PSY Stats Test 1

Σ(2X)^2 = _______

196

Are standardized scores and z-scores the same thing?

no

What is the value of ΣX^2 for the following scores? Scores: 1, 0, 2, 4 A. 21 B. 49 C. 14 D. 28

A

Which of the following symbols identifies the sample variance? A. s B. σ C. s^2 D. σ^2

C

the values of data measured on this scale cannot be rank ordered

Nominal Scale

values of data measured on this scale can be rank ordered

Ordinal Scale

A population of N = 10 scores has a mean of σ = 6. After one score is removed, the mean is found to be M = 5. What is the value of the score that was removed? A. X = 3 B. X = 10 C. X = 15 D. X = 5

C

A researcher interested in vocabulary development obtains a sample of 3-yr-old children to participate in a research study. The average score for the group of 20 is an example of a parameter. A. true B. false

B

If a set of exam scores forms a symmetrical distribution, what can you conclude about the students' scores? A. it is not possible to draw any conclusions about the students' scores B. most of the students had relatively high scores C. about 50% of the students had high scores and the rest had low scores D. most of the students had relatively low scores

C

On an exam with a mean of μ = 70, you have a score of X = 65. Which of the following values for the standard deviation would give you the highest position within the class? A. σ = 1 B. σ = 5 C. σ = 10 D. it cannot be determined from the given information.

C

A population has SS = 100 and σ^2 = 4. How many scores are in the population? A. 400 B. 200 C. 26 D. 25

D

What is the area of the normal distribution between z = -1.72 and z = +0.72?

0.7215

Josh is a very good singer. In fact, he participated in a study recently for the music department and he was told that he was one standard deviation above the mean in holding a tune. Based on the 1-2-3 Rule, what is Josh's percentile rank?

84%

For a sample with M = 50 and s = 12, what is the X value corresponding to z = -0.25? A. 54 B. 47 C. 46 D. 53

B

A researcher finds that the average reading score for a group of n=64 children is M = 46 and their standard deviation is 7. These children are in a program for children of abusive relationships and the researcher thinks that emotional issues may interfere with development of reading skills. The reading test has a known mean of mu = 50. Conduct the appropriate statistical test to determine if the sample mean is statistically significantly different from the population mean. Enter the value of the statistic below, rounded to two places to the right of the decimal.

-4.57

Although a research study is typically conducted with a relatively small group of participants known as a _____, most researchers hope to generalize their results to a much larger group known as a _______. A. population; sample B. sample; population C. statistic; sample D. parameter; population

B

What is the final step to be performed when computing Σ(X - 2)^2? A. square each value B. subtract 2^2 from each X^2 value C. subtract 2 points from each score D. sum the squared values

D

What is the sample variance and the estimated standard error for a sample of n = 9 scores with SS = 72? A. s^2 = 3 and sm = 3 B. s^2 = 9 and sm = 3 C. s^2 = 3 and sm = 1 D. s^2 = 9 and sm = 1

D

A jar contains 10 red marbles and 30 blue marbles. What is the probability of randomly selecting a red marble from the jar? A. 1/10 B. 10/30 C. 10/40 D. 1/40

C

values of data measured on this scale can be rank ordered. In addition, the differences between 2 adjacent ranks are equal

Interval Scale

Correct order to test a hypothesis about an unknown population mean: 1. select a sample and compute the z-score for the sample mean 2. determine the probability at which you will conclude that the sample outcome is very unlikely. 3. determine the null and alternative hypotheses 4. decide whether to reject or fail to reject the null hypothesis

3, 2, 1, 4

For a population with μ = 80 and σ = 20, the distribution of sample means based on n = 16 will have an expected value of ____ and a standard error of ______. A. 5; 80 B. 80; 5 C. 20; 20 D. 80; 1.25

B

For the following distribution, what is the width of each class interval? X: 20-24 15-19 10-14 5-9 f: 2 5 4 1 A. 10 B. 5 C. 4.5 D. 4

B

The critical boundaries for a hypothesis test are z = +/- 1.96. If the z-score for the sample data is z = 1.90 then what is the correct statistical decision? A. fail to reject H1 B. fail to reject H0 C. reject H0 D. reject H1

B

When is there a risk of a Type II error? A. The risk of a Type II error is independent of the decision from a hypothesis test B. whenever the decision is "fail to reject H0" C. whenever H0 is rejected D. whenever H1 is rejected

B

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

A

If random samples, each with n = 9 scores, are selected from a normal population with μ = 80 and σ = 36, then what is the expected value for the distribution of sample means? A. 80 B. 12 C. 4 D. 16

A

determining a person's reaction time (in milliseconds) would involve measurement on a(n) ____ scale of measurement. A. ordinal B. interval C. ratio D. nominal

C

A researcher measures eye color for a sample of n = 50 people. Which measure of central tendency would be appropriate to summarize the measurements? A. any of these measures could be used. B. median C. mean D. mode

D

What is the shape of the distribution for the following set of data? Scores: 1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6 A. symmetrical B. cumulative C. negatively skewed D. positively skewed

C

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? A. X = 61 B. X = 53 C. X = 58 D. X = 55

D

What term is used to identify the mean of the distribution of sample means? A. the sample mean B. the standard error of M C. the expected value of M D. the central limit mean

C

In a frequency distribution graph, frequencies are presented on the _____ and the scores (categories) are listed on the _____. A. y axis/x axis B. x axis/y axis C. horizontal line/vertical line D. class interval/horizontal line

A

On an exam with μ = 52, you have a score of X = 44. Which value for the standard deviation would give you the highest position in the class distribution? A. σ = 8 B. σ = 4 C. It cannot be determined from the information given D. σ = 2

A

The distribution of sample means _____. A. will be normal if either the population is normal or the sample size is n ≥ 30 B. will be normal only if the population distribution is normal C. will be normal only if the sample size is at least n = 30 D. is always a normal distribution

A

What percentage of the normal distribution is below the mode? A. 50% B. 25% C. 85% D. unable to determine from the info above

A

Which set of scores has the smallest standard deviation? A. 145, 143, 145, 147 B. 27, 105, 10, 80 C. 11, 17, 31, 53 D. 5, 11, 42, 22

A

For the following distribution of quiz scores, if a score of X = 3 or higher is needed for a passing grade, how many individuals passed? X: 5 4 3 2 1 f: 6 5 5 3 2 A. 11 B. 16 C. cannot be determined D. 3

B

The students in a psychology class seemed to think that the midterm exam was very easy. If they are correct, what is the most likely shape for the distribution of exam scores? A. positively skewed B. negatively skewed C. normal D. symmetrical

B

The sum of the squared deviation scores is SS = 20 for a sample of n = 5 scores. What is the variance for this sample? A. 4 B. 5 C. 100 D. 80

B

A sample consists of n = 16. How many of the scores are used to calculate the range? A. 8 B. 4 C. 2 D. all 16

C

The IQ distribution has a population mean of 100 and standard deviation of 15. Approximately what percentage of people have IQs between 70 and 130? A. 90% B. 68% C. 95% D. 50%

C

With alpha = .05 and df = 8, the critical values for a two-tailed t test are t = +/-2.306. Assuming all other factors are held constant, if the df value were increased to df = 20, what would happen to the critical values for t? A. there is not enough information to answer this question. B. they would decrease (move closer to zero) C. they would increase (move farther from zero) D. they would stay the same

B

The locations on the curve of the normal distribution where positive acceleration changes to negative acceleration is called the A. median B. variance point C. point of no return D. point of inflection

D

What happens to the standard error of M as sample size increases? A. it also increases B. is stays constant C. the standard error does not change in a predictable manner when sample size increases D. it decreases

D

If a frequency distribution is shown in a bar graph, what scale was used to measure the scores? A. nominal B. ratio C. nominal or ordinal D. interval or ratio

C

One sample with n = 4 scores has a mean of M = 12, and a second sample with n = 6 scores has a mean of M = 8. If the two samples are combined, what is the mean for the combined set of scores? A. 4.8 B. 10.0 C. 9.6 D. 19.2

C

The classrooms in the psychology department are numbered from 100 to 108. A professor records the number of classes held in each room during the fall semester. If these values are presented in a frequency distribution graph, what kind of graph would be appropriate? A. a histogram B. a polygon C. a histogram or a polygon D. a bar graph

D

Which combination of factors will produce the smallest value for the standard error? A. a small sample and a small SD B. a small sample and a large SD C. a large sample and a large SD D. a large sample and a small SD

D

determining the class standing (1st, 2nd, and so on) for the graduating seniors at a high school would involve measurement on a(n) ____ scale of measurement. A. nominal B. ratio C. interval D. ordinal

D

What is measured by the denominator of the z-score test statistic? A. the average distance between M and mu that would be expected if H0 was true B. the position of the sample mean relative to the critical region C. whether or not there is a significant difference between M and mu D. the actual distance between M and mu

A

Which of the following statements cannot be true for a distribution of scores? A. all of these options are false statements. B. 60% of the scores are above the median. C. 60% of the scores are above the mean D. 60% of the scores are above the mode

B

Samples of size n = 9 are selcted from a population with μ = 80 with σ = 18. What is the standard error for the distribution of sample means? A. 80 B. 2 C. 6 D. 18

C

What is the median for the following set of scores? Scores: 1, 2, 6, 11, 17 A. 8 B. 4 C. 6 D. 8.5

C

What z-score is the cutoff for the lowest 15% of the normal distribution?

-1.03

A sample obtained from a population with σ = 12 has a standard error of 2 points. How many scores are in the sample? A. n = 24 B. n = 6 C. n = 3 D. n = 36

D

Even if a treatment has no effect, it is still possible to obtain an extreme sample mean that is very different from the population mean. What outcome is likely if this happens? A. correctly reject H0 B. correctly fail to reject H0 C. fail to reject H0 and make a Type II error D. reject H0 and make a Type I error

D

What is the value of Σ(X + 1) for the following scores? Scores: 2, 4, 7 A. 13 B. 16 C. 10 D. 11

B

What proportion of the normal distribution is more extreme than 1.25 standard deviations from the mean?

0.2112

The mean extraversion score for a population is known to be mu = 9.0 with a population standard deviation of sigma =5. A group of 25 people in an acting class are given the extraversion test and the researcher finds that their mean is M=11.5 and the sample standard deviation is s=3. What is the value of the appropriate statistic to test to see if this sample mean is significantly different from the population mean?

2.50

A population with a mean of M = 6 has ΣX = 42. How many scores are in the population? A. N = 6/42 = 1/7 B. N = 7 C. N = 252 D. it cannot be determined from the information given.

B

A random sample of n = 4 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. 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. D. the scores in the population will form a normal distribution.

B

A sample of n = 100 scores is selected from a population with μ = 80 with σ = 20. On average, how much error is expected between the sample mean and the population mean? A. 0.8 points B. 2 points C. 4 points D. 0.2 points

B

values of data measured on this scale can be rank ordered and have meaningful differences between scale points. For this scale, there is also an absolute zero point.

Ratio Scale

What is the value of SS for the following sample? Sample: 2, 3, 4, 7 A. 14 B. 28 C. 72 D. 14/3 = 2.67

A

A set of three scores consists of the values 6, 3, and 2. Σ2(X - 3) = _______

4

You have population with a mean of 50 (mu = 50) and a standard deviation of 10 (sigma = 10). What score (X) separates the highest 75% of the scores from the lowest 25%?

43.3

What is the mean for the following sample of scores? Scores: 1, 4, 5, 10 A. 5 B. 20 C. 10 D. 4

5

A set of 10 scores has SS = 90. If the scores are a sample, the sample variance is ______ and if the scores are a population, the population variance is _________. A. s^2 = 10; σ^2 = 10 B. s^2 = 9; σ^2 = 9 C. s^2 = 9; σ^2 = 10 D. s^2 = 10; σ^2 = 9

D

The participants in a research study are classified as high, medium, or low in self-esteem. This classification measurement on a nominal scale. A. True B. False

B

A population of scores has μ = 50 and σ = 5. If every score in the population is multiplied by 3, then what are the new values for the mean and standard deviation? A. μ = 50; σ = 5 B. μ = 50; σ = 15 C. μ = 150; σ = 15 D. μ = 150; σ = 5

C

What is the mean for the population of scores shown in the frequency distribution table? X: 5 4 3 2 1 f: 1 2 3 4 2 A. 15/5 = 3 B. 32/5 = 6.60 C. 32/12 = 2.67 D. 15/12 = 1/25

C

After every score in a sample is multiplied by 3, the mean is calculated and found to be M = 21. What was the mean for the original score? A. it cannot be determined from the information given. B. 21 C. 63 D. 7

D

A researcher develops a HAPPINESS scale. It is standardized so the population mean is 25 and the population standard deviation is 5. The distribution is normal. What percentage of the population has a HAPPINESS score between 20 and 35?

81.5%

A researcher conducts a hypothesis test using a sample of n = 40 from an unknown population. What is the df value for the t statistic? A. 39 B. it cannot be determined from the information given C. 40 D. 41

A

A sample of n = 20 scores is transformed into z-scores. What is the mean for the set of 20 z-scores? A. 0 B. 1 C. 10 D. It cannot be determined without more information

A

For a population with a standard deviation of σ = 6, what is the z-score corresponding to a score that is 12 points above the mean? A. z = 2 B. z = 6 C. z = 12 D. z = 1

A

For a population with μ = 40 and σ = 8, what is the z-score corresponding to X = 46? A. +0.76 B. +0.50 C. +1.00 D. +1.50

A

A population of N = 100 scores has μ = 30 and σ = 4. What is the population variance? A. 16 B. 2 C. 8 D. 4

A

To determine how much difference there is between two individuals, you must use either an interval or a ratio scale of measurement. A. true B. false

A

Which of the following accurately describes the effect of increasing the alpha level? A. increases the standard error and has no effect on the risk of a Type I error B. increases the risk of a Type I error and has no effect on the standard error C. decreases the standard error and has no effect on the risk of a Type I error D. Decreases the risk of a Type I error and has no effect on the standard error

B

A population distribution has σ = 6. What position in this distribution is identified by a z-score of z = +2.00? A. two points above the mean B. two points below the mean C. twelve points below the mean D. twelve points above the mean

D

Which of the following z-score values represents the location closest to the mean? A. z = -2.00 B. z = -1.00 C. z = +1.00 D. z = +0.50

D

What is the variance for the following population of scores? Scores: 5, 2, 5, 4 A. 1.22 B. 1.5 C. 2 D. 6

B

Which of the following samples will have the smallest value for the estimated standard error? A. n = 25 with s^2 = 100 B. n = 100 with s^2 = 100 C. n = 25 with s^2 = 400 D. n = 100 with s^2 = 400

B

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 population will form a normal distribution. B. the scores in the sample 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

For the following frequency distribution of exam scores, what is the lowest score on the exam? X: 90-94 85-89 80-84 75-79 70-74 f: 3 4 5 2 1 A. x = 70 B. x = 74 C. cannot be determined D. x = 90

C

Which ONE of the following is NOT one of the "selection criteria" that define random sampling? A. Each individual must be selected independently of any other individual. So selection of one individual has no effect on who else is selected. B. Every individual in the population must have an exactly equal chance of being selected for the sample. C. There can be no patterns of characteristics in the group of individuals selected. Every characteristic of the individuals in the sample (e.g., gender, age, etc.) must be equally represented. D. Every single possible combination of individuals must have exactly the same probability of being the particular sample that is chosen.

C

Which one of the following is a fundamental difference between the z-test and the t-test? A. All of the above. B. The t-statistic computes standard error by dividing by the square root of n-1 rather than the square root of n. C. The t-test finds standard deviation based on variance calculated using n-1 rather than n. D. The t-statistic uses the sample mean in place of the popualtion mean.

C

If random samples, each with n = 36 scores, are selected from a normal population with μ = 80 and σ = 18, how much difference, on average, should there be between a sample mean and the population mean? A. 3 points B. 6 points C. 18 points D. 2 points

A

The results of a hypothesis test are reported as follows: t(15) = 2.70, p < .05. Based on this report, how many individuals were in the sample? A. 16 B. it cannot be determined from the information provided C. 14 D. 15

A

You are interested in estimating the mean of a population. You plan to take a random sample from the population and use the sample's mean as an estimate of the population mean. Assuming that the population from which you select your sample is not normal, which of the statements about M are true? Choose all that apply. A. the sampling distribution of the z-score of M is normal for any sample size. B. you can assume that the sampling distribution of M is normally distributed for any sample size. C. You can only assume that the sampling distribution of M is normally distributed for sufficiently large sample sizes. D. the expected value of M is equal to the value of the population mean

C, D

What is the total number of scores for the distribution shown in the following table? X: 4 3 2 1 f: 3 5 4 2 A. 37 B. 4 C. 10 D. 14

D