Psy Statistics

What z-score corresponds to a score that is above the mean by 2 standard deviations?​

+2

For a particular population, a sample of n = 4 scores has a standard error of 6. For the same population, a sample of n = 16 scores would have a standard error of _____. ​

3

For a sample of n = 30 scores, a score that is 6 points above the mean has a z-score of z = 1.50. What is the sample standard deviation?​

4

A sample of n = 4 scores is selected from a population with μ = 40 with σ = 8, and the sample mean is M = 43. What is the expected value for the sample mean?​

40

For a sample with M = 50 and s = 12, what is the X value corresponding to z = -0.25?​

47

A sample of n = 4 scores has a standard error of 10 points. For the same population, what is the standard error for a sample of n = 16 scores? ​

5

For a population with μ = 100 and σ = 20, what is the X value corresponding to z= -0.75?​

85

A sample is selected from a population with a mean of µ = 40. If the sample mean is M = 45, which of the following combinations would make the sample mean a good, representative value for the population?​

A large sample and a large population standard deviation

What is measured by the denominator of the z-score test statistic?​

A likely distance between M and µ that would be expected if H0 was true

​ 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?

A sample mean much different than 80 for a large sample

What is the effect of decreasing the alpha level (for example, from α = .05 to α = .01)?​

All of the other options are results of decreasing alpha.

​ What is the relationship between the alpha level, the size of the critical region, and the risk of a Type I error?

As the alpha level increases, the size of the critical region increases, and the risk of a Type I error increases.

What is the consequence of a Type II error?​

Concluding that a treatment has no effect when it really does

Which of the following is an accurate definition of a Type II error?

Failing to reject a false null hypothesis

A jar contains 10 red marbles and 20 blue marbles. If you take a random sample of two marbles from this jar, and the first marble is blue, then the probability that the second marble is blue is p = 19/29. ​

False

A population has µ = 60 and σ = 30. For a sample of n = 25 scores from this population, a sample mean of M = 55 would be considered an extreme value.​

False

​ What happens to the standard error of M as sample size increases?

It decreases

If a hypothesis test produces a z-score in the critical region, what decision should be made? ​

Reject the null hypothesis

Which of the following is an accurate definition for the power of a statistical test?

The probability of rejecting a false null hypothesis

​ Transforming an entire distribution of scores into z-scores will not change the shape of the distribution.

True

When is there a risk of a Type II error?​

Whenever the decision is "fail to reject H0"

You complete a hypothesis test using α = .05, and based on the evidence from the sample, your decision is to fail to reject the null hypothesis. If the treatment actually does have an effect, which of the following is true?​

You have made a Type II error.

What is the probability of randomly selecting a z-score less than z = 1.25 from a normal distribution?​

c. ​0.8944

What z-score values form the boundaries for the middle 60% of a normal distribution? ​

z = +0.84 and z = -0.84

If the sample size is equal to the population variance (n = σ2), then the standard error is equal to 1.​

True

On average, a sample of n = 16 scores will provide a better estimate of the population mean than you would get with a sample of n = 9 scores from the same population.​

True

For a normal distribution with µ = 50 and σ = 10, the line separating the highest 10% of the scores from the rest is located at X = 51.28.​

False

For a population with μ = 34, a score of X = 31 corresponds to z = -1.00. The standard deviation for the population is σ = 6.​

False

If the sample size is doubled, the standard error will be cut in half.​

False

For any normal distribution, the proportion in the tail beyond z = 2.00 is p = 0.0228.​

True

If other factors are held constant, then increasing the sample size will increase the likelihood of rejecting the null hypothesis.​

True

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

True

You have a score of X = 65 on an exam. Which set of parameters would give you the best grade on the exam?​

μ = 60 and σ = 5

Even if a treatment has an effect, it is still possible to obtain a sample mean after the treatment that is very similar to the original population mean. What outcome is likely if this happens?

​Fail to reject H0 and make a Type II error

A score that is 2 points higher than the sample mean has a z-score of z = 0.50, and a score of X = 44 has a z-score of -1.00. What is the sample mean? ​

​M = 48

​ 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?

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

For a population with µ = 80 and σ = 6, what is the z-score corresponding to X = 68? ​

-2.00

A sample of n = 20 scores is transformed into z-scores. What is the mean for the set of 20 z -scores? ​

0

What is the probability of randomly selecting a z-score less than z = -1.25 from a normal distribution?​

0.1056

A normal distribution has a mean of µ = 40 with σ = 8. If one score is randomly selected from this distribution, what is the probability that the score will be less than X = 34?

0.2266

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?​

0.2743

A random sample of n = 9 scores is obtained from a normal population with µ = 40 and σ = 18. What is the probability that the sample mean will be greater than M = 43?​

0.3085

What proportion of a normal distribution is located between z = 0 and z = +1.50?

0.4332

If a sample of n = 4 scores is obtained from a population with μ = 70 and σ = 12, what is the z-score corresponding to a sample mean of M = 73?​

0.50

What is the probability of randomly selecting a z-score greater than z = -0.75 from a normal distribution?

0.7734

What proportion of a normal distribution is located between z = -1.25 and z = +1.25?​

0.7888

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 greater than X = 58?​

0.8413

Which combination of factors will produce the largest value for the standard error? ​

A small sample and a large standard deviation

Which of the following accurately describes the proportions in the body of a normal distribution?

Body proportions on either side of the z-score are greater than 0.50.

With α = .05, how are the boundaries for the critical region determined?​

Boundaries are drawn so there is 2.5% (.025) in each tail of the distribution.

​ Which of the following will increase the power of a statistical test?

Change the sample size from n = 25 to n = 100

What is the consequence of a Type I error?​

Concluding that a treatment has an effect when it really has no effect

A population with μ = 41 and σ = 4 is standardized to create a new distribution with μ = 50 and σ = 10. In this transformation, a score of X = 39 from the original distribution will be transformed into a score of X = 55.

False

A sample of n = 25 scores is selected from a population with a mean of µ = 80 and a standard deviation of σ = 20. The standard error for the sample mean is 20.​

False

A sample of n = 25 scores is selected from a population with μ = 50 and σ = 10. The probability of obtaining a sample mean greater than 55 is p = 0.3085.​

False

A sample of n = 25 scores is selected from a population with μ = 70 and σ = 20. It is very unlikely that the sample mean will be greater than 72.​

False

A score that is 6 points above the mean corresponds to a z-score of z = +0.50. For this population, the standard deviation is σ = 3.​

False

A vertical line drawn through a normal distribution at z = -0.75 separates the distribution into two sections. The proportion in the smaller section is 0.2734.​

False

For a normal distribution with µ = 100 and σ = 20, the score that separates the top 60% of the distribution from the bottom 40% is X = 105.

False

If one score is randomly selected from a normal distribution with µ = 100 and σ= 20, the probability of obtaining a score between X = 80 and X = 120 is p = 0.3413.​

False

If one score is randomly selected from a normal distribution with µ = 100 and σ= 20, the probability of obtaining a score between X = 90 and X = 100 is p = 0.3085.

False

If one score is randomly selected from a normal distribution with µ = 100 and σ= 20, the probability of obtaining a score less than X = 130 is p = 0.9987.​

False

In a distribution with µ = 80 and σ = 20, a score of X = 95 corresponds to z = 1.50.

False

In a sample of n = 40 scores, X = 31 corresponds to z = -1.50 and X = 39 corresponds to z = +0.50. The sample mean is M = 36.

False

​ For a normal distribution, the proportion located between z = -1.00 and z = +1.00 is p = 34.13%

False

What happens to the expected value of M as sample size increases?

It stays constant

​ What happens to the expected value of M as sample size increases?

It stays constant.

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?​

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?

M is less than 38 for a sample of n = 4

Last week, Sarah had exams in math and in Spanish. On the math exam, the mean was µ = 30 with σ = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was µ = 60 with σ = 8, and Sarah had a score of X = 68. For which class should Sara expect the better grade?​

Math

​ A two-tailed hypothesis test is being used to evaluate a treatment effect with α = .05. If the sample data produce a z-score of z = − 2.24, what is the correct decision?

Reject the null hypothesis and conclude that the treatment has an effect

What is the standard error of M?​

The standard deviation of the distribution of sample means

​ A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a hypothesis test, what does the alternative hypothesis ( H 1 ) say about the treatment?

The treatment causes a change in the scores.

A Type II error occurs when a treatment actually does have an effect on the scores but the effect was not large enough to reject the null hypothesis.

True

A sample is selected from a population with µ = 30 and σ = 10. If the sample mean of M = 34 corresponds to z = +2.00, then the sample size is n = 25.

True

A vertical line drawn through a normal distribution at z = -0.50 separates the distribution into two sections. The proportion in the larger section is 0.6915.​

True

A vertical line is drawn through a normal distribution so that 47.5% of the distribution is located between the line and the mean. The line is drawn at z = 1.96 or at z = -1.96.​

True

A vertical line is drawn through a normal distribution so that the proportion in the tail is 0.1841. The line was drawn at z = 0.90 or at z = -0.90.

True

A z-score of z = +1.00 always indicates a location exactly 1 standard deviation above the mean.​

True

For any distribution of scores, the location identified by z = +1 and the location identified by z = -1 are exactly the same distance from the mean.

True

If samples are selected from a normal population, the distribution of sample means will also be normal.​

True

On an exam with σ = 6, Tom's score of X = 54 corresponds to z = -1.00. The mean for the exam must be µ = 60.​

True

The mean for the distribution of sample means is always equal to the mean for the population from which the samples are obtained.​

True

The null hypothesis predicts a specific value for the population mean.

True

The proportion in the tail of a normal distribution can never be more than 0.50.​

True

Two samples probably will have different means even if they are both the same size and they are both selected from the same population.​

True

When the z-score value in a normal distribution is negative, the body is on the right-hand side of the distribution.​

True

​ For a sample with a standard deviation of s = 10, a score with a deviation of +5 will have a z-score of z = 0.50.

True

​ In most situations, researchers would like the hypothesis test to reject the null hypothesis.

True

​ There is always a possibility that the decision reached in a hypothesis test is incorrect.

True

Scores on the SAT form a normal distribution with a mean of µ = 500 with σ = 100. If the state college only accepts students who score in the top 60% on the SAT, what is the minimum score needed to be accepted?​

X = 475

​ A sample of n = 9 scores is obtained from a population with μ = 70 and σ = 18. If the sample mean is M = 76, what is the z -score for the sample mean?

z = 1.00

What z-score value separates the highest 10% of the scores in a normal distribution from the lowest 90%?​

z = 1.28​

A sample of n = 20 scores has a mean of M = 45 and a standard deviation of s = 8. In this sample, what is the z-score corresponding to X = 57?​

z = 1.50

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?​

z = 2.00

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?

σ = 2

A researcher administers a treatment to a sample of participants selected from a population with µ = 80. If the researcher obtains a sample mean of M = 88, which combination of factors is most likely to result in rejecting the null hypothesis?

σ = 5 and α = .05

A vertical line drawn through a normal distribution at z = -1.00 separates the distribution into two sections, the body and the tail. What proportion of the distribution is in the tail? ​

​0.1587

If an entire population with μ = 60 and σ = 8 is transformed into z-scores, then the distribution of z-scores will have a mean of ___ and a standard deviation of ___. ​

​0; 1

Samples of size n = 9 are selected from a population with μ = 80 with σ = 18. What is the expected value for the distribution of sample means?​

​80

The critical boundaries for a hypothesis test are z = +1.96 and − 1.96. If the z-score for the sample data is z = − 1.90, what is the correct statistical decision?​

​Fail to reject H0

A sample is selected from a normal population with μ = 50 and σ = 12. Which of the following samples would be considered extreme and unrepresentative for this population?​

​M = 56 and n = 16

Using z-scores, a population with µ = 37 and σ = 6 is standardized so that the new mean is µ = 50 and σ = 10. After the standardization, one individual has a score of X = 55. What was this individual's score in the original distribution? ​

​X = 40

A distribution with µ = 55 and σ = 6 is being standardized so that the new mean and standard deviation will be µ = 50 and σ = 10. When the distribution is standardized, what value will be obtained for a score of X = 58 from the original distribution?​

​X = 55

A sample from a population with μ = 40 and σ = 8 has a mean of M = 36. If the sample mean corresponds to a z = -1.00, then how many scores are in the sample?​

​n = 4