ = 4 c.σ = 2 d.σ = 8

c.σ = 2

Which of the following is an accurate definition for the power of a statistical test? Select one: a. the probability of supporting a false null hypothesis b. the probability of rejecting a true null hypothesis c. the probability of supporting true null hypothesis d. the probability of rejecting a false null hypothesis

d. the probability of rejecting a false null hypothesis

In N = 25 games last season, the college basketball team averaged µ = 76 points with a standard deviation of σ = 6. 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 _____. Select one: a.There is not enough information to compare last year with the average. b.above average, but it is impossible to describe how much above average c.a little above average d.far above average

d. far above average

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 = 90 and X = 120? Select one: a.0.4672 b.0.1498 c.0.2996 d.0.5328

d.0.5328

A vertical line is drawn through a normal distribution at z = 1.20. What proportion of the distribution is on the left-hand side of the line? Select one: a.0.7698 b.0.3849 c.0.1151 d.0.8849

d.0.8849

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

d.10 points

Probability values are always _____. Select one: a.greater than or equal to 0 b.less than or equal to 1 c.positive numbers d.All of the other 3 choices are correct

d.All of the other 3 choices are correct

A random sample of n = 4 scores is selected from a population. Which of the following distributions definitely will be normal? Select one: 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.

d.Neither the sample, the population, nor the distribution of sample means will definitely be normal.

A normal distribution has μ = 80 and σ = 10. What is the probability of randomly selecting a score greater than 75 from this distribution? Select one: a.p = 0.50 b.p = 0.3085 c.p = 0.25 d.p = 0.6915

d.p = 0.6915

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? Select one: a.σ = 0 b.σ = 12 c.cannot be determined from the information given d.σ = 1.00

d.σ = 1.00