Midterm Quizzes Practice

A normal distribution with a mean of 25 and a standard deviation of 5. What is the corresponding Z score for a case having a value of 10? A. -3 B. 0 C. 1 D. -15

A. -3 (10-25)/5=-3 please refer to the z score calculation

The mean of a standard normal distribution is: A. 0 B. 1.0 C. -1.0 D. 100

A. 0

Alice tossed a six-sided die three times. What's the probability that she gets ones (number 1 upside) on all three throws? A. 0.00463 B. 0.08 C. 1/6 D. 1/2

A. 0.00463

Jason got a bag full of colorful jelly beans. There were 40 of them: 10 were red, 4 were yellow, 5 were orange, and 21 were blue. After shaking the bag, he randomly selected two jelly balls from the bag. What's the probability that the first one was yellow and the second one was also yellow? A. 0.0077 B. 0.001 C. 0.005 D. 0.053

A. 0.0077

Nick got a bag full of colorful jelly beans. There were 40 of them: 10 were red, 4 were yellow, 5 were orange, and 21 were blue. After shaking the bag, he randomly selected two jelly beans from the bag. What's the probability that the first one was yellow and the second one was red? A. 0.026 B. 0.1 C. 0.39 D. 0.05

A. 0.026

If you throw a six sided die twice, what is the probability that you will get a one on the first throw or a two on the second throw? A. 0.306 B. 0.5 C. 1/6

A. 0.306 Solution: define event A as number 1 upside, and event B as number 2 upside. Then the question is P(A or B). You can find this calculation in slide 22 of the ppt. P(A or B)=P(A)+P(B)-P(A and B)=1/6+1/6-1/36=12/36-1/36=11/36=0.305555556=0.306

If the base rate of the disease is 4%, the false positive rate is 6%, the miss rate is 2% What is the probability that you have the disease given that the test was positive? A. 0.4 B. 0.2 C. 0.6 D. 0.8

A. 0.4 For the current example, the event is that you have Disease X. Let's call this Event D. Base rate means that 4% of people have Disease X, the prior probability of Event D is 0.04. P(D) = 0.04. If P(D') represents the probability that Event D is false (the probability of who do not have the disease), then P(D') = 1 - P(D) = 0.96. To define the diagnostic value of the test, another event is defined: that you test positive for Disease X. Let's call this Event T. The diagnostic value of the test depends on the probability you will test positive given that you actually have the disease, written as P(T|D), and the probability you test positive given that you do not have the disease, written as P(T|D'). Bayes' theorem shown below allows you to calculate P(D|T), the probability that you have the disease given that you test positive for it. The miss rate means you have 2% probability to get false test that you actually have the disease. Therefore, the positive test given that you actually have the disease is P(T|D). P(T|D) =1-0.02=0.98. The false positive rate means the rate of people who have positive test given actually having no disease. P(T|D') =0.06. Using the formula for Bayes' Theorem presented in this section, the probability that you have the disease given that you tested positive is: P(D|T) = [(0.98)(0.04)]/[(0.98)(0.04) + (0.06)(.96)] = .40

Consider a normal distribution with a mean of 10 and a standard deviation of 25. What's the Z score for the value of 35? A. 1 B. 5 C. 25

A. 1

The area under the curve of a probability distribution is A. 1 B. 0.5 C. 0.9 D. 2

A. 1

Mary was tossing a coin. She tossed three times. What's the probability that at the first toss she got a head, the second toss she got a tail at and the third time she got a tail? A. 1/8 B. 0.2 C. 0.5 D. 3/8

A. 1/8

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 mode of LDL scores: A. 110 B. 110.6 C. 120 D. 140

A. 110

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 median LDL score: A. 123.5 B. 124.7 C. 152.3 D. 114

A. 123.5

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 A. 141.1429 B. 111.1623 C. 116 D. 118.8712

A. 141.1429

For a standard normal distribution, what's the probability of getting a positive number? A. 50% B. 95% C. 68% D. We cannot tell from the given information

A. 50% For a standard normal distribution, half is positive number and half is negative number. The mean of standard normal distribution is 0.

Imagine a city with 50,000 people. Twenty percent of the population consists of children younger than five years of age. For children under five years old, the base rate of malnutrition is 6%. How many children under five years of age in that city are malnourished? A. 600 B. 1000 C. 10000 D. 6000

A. 600

In a normal distribution, __ percentage of the area under the curve is within one standard deviation of the mean? A. 68% B. 100% C. 95% D. It depends on the values of the mean and standard deviation.

A. 68%

Hans scored 16 points above the mean with a z-score of +2.00. What was the standard deviation for the distribution? A. 8 B. 14 C. 18 D. 32

A. 8

Fifty students took an Introduction to Chemistry exam. Assume that their scores formed a normal distribution with a mean of 80 and a 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? A. 88 B. 86 C. 80 D. 84

A. 88

Consider a normal distribution with a mean of 25 and a standard deviation of 4. Approximately, what proportion of the area lies between values of 17 and 33. A. 95% B. 68% C. 99% D. 50%

A. 95%

Which of the following description of distribution is correct? A. A Binomial distribution is a probability distribution for independent events for which there are only two possible outcomes B. You cannot use the normal distribution to approximate the binomial distribution C. Normal distributions cannot differ in their means and in their standard deviations. D. Standard normal distributions can differ in their means and in their standard deviations.

A. A Binomial distribution is a probability distribution for independent events for which there are only two possible outcomes Normal distributions can differ in their means and in their standard deviations. The standard normal distribution has a constant mean value (0) and standard deviation (1).

In a normal distribution, the median is ____it's mean and mode. A. Approximately equal to B. Bigger than C. Smaller than D. Unrelated to

A. Approximately equal to

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: A. Descriptive statistics B. Inferential statistics

A. Descriptive statistics

theoretical probability distributions is ___________. A. Parametric distribution B. non-parametric distribution

A. Parametric distribution

Which of the following statements is NOT true regarding z-scores? A. They describe an average amount that an entire distribution of scores deviates from the mean. B. They describe how far a particular raw score deviates from the mean. C. They are in standard deviation units. D. Negative z-scores reflect deviations below the mean.

A. They describe an average amount that an entire distribution of scores deviates from the mean.

A frequency distribution contains the frequency of every value in the distribution. A. True B. False

A. True

A non-parametric distribution has no assumption made about the distribution. A. True B. False

A. True

Bernoulli distribution is simply a binomial distribution with the parameter n equal to 1. A. True B. False

A. True

The numerator in the formula for a z-score is A. a deviation score. B. the standard deviation. C. SS D. sum up (square(X))

A. a deviation score.

In statistics, a population is made up of: A. an entire group with something in common B. a subset of a larger group C. the entire world D. the individuals chosen to be in an experiment

A. an entire group with something in common

Probability "mass" function is for____ distribution A. discrete B. continuous

A. discrete

The probability P(x;n)=1/n is A. discrete distribution B. uniform distribution C. continuous distribution D. binomial distribution if n=2

A. discrete distribution or B. uniform distribution

In statistics, a sample is made up of: A. subset of a larger group B. the entire world C. the citizens of a specific location D. an entire group with something in common

A. subset of a larger group

If someone obtains a z-score close to 0, that would indicate that A. the person scored close to the mean. B. the person scored very low. C. there was very little variability in the distribution. D. the person scored better than most.

A. the person scored close to the mean.

The t-distribution is a ______________ distribution whose shape changes according to the ________________. A. theoretical; size of the sample B. empirical; size of the sample C. theoretical; standard deviation D. empirical; standard deviation

A. theoretical; size of the sample

Two events, what does "A or B" mean? A. union B. intersect C. Event A but not B

A. union

Which of the following endings is NOT true: Studying statistics is important because doing so... A. will answer all of the important questions about life. B. allows me to remain abreast of new developments in my field of study. C. is how we gain knowledge about people and the world around us. D. enhances my critical thinking skills.

A. will answer all of the important questions about life.

You are at the doctor's office and have just tested positive for a disease. The test accurately indicates the disease in 98% of the people who have it. What is the miss rate (probability of a miss)? A. 0.04 B. 0.02 C. 0.98 D. more information is needed

B. 0.02 Misses occur when this test inaccurately indicates that the person doesn't have the disease when he/she really does. 1 - .98 = .02

The test accurately indicates the disease in 98% of the people who have it, and it accurately indicates no disease in 94% of the people who do not have it. What is the false positive rate (probability of a false positive)? A. 0.02 B. 0.06 C. 0.04 D. 0.01

B. 0.06 1-94%=6%=0.06 98% is the base rate. The false positive rate means the rate of people who have positive test given actually having no disease.

The mean of a z-score distribution is _________ and the standard deviation is __________. A. 1; 0 B. 0; 1 C. 100; 1 D. 1; 100

B. 0; 1

The standard deviation of the mean for a standard distribution is: A. 0.0 B. 1.0 C. 100 D. 68%

B. 1.0

For the scores 3, 5, 8, 10, 14, 17, 21, 25, calculate the 50th percentile using the following formula: R = P/100 x (N + 1) A. 10 B. 12 C. 14 D. 12.5

B. 12

For a normal distribution with a mean of 16 and a standard deviation of 2, what's the probability of getting a number greater than 20? A. 2.5 B. 2.5% C. 25% D. 2

B. 2.5%

If the sample size for both groups in an independent samples t-test is n = 15, what degrees of freedom should be used? A. 30 B. 28 C. 29 D. 14

B. 28

A distribution has mean = 40 and standard deviation = 5. Yan scored two standard deviations above the mean. Yan's score was ________. A. 45 B. 50 C. 55 D. 60

B. 50

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? A. 25% B. 50% C. 75% D. We need to calculate the standard deviation and then decide.

B. 50%

A distribution has a mean = 46 and a standard deviation = 4. What is the equivalent raw score for a person with a z-score of 1.5? A. 54 B. 52 C. 50 D. 40

B. 52

Imagine that 200 people who did not have Hepatitis C participated in a Hepatitis C screening. The screening indicated that 92.3% of them had a negative test result. What's the false positive rate? A. 17.7% B. 7.7% C. 77 D. 77%

B. 7.7%

A large pool has 50 green balls and 50 red balls. You randomly draw one ball, what is the probability that the ball is green. What distribution is used to answer this question? A. Normal distribution B. Bernoulli distribution C. Binomial distribution when the parameter n is 2 D. Poisson distribution when the parameter u is 1

B. Bernoulli distribution

Suppose a random experiment with exactly two outcomes is repeated n times independently. The probability of success is p and that of failure is q. Assume that out of these n times, we get success for x times and failure for the remaining i.e., n−x times. This random variable X is ____distribution. A. Normal B. Binomial C. Gaussion D. Uniform

B. Binomial

A normal or bell-shaped distribution has the greatest probability density in its tails. A. True B. False

B. False

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? A. Kids are not waiting 40 minutes after eating to swim B. In summer both ice cream consumption and swimming increases C. A full stomach makes it harder to swim

B. In summer both ice cream consumption and swimming increases

Uncertainty regarding conclusions about a population can be eliminated if you do the following: A. Use a large random sample B. Obtain data from all members of the population C. Depend upon the t-distribution D. Both a and b

B. Obtain data from all members of the population Using a large random sample cannot eliminate the uncertainty, it may reduce the uncertainty.

A discrete variable is _____ A. One that can take on any value in a certain range B. One that can only take on a finite number of values

B. One that can only take on a finite number of values

A normal distribution with a mean of 15 and standard deviation of 5. 95% of its area is within__ A. One standard deviation of the mean B. Two standard deviations of the mean C. Three standard deviations of the mean D. It depends on the value of the mode

B. Two standard deviations of the mean Three rules: 68-95-99.7 (one standard deviation of the mean, two standard deviations of the mean, three standard deviations of the mean)

A z-score provides information about A. the distribution's overall variability. B. a person's relative position in a distribution. C. the most representative value in a distribution. D. the range of scores in a distribution.

B. a person's relative position in a distribution.

Measures of central tendency A. indicate how much the scores vary from one another. B. describe the most typical score in an entire distribution. C. indicate the most frequently occurring score in a distribution of scores. D. all of the above are true.

B. describe the most typical score in an entire distribution.

A symmetric distribution A. has equal positive and negative skews. B. has no skew. C. can have either positive or negative skew, but not both.

B. has no skew.

Two events, what does "A and B" mean? A. union B. intersect C. Event A but not B

B. intersect

Which measure of central tendency should a researcher use to describe the most representative gender in a study? A. median B. mode C. mean D. standard deviation

B. mode

To determine which measure of central tendency to use, we need to identify A. the independent variable(s) and dependent variable. B. the shape of the distribution and the scale of measurement. C. the extraneous variables. D. the standard deviation.

B. the shape of the distribution and the scale of measurement.

The denominator in the formula for a z-score is A. a deviation score. B. the standard deviation. C. SS D. sum up (X2)

B. the standard deviation.

In a university with 3650 students, the professor wanted to know the probability that at least two students shared the same birthday. The probability will be: A. 0.1 B. Much smaller than 0.1 C. Much bigger than 0.1 D. Not possible

C. Much bigger than 0.1 Solution: At least two students share the same birthday (event A); students don't share any same birthdays (Event B), P(A)+ P(B)=1, P(A)=1-P(B) . What do you think about the probability of no one among 3650 sharing any same birthday with any other? Not possible because there are only 365 days in a year. All the 3650 students cannot have distinct birthdays for each one. So, P(B) (students don't share any same birthdays (Event B)) is 0. Then P(A) is 1. 1 is much larger than 0.1.

All of the following are true of the mode, except that it A. ignores all other scores. B. lacks stability. C. is the frequency of the highest score. D. can change dramatically if one score changes.

C. is the frequency of the highest score.

An unscrupulous CEO of a large tech company is recruiting for new hires. The top few executives in the company earn huge salaries, but most of the other employees earn salaries that are quite a bit lower. Since he wants to make a good impression, which measure of central tendency does the CEO report to the potential new hires? A. mode B. median C. mean D. standard deviation

C. mean

Which is the only measure of central tendency that takes all score values into consideration? A. mode B. median C. mean D. standard deviation

C. mean

The df value for an two independent samples t-test is A. n - 1. B. n -2. C. n1 + n2 -2 D. n1 +n2

C. n1 + n2 -2

The mean, mode, and median will all be in the same location in a A. positively skewed distribution. B. negatively skewed distribution. C. normally shaped distribution. D. bimodal distribution.

C. normally shaped distribution.

To determine the mean for a set of scores, A. start by dividing the distribution of scores in half. B. start by looking for the most common score. C. start by adding up all of the scores in the distribution. D. multiply the sum of the scores by the total number of scores.

C. start by adding up all of the scores in the distribution.

A researcher using the amount of time to complete a task should use which measure of central tendency? A. the mean if the distribution is skewed B. the median if the scores are normally distributed C. the mean if the distribution is symmetrical D. the mode if the distribution is skewed

C. the mean if the distribution is symmetrical

The mean value of Poisson distribution is μ , what is the variance of Poisson distribution. Please note: u in the answer is μ . A. 2u (two times of mean value) B. 3u C. u D. sqrt(u)

C. u

The value ___ is subtracted to define "no kurtosis" as the kurtosis of a normal distribution. 1 2 3 4

3

The average number of homes sold by the Acme Realty company is 3 homes per day. What is the probability that exactly 4 homes will be sold tomorrow? A. 0.180 B. 0.156 C. 0.168 D. 0.234

C. 0.168

An exam has a mean of 75 and a standard deviation of 8. What exam score is 1.5 standard deviations above the mean? A. 83.5 B. 76.5 C. 87 D. 91

C. 87

Which of the following statements is NOT true of the sample mean? A. It is an unbiased estimate of the population mean. B. It takes every score value into consideration. C. It is a biased estimate of the population mean. D. It can be used for further statistical operations.

C. It is a biased estimate of the population mean.

Which of the following statements is true of the median? A. It takes all score values into consideration. B. It is biased by extreme scores in the distribution. C. It may not be an actual score. D. It is the measure of central tendency used most often in statistics.

C. It may not be an actual score.

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. A. It was very good, much better than almost all of the other students B. It was so-so but still better than half of the students. C. It was not that good, but not at the bottom of the distribution D. It was very bad and she needs to work much harder next time

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

Imagine a researcher has developed a new device for estimating blood alcohol content from a breath sample. Imagine that the new test accurately indicates a drunken condition in 95.6% of the people who are drunk. What's the miss rate? A. 14.4% B. 44% C. 0.44 D. 4.4%

D. 4.4%

A distribution has a mean of 100 and a standard deviation of 10. Sarah has a z-score of -2.00. What is her raw score? A. 120 B. 10 C. 90 D. 80

D. 80

Which of the following are measures of central tendency? A. mean B. median C. mode D. All of the choices

D. All of the choices

Which of the following is a quantitative variable? A. Gender B. Religion C. Ethnicity D. Average daily temperature

D. Average daily temperature

You find out that a test for a disease is 90% accurate. What is the probability that you have this disease? A. 90% B. 10% C. 45% D. Correct! more information is needed

D. Correct! more information is needed Before determining the probability, you need to consider more information, such as the base rate of the disease in the population and the frequency of misses and false positives.

Mutually Exclusive (you can't do both at the same time) Which is NOT true? A. Turning left and turning right are Mutually Exclusive B. Tossing a coin: Heads and Tails are Mutually Exclusive C. Draw a Card: Kings and Aces are Mutually Exclusive D. Draw a Card: Kings and Hearts are Mutually Exclusive

D. Draw a Card: Kings and Hearts are Mutually Exclusive

Which of the following pairs are NOT independent events? A. Flipping a coin twice B. Throwing a die twice C. Drawing a heart from a set of pokers card, putting it back, and then drawing another heart. D. Drawing a heart from a set of pokers card, not putting it back and then drawing a diamond.

D. Drawing a heart from a set of pokers card, not putting it back and then drawing a diamond.

Which of the following statements is true of the sample mean? A. It systematically overestimates the value of the population mean. B. It systematically underestimates the value of the population mean. C. It cannot be used to estimate the value of the population mean. D. It is an unbiased estimate of the population mean.

D. It is an unbiased estimate of the population mean.

A Biased sample is one that: A. Is too small B. Will always lead to a wrong conclusion C. Will likely have certain groups from the population over-represented or under-represented due only to chance factors D. Will likely have certain groups from the population over-represented or under-represented due only to systematic sampling factors

D. Will likely have certain groups from the population over-represented or under-represented due only to systematic sampling factors

If a person earned 98 points on an exam, you can be certain that A. the person did quite well. B. the person did quite poorly. C. the person passed with flying colors. D. more information is needed.

D. more information is needed.

Parameter and Statistic correspond for ___ and ____ A. sample, population B. mean and standard deviation C. standard deviation and mean D. population and sample

D. population and sample

The t-distribution is used if A. samples are larger than 60. B. the population mean is not known. C. the population standard deviation is known D. the population standard deviation is unknown.

D. the population standard deviation is unknown.

Which of the following are measures of variability? A. mean B. median C. mode D. variance

D. variance