Psychological Statistics Midterm Examination

Psychological Statistics

Midterm Examination

Multiple Choice

A normal distribution with a mean of 15 and standard deviation of 5. 95% of its area is within

• One standard deviation of the mean

• Two standard deviations of the mean

• Three standard deviations of the mean

• It depends on the value of the mode

Multiple Choice

The mean of a standard normal distribution is:

• 0

• 1.0

• -1.0

• 100

Multiple Choice

The standard deviation of the mean for a standard distribution is:

• 0.0

• 1.0

• 100

• 68%

Fill in the Blank

A normal distribution with a mean of 25 and standard deviation of 5. What is the corresponding Z score for a case having a value of 10?

Multiple Choice

Consider a normal distribution with a mean of 25 and standard deviation of 4. Approximately, what proportion of the area lies between values of 17 and 33.

• 95%

• 68%

• 99%

• 50%

Fill in the Blank

Consider a normal distribution with a mean of 10 and standard deviation of 25. What’s the Z score for the value of 35?

Multiple Choice

For a standard normal distribution, what’s the probability of getting a positive number?

• 50%

• 95%

• 68%

• We cannot tell from the given information

Fill in the Blank

For a normal distribution with a mean of 16 and standard deviation of 2. What is the probability of getting a number greater than 20?

Fill in the Blank

Fifty students took an Introduction to Psychology exam. Assume that their scores formed a normal distribution with a mean of 80 and standard deviation of 4. The professor decided to adjust the scores by creating z scores. Only the first 2.5% of students got an A. Students were curious what actual scores would be A’s?

Multiple Choice

Two-hundred students took a statistics class. Their professor creatively decided to give each of them their Z-score instead of their grade. Rachel got her Z-score of -0.2. She was wondering how well she did on the exam.

• It was very good, much better than almost all of the other students

• It was so-so, but still better than half of the students.

• It was not that good, but not at the bottom of the distribution

• It was very bad and she needs to work much harder next time

Multiple Choice

A researcher collected some data and they form a normal distribution with a mean of zero. What’s the probability of getting a positive number from this distribution?

• 25%

• 50%

• 75%

• We need to calculate the standard deviation and then decide

Multiple Choice

What is the variance of the sampling distribution of the mean?

• Population variance divided by N

• Sample variance divided by the sample size squared

• Sample mean divided by the population mean

• all of the above

Multiple Choice

Which of the following appropriately describes standard error of the mean?

• Standard error is the square root of the variance of the population

• Standard error is the square root of the sample standard deviation

• Standard error is the standard deviation of the sampling distribution of the mean

• Standard error is a measure that is only appropriate for a normal distribution

Multiple Choice

Eric wants to understand how students’ blood pressure is distributed in his school. Imagine that there are 500 students. Eric wants to know whether or not it makes a difference if he measures more students or less. Thus, you suggest to him:

• When you measure more of the students, your standard error of the mean will be smaller

• When you measure less students, your sample distribution is closer to the distribution of all students’ blood pressure

• There is no difference if you measure 10 students or 200 students

• You’d better select all 500 students

Multiple Choice

Which of the following description is correct?

• The mean of the sampling distribution of the means is the mean of the population from which the samples were drawn

• The mean of the sampling distribution of the mean is not equal to the mean of the population from which the scores were sampled

• The mean of the sampling distribution of the mean is the mean of the population from which the scores were sampled

• The mean of the sampling distribution of the mean is the mean of the population from which the scores were sampled only when the sample size is close to the population

Fill in the Blank

In a district, a researcher weighted all the students in the 3rd grade and the 5th grade. The average weight of students in the 3rd grade was 35kilogram and the variance of the mean was 2.5. The average weight of students in the 5th grade was 44 kilogram and the variance of its mean was 5. The researcher sampled 25 students from the 3rd grade and 25 students from the 5th grade. What’s the variance of sample distribution of the difference between the means ?

Fill in the Blank

Imagine our population of interest is all of the students who took a chemistry quiz. The average quiz score from all of the students in the class was 85 and the variance was 5. Imagine we could select several different samples from this population of 85 students. What would the standard deviation of the sampling distribution of the mean be for N=5?

Multiple Choice

The newspaper reports that higher rates of drowning and ice cream consumption correspond. Does that mean that eating ice cream can put you at risk of drowning? What might be the reason behind this phenomenon?

• Kids are not waiting 40 minutes after eating to swim

• In summer both ice cream consumption and swimming increases

• A full stomach makes it harder to swim

Multiple Choice

A prospective graduate student may be interested in gender balance at the university s/he will attend. Data on how many males and females attend the institution are examples of:

• Descriptive statistics

• Inferential Statistics

Multiple Choice

When participants who arrive for a research study are put into treatment groups on the basis of chance, ___________

• The statistical conclusions will also be absolutely correct

• Random sampling has occurred

• Random assignment has occurred

• The research findings will be compromised because you should never randomly assign to groups

Multiple Choice

True or False? Using a random sample is to accept some uncertainty about the conclusions.

• True

• False

Multiple Choice

A grouped frequency distribution should be used instead of a frequency distribution when the:

• Distribution is bimodal

• Variable is continuous

• Distribution is skewed

Multiple Choice

The following distribution has:

• A positive skew

• A left skew

• No skew

Multiple Choice

The area under the curve of a probability distribution is

• 0

• 100

• 0.68

• 1.00

Multiple Choice

Which of the following is a qualitative variable?

• Weight in kilograms

• Number of days without precipitation

• Ethnicity

• Average daily temperature

Multiple Choice

In an experiment on the effect of sleep on memory, the independent variable is (choose only one answer)

• Number of hours of sleep

• Recall score on a memory test

• Gender of the subjects

• Gender of the experimenter

Multiple Choice

A discrete variable is

• One that can take on any value in a certain range

• One that can only take on a finite number of values

Multiple Choice

For the scores 3, 5, 8, 10, 14, 17, 21, 25, calculate the 25th percentile using the following formula: R = P/100 x (N + 1)

• 2.25

• 2

• 5.75

• 5

Multiple Choice

Identify the scale of measurement for the following military hierarchy: Lieutenant, Captain, Major

• Interval

• Nominal

• Ratio

• Ordinal

Multiple Choice

For the following data,

• 3

• 7

• 2

• 12

Multiple Choice

According to the text, Pie charts are effective for displaying the relative frequencies of a______ number of categories. They are not recommended, however, when you have a _______ number of categories.

• Small, large

• Large, small

Multiple Choice

Based on the frequency polygon displayed below, the most common test grade was around what score?

• 35

• 85

• 95

• 175

Multiple Choice

Response times were generally shorter to the:

• Large target

• Small target

Multiple Choice

Bar charts are particularly useful for showing change over time.

• True

• False

Multiple Choice

The following bar chart shows the percent increase in the consumer price index for four three-month periods ending the date shown: In which quarter did the CPI increase the least, in percentage terms?

• the quarter ending July 2000

• the quarter ending October 2000

• the quarter ending January 2001

• the quarter ending April 2001

Multiple Choice

In a histogram, frequencies are represented by

• Lines

• Bars

• portion of the pie

• leaves

Multiple Choice

For the following histogram of test scores, The majority of scores came between

• 39.5 and 49.5

• 89.5 and 99.5

• 79.5 and 89.5

• 159.5 and 169.5

Fill in the Blank

Low-density lipoprotein (LDL) is an important part of blood cholesterol tests. LDL higher than 130mg/dl is a risk factor for developing cardiovascular disease. To prevent cardiovascular disease, a health center had a free blood cholesterol test for all the people older than 65 in the community. A total of eight people attended the blood screening and their blood test results are listed below: LDL(mg/dl): 130,143,114,110,123,110,134,124 After the blood test, the nurse wants to know the mean LDL score:

Fill in the Blank

Low-density lipoprotein (LDL) is an important part of blood cholesterol tests. LDL higher than 130mg/dl is a risk factor for developing cardiovascular disease. To prevent cardiovascular disease, a health center had a free blood cholesterol test for all the people older than 65 in the community. A total of eight people attended the blood screening and their blood test results are listed below: LDL(mg/dl): 130,143,114,110,123,110,134,124 After the blood test, the nurse wants to know the mode of LDL scores:

Fill in the Blank

Low-density lipoprotein (LDL) is an important part of blood cholesterol test. LDL higher than 130mg/dl is a risk factor of developing cardiovascular disease. To prevent cardiovascular disease, a health center had a free blood cholesterol test for all the people older than 65 in the community. A total of eight people attended the blood screening and their blood test results are listed below: LDL(mg/dl): 130,143,114,110,123,110,134,124 After the blood test, the nurse wants to know the range of LDL scores:

Fill in the Blank

Low-density lipoprotein (LDL) is an important part of blood cholesterol test. LDL higher than 130mg/dl is a risk factor of developing cardiovascular disease. To prevent cardiovascular disease, a health center had a free blood cholesterol test for all the people older than 65 in the community. A total of eight people attended the blood screening and their blood test results are listed below: LDL(mg/dl): 130,143,114,110,123,110,134,124 After the blood test, the nurse wants to know the variance of LDL scores

Fill in the Blank

Low-density lipoprotein (LDL) is an important part of blood cholesterol test. LDL higher than 130mg/dl is a risk factor of developing cardiovascular disease. To prevent cardiovascular disease, a health center had a free blood cholesterol test for all the people older than 65 in the community. A total of eight people attended the blood screening and their blood test results are listed below: LDL(mg/dl): 130,143,114,110,123,110,134,124 After the blood test, the nurse wants to know the standard deviation of LDL scores

Multiple Select

Which of the following are measures of central tendency? Select all that apply

• mean

• median

• mode

• variance

• standard deviation

Multiple Choice

Janelle and Rhodz are discussing how the mean value and variance affect the distribution graph. As the following graph shows, there are two distributions: A and B. Rhodz said that distribution A has a fatter tail because it has a bigger standard deviation than the distribution B. Janelle's answer is different: she thinks the distribution A has a smaller standard deviation than the distribution B. Who do you think is right?

• Rhodz

• Janelle

• None of them are right. Distribution A and Distribution B have the same standard Deviation

Multiple Choice

Sometimes we need to use median instead of mean to better measure central tendency in a sample if

• The sample has a large variance

• The distribution is extremely right-skewed

• We have measurement error when collecting the sample

• The sample mean is too small

Multiple Choice

In a bell-shaped distribution, changing ___can make the distribution flatter (i.e. more compressed); and changing ___ can shift the distribution to the left or to the right.

• Variance, mean

• Mean, variance

• Range, standard deviation

• Mode, range

• Mean, range

Multiple Choice

If a distribution is left-skewed, its mean is usually___ its median

• bigger than

• smaller than

• equal to

• we can not know

Multiple Choice

In a normal distribution, the median is ____it’s mean and mode.

• Approximately equal to

• Bigger than

• Smaller than

• Unrelated to

Multiple Choice

What is the best measure of central tendency for the following set of numbers? 98,78,56,23,587

• Mean

• Mode

• Median

• Standard deviation

Multiple Choice

In a normal distribution, __ percentage of the area under the curve is within one standard deviations of the mean?

• 68%

• 100%

• 95%

• It depends on the values of the mean and standard deviation

Multiple Choice

The difference between interval and ratio scales of measurement is that interval scales

• Do not have magnitude.

• Do not have equal intervals.

• Do not have absolute zeros.

• Do not have categorical organization of scores

Multiple Choice

Find the mean, median, and mode for the following sample of score: 6, 2, 4, 1, 2, 2, 3, 4, 3, 2.

• The mean is 2.9, the median is 2.5, and the mode is 2.

• The mean is 3, and the median is 3, and the mode is 3.

• The mean is 4, and the median is 2, and the mode is 2

• The mean is 3, and the median is 2.5 and the mode is 2.

Multiple Choice

This is the most widely used measure of variability that refers to how close or far away the scores are from the mean.

• Mean

• Range

• Mode

• Standard deviation

Multiple Choice

For df = 15, find the values of t associated with the top 5% of the distribution

• t = +1.753

• t = +/-2.947

• t = +/- 2.131

• t = -2.131

Multiple Choice

Find the t values that form the boundaries of the critical region for a two tailed test with α = .05 for a sample size of 12.

• t = +/-2.571

• t = +/-2.069

• t = +/-2.201

• t = -2.201

Multiple Choice

A teacher who used a normal curve in describing the scores of her students at an achievement test saw that there were more students who got low scores than high scores. What does this tell us?

• The curve is positively skewed

• The curve is negatively skewed

• The curve is a normal curve

• The curve is platykurtic

Multiple Choice

Consider the following scores and their corresponding z-scores: Reading – 24, z=1.02; Math – 42, z= 1.02. What can we conclude from this presented information?

• The performance in relation to the norm is the same.

• Though the score on math is higher, the performance in reading in relation to the norm is higher.

• Though the score on reading is lower, the performance in math in relation to the norm is higher.

• Though the z-scores are the same, the difference in raw scores call for a calculation of the T-score

Multiple Choice

In statistics, the Roman letter S refers to ____________

• The variance of a population

• The variance of a sample

• The standard deviation of a population

• The standard deviation of a sample.

Multiple Choice

ANOVA is a statistical procedure that compares two or more treatment conditions for differences in variance

• True

• False

Multiple Choice

What happens to the value of F-ratio if differences between treatments are increased? What happens to the F-ratio if variability inside the treatments is increased?

• As differences between treatments increases, the F ratio increases.

• As variability within treatments increases, the F-ratio decreases.

• As differences between treatments increases, the F ratio decreases.

• a and b is correct

Fill in the Blank

A researcher obtains F=4.18 with df = 2, 15. Is this value sufficient to reject the null hypothesis with alpha level 0.05?

Fill in the Blank

Imagine an experiment with 8 groups and within each group there are 25 subjects. The sum of squares total is equal to 200, and the sum of squares condition is equal to 120. What would the F-ratio be?

Multiple Select

Which of the following assumptions is required to conduct an ANOVA test? (Select all that apply)

• The populations have the same variance for the variable of interest

• The populations are normally distributed for the variable of interest

• Each value is sampled independently from each other value for the variable of interest

• The populations have difference variances for the variable of interest

• The populations have the same mean for the variable of interest

Fill in the Blank

The singular form of the word “dice” is “die”. Tom was throwing a six-sided die. The first time he threw, he got a three; the second time he threw, he got a three again. What’s the probability of getting a three at the third time?

Multiple Choice

Corazon scored on the 79th percentile in an intelligence test. This would suggest that

• Corazon scored 79% correct on all items in the test

• Corazon scored highly on the exam

• Corazon is the 79th person who scored the highest score

• Corazon score is better than 79% of the takers

Multiple Choice

Suppose there were 50 people in your class and you obtained the 20^th highest score. Your percentile rank would be ____________

• 20

• 50

• 40

• 60

Multiple Choice

When the variability of a group of data is high, you would expect that the graph would be

• Normal

• Platykurtic

• Skewed

• Leptokurtic

Multiple Choice

Arthur obtained a raw score of 120 on a history test where the class average was 116 and a SD of 7. He also obtained a raw score of 52 on a geography test where the mean was 48and the SD was 5.We can conclude that

• he did better on the history exam

• he did better on the geography exam

• he did equally well on both exams

• we need to know what the range of scores was

Multiple Choice

Student A got the following periodical examination scores; English = 75/105, Math = 79/110, & Science 100/120. How will you determine which among the three subjects she performed the weakest?

• By computing the z-scores

• By computing the standard deviation

• by computing the confidence interval

• None of the Above

Multiple Choice

Matet score on AbPsych and TOP in the board exam are 84 (M=65, SD=16) and 89 (M=74, SD=15) respectively. With this, we can say that

• There is a small difference, but Matet performed better in TOP than in AbPsych.

• There is a small difference, but Matet performed better in AbPsych than in TOP.

• There is a small difference, and so Matet performed equally well on both subjects.

• There is a small difference, so it doesn’t matter as long as Matet passed the board.

Multiple Choice

A curve that is skewed to the left would indicate that

• .More students got high scores than low scores

• More students got low scores than high scores

• Confounding variables altered the result of the test

• More students got scores closer to the average

Multiple Choice

The mean of a distribution of Z scores is always exactly

• 0

• 1

• 2

• 3

Multiple Choice

The standard deviation _______________

• Reflects the similarity among a set of scores

• Equals the sum of all scores minus the mean squared

• is an approximation of the average deviation around the mean.

• Always equals 0.

Multiple Choice

A Z score _________________

• Is the difference between a score and the mean, divided by the standard deviation

• Tells us how many standard deviations the score is below the average score.

• Tells us how many standard deviations the score is below the mean

• Is the standard deviations of a population.

Multiple Choice

The square root of the variance is the _________________.

• True variance

• Standard deviation

• mean

• variability of the population.

Multiple Choice

A researcher is comparing two new designs for cell phones by having a group of high school students send a scripted text message on each model and measuring the difference in speed for each student.

• Independent – measures experiment with two separate samples

• Repeated measures

• One sample test

• Matched subjects design

Multiple Choice

Assume that the data are from repeated measures study using the same sample of n = 6 participants in both treatment conditions. Compute the variance for the sample of difference scores and the estimated standard error for the mean difference.

• For the difference scores the variance is 24, the estimated standard error is 2.

• For the difference scores the variance is 25, the estimated standard error is 2.

• For the difference scores the variance is 24, the estimated standard error is 1.

• For the difference scores the variance is 25, the estimated standard error is 1.

Fill in the Blank

Imagine an experiment with 8 groups, and within each group there are 20 participants. How many degrees of freedom are there for the between subjects factor?

Multiple Choice

Which of the following is correct?

• An ANOVA conducted on a design in which there is only one factor is called a one-way ANOVA

• An ANOVA conducted on a design in which there is only one level is called a one-way ANOVA

• The factors in an ANOVA test are the dependent variables.

• We can only have within-subject factor; it is impossible to have between-subject factor

Multiple Choice

Which of the following description correct?

• When confounded sums of squares are apportioned to sources of variation, the sums of squares are called Type I sums of squares.

• In Type III sums of squares, confounded sums of squares are apportioned to sources of variation

• Type III sums of squares are always equal to type I sums of squares

• The null hypothesis of ANOVA test is that means of all groups are not equal.

Multiple Choice

Which of the following is correct?

• An ANOVA conducted on a design in which there is only one factor is called a one-way ANOVA

• An ANOVA conducted on a design in which there is only one level is called a one-way ANOVA

• The factors in an ANOVA test are the dependent variables.

• We can only have within-subject factor; it is impossible to have between-subject factor

Multiple Choice

If the arithmetic means of two sets of log-transformed data are equal, then the geometric means of the sets are _________ .

• Equal

• Zero

• One

• Unequal

Multiple Choice

A researcher collected BMI (Body Mass Index) of 50 students in an Engineering school. He found the mean BMI was much smaller than the median BMI. The reason for this might be___

• Several students had much smaller BMI scores than the other students

• Several students had much larger BMI scores than the rest

• The researcher made some measurement errors

• All the students had smaller BMI scores, compared to national average

Multiple Choice

Many statistical methods, such as t tests and the analysis of variance assume normal distributions. Transforming the distributions for these tests to reduce skew can markedly decrease their power.

• true

• false

Multiple Choice

When different subjects are used for the levels of a factor, the factor is called a____; when the same subjects are used for the levels of a factor, the factor is called a___.

• within-subjects factor; Between-subjects factor

• Between-subjects factor; Within-subjects factor

• Inter-subjects factor; repeated measures factor

• Repeated measures factor; inter-subject factor

Multiple Choice

The probability value for the F-ratio is a(an)___probability (Select all that apply)

• one-tailed

• two-tailed

• left-skewed

• right-skewed

Fill in the Blank

Imagine an experiment having three conditions and 20 subjects within each condition. The mean and variances of each condition are listed below. What’s the value of mean squares between groups (MSB)?

Fill in the Blank

10 students participate in Statistics quiz 2, their grades are:

98, 85,89,73,76,85,87,92,85,56

The professor wants to know the range of the grades

Multiple Choice

Sometimes we need to use median instead of mean to better represent the central tendency for a sampe if

• The distribution is extremely skewed

• The distribution has a bell shape

• The sample size is too small

Multiple Choice

When the same subjects are used for the levels of the factor, the factor is called a ___

• Within-subjects factor

• Inter-subject factor

• Between subjects factor

• Repeated measures factor

Multiple Choice

The shape of the F-statistic distribution is___

• Normal distributed

• Positive skewed

• Negative skewed

• Binominal distributed

Multiple Choice

As the sample size increases, we can tell

• The sample distribution of the means becomes increasingly skewed

• The sample distribution of the means is approaching a normal distribution

• The sample distribution of the mean is less and less predictable

• the sample distribution of the mean is approaching the distribution of the population

Fill in the Blank

In a school with 3000 students, 2900 of them had driver licenses. If you take a sample of 20 of them, what’s the standard error of the proportion (p) of those who had licenses?

Fill in the Blank

A toy factory makes 5,000 teddy bears per day. The supervisor randomly selects 10 teddy bears from all 5,000 teddy bears and uses this sample to estimate the mean weight of teddy bears and the sample standard deviation. How many degrees of freedom are there in the estimate of the standard deviation?

Fill in the Blank

A researcher tries to compare grades earned on the first quiz by boys and girls. He randomly chooses 10 students from boys and 15 students from girls and calculates the confidence interval on difference between means. How many degrees of freedom will you get in this t distribution?

Multiple Choice

Which of the following assumptions is NOT required to conduct an ANOVA test?

• The populations have the same variance for the variable of interest

• The populations are normally distributed for the variable of interest

• Each value is sampled independently from each other value for the variable of interest

• The populations have the same mean for the variable of interest

Multiple Select

Imagine a researcher designed an experiment with 5 groups, and within each group, there were 120 participants. The sum of squares total was equal to 30 and the sum of squares condition was equal to 15. If this researcher uses an ANOVA test to see if all the groups had the same outcome, he could conclude: (Select all that apply)

• He should reject the null hypothesis

• He failed to reject the null hypothesis

• The probability was smaller than 0.05

• The F-ratio was 600

Fill in the Blank

In a two-factor ANOVA test, if one variable has 8 levels and the other has 3 levels, how many degrees of freedom are there for the interaction?

Multiple Choice

A researcher believed that there was a difference in the amount of time boys and girls at 7th grade studied by using a two-tailed t test. Which of the following is the null hypothesis?

• Mean of hours that boys studied per day was equal to mean of hours that girls studied per day

• Mean of hours that boys studied per day was greater than mean of hours that girls studied per day

• Mean of hours that boys studied per day was smaller than mean of hours that girls studied per day

• Mean of hours that boys studied per day was smaller than or equal to mean of hours that girls studied per day

Multiple Choice

A researcher believed that women in their 20s drank more soda per day than men. Which of the following was the null hypothesis?

• The amount of Soda women drank per day was greater than the amount of Soda men drank per day

• The amount of Soda women drank per day was equal to the amount of Soda men drank per day

• The amount of Soda women drank per day was smaller than the amount of Soda men drank per day

• The amount of Soda women drank per day was greater than or equal to the amount of Soda men drank per day

Fill in the Blank

Imagine an experiment with 7 groups and within each group there are 120 participants. The sum of squares total is equal to 100 and the sum of squares condition is equal to 40. What is the mean square within (MSE)?

Fill in the Blank

Imagine an experiment with 7 groups and within each group there are 120 participants. The sum of squares total is equal to 100 and the sum of squares condition is equal to 40. What is the mean square within (MSE)?