Stats test 1

If a person rolls a fair die, what is the probability that a number 0 will come up?

0

How many possible combination outcomes consist of two heads when you toss a fair coin four times? (6.25 points) a. 4 b. 5 c. 6 d. 7 e. None of these

c. 6 Correct Answer

If a person rolls a fair die, what is the probability that an odd number will come up?

.5

If a person tosses two coins, what is the probability that one head and one tail will come up?

.5

If a person tosses two coins, what is the probability that two heads will come up?

1/4

If a person rolls a die, what is the probability that the number 5 will come up?

1/6

If a person rolls two fair dice, what is the probability that doubles (two of the same numbers) will come up

1/6

If a person picks randomly a Month from the above Tornado data, what is the probability that this will be a month that has 31 days? a. 1 b. 10/12 = 5/6 c. 7/12 d. 6/12 = 1/2

7/12

If one randomly picks two different months from the Tornado data list. What is the probability that they both are winter months? a. 1/12 b. 2/12 c. 3/66

3/66

If a person randomly picks a month from the above Tornado data, what is the probability that this will be a summer month?

Correct answer: There are 12 different months and three of them are summer months {June, July, August}. Thus the probability is 3-out-of-12=3/12=1/4.

If a person rolls a die, what is the probability that an even number will come up?

Correct answer: 1/2, out of six possible outcomes from a die, three will produce an even number, thus: 3/6=1/2

If a person rolls two dice, what is the probability that two sixes come up (that is 6 & 6)?

Correct answer: 1/36, when two dice are rolled we can expect 36 possible outcomes {(1,1),(1,2),....(6,5),(6,6)}, thus 1/36.

If one randomly picks two different months from the Tornado data list, what is the probability that they both are winter months? (Dec.Jan.Feb)

Correct answer: 3/66=1/22. Just observe that on the Table there are 66 different 2-month pairs and only 3 of these pairs satisfy the requirement (Dec-Jan, Dec-Feb, Jan-Feb).

If one randomly picks two different months from the Tornado data list, what is the probability that their Correlation will be negative? Hint: Check the correlation table.

Correct answer: 9/66=3/22. Again, out of 66 2-month pairs only 9 have negative correlation.

Pick at random any two (different) months. What is the probability that both months are summer months?

Correct answer: From the Table in Task 1, we can see that one could end up with any of the 66 such picks. All we need now is to check which of these satisfy the criteria: summer months. And here they are: {(June, July), (June, August), (July, August)}. There are three such combinations, thus the probability is 3/66=1/22.

If a person rolls two dice, what is the probability that the sum of the numbers is equal to 11?

Correct answer: If one lists all possible 2-die outcomes {(1,1),(1,2),.....,(6,6)} one gets 36 combinations. However, only these two pairs {(5,6),(6,5)} yield the desired sum of 11. Thus the answer is 2/36=1/18.

If a person tosses three coins, what is the probability that he will not have any Tails?

Correct answer: If one lists all possible 3-coins outcomes {(H,H,H), (H,H,T),(H,T,H),...,(T,T,T) } one realizes that there are 8 such outcomes and only one-out-of-eight has no Tails . Thus the answer is 1/8.

A person picks a pair of months, where the first one is always chronologically before the second. How many different pairs are there?

Correct answer: Just count the entrees in the Correlation table in Task 1 (and do not count the diagonal, all "1" entrees). There are 66 of them.

If a person rolls two dice, what is the probability that the number on the first die is three times as large as the number on the second die?

Correct answer: Since we have the list of all outcomes (i.e. sample space) the answer is easy. We just need to list the cases of interest: {(3,1), (6,2)}, and observe that there are just two such cases. Thus the probability is 2/36=1/18.

If a person randomly picks a year from the above Tornado data, what is the probability that this year will be prior to 1960?

Correct answer: There are 45 years in the Tornado data, from 1950 till 1994. And exactly ten of those years are prior to 1960. They are the years {1950,1951,...,1959}. Thus the probability is 10-out-of-45=10/45=2

If a person tosses three coins, what is the probability that the number of heads is equal to 2?

Correct answer: There are eight different ways for three coins to come up {(H,H,H), (H,H,T),(H,T,H),(H,T,T), (T,H,H), (T,H,T),(T,T,H),(T,T,T)}, where T stands for Tails and H for Heads. Clearly, the three particular outcomes {(H,H,T),(H,T,H),(T,H,H)} have two heads. Thus the probability is 3-out-of-8=3/8.

If a person tosses three coins, what is the probability that there are more Tails than Heads?

Correct answer: We just learned that there are 8 possible outcomes and they are all listed above. Thus, one only needs to count the cases where there are more Tails than Heads. And here they are: {(H,T,T), (T,H,T),(T,T,H),(T,T,T)}. Clearly we have 4 such cases, thus the probability is 4-out-of-8=4/8=1/2.

If a person rolls two dice, what is the probability that the sum of the numbers is equal to 4?

First we must discuss the space of all outcomes, also called sample space.In this case, it consists of all the pairs of the following type:(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)A careful count yields 36 possible outcomes.Next we check for which outcomes we have that the sum of the numbers equal to 4. And here they are:{ (1,3),(2,2),(3,1)}. Thus the answer is 3-out-of-36=3/36=1/12.

Given the two data uploaded in this lecture, the Height-Weight-Gender data as well as the US Crime data, answer the following questions: Which, if any, of the two data files was collected using the random sampling method? Which, if any, of the two data files was collected using the Census method?

Height-Weight-Gender The US Crime Data

In Statistics, we distinguish data by their types: Categorical or Numerical. The latter are often differentiated into Integer data, (whole numbers like 1, 5, 14,.. ) or Real numbers (like 2.33 or 4.35). An example of Integer data would be the number of credits a student has taken and an example of Real data type would be the student's GPA. Categorical data are non-numerical data. For example, imagine that someone wants to make a statistical analysis of students' names. The list of all these names would be characterized as the categorical data. Typically, one would transform these names into the appropriate list of numbers. For example there were 45 Roberts, 22 Toni's ect. Discrete are whole #'s

T

How many possible combination outcomes consist of at least three tails when you toss a fair coin four times? (6.25 points) a. 3 b. 4 c. 5 d. 6 e. None of these

c. 5 Correct Answer

Which of the following is FALSE? a. The rule of thumb suggests that 95% of data are within 2 Standard Deviations from the mean. b. The rule of thumb suggests that 65% of data are within 1 Standard Deviations from the mean. c. The rule of thumb suggests that 95% of data are within 4 Standard Deviations from the mean. d. The standard deviation tells us, roughly, how much the data deviate from the average.

The rule of thumb suggests that 95% of data are within 4 Standard Deviations from the mean

95% of data are within the interval

[Average - 2*St Dev, Average + 2*StDev]

65% of data are within the interval

[Average - StDev, Average + StDev]

13. What is the probability of you getting no heads at all for tossing a fair coin three times? (6.25 points) a. 1/2 b. 1/4 c. 1/8 d. 1/16

c. 1/8 Correct Answer

What is the probability of you getting three heads straight for tossing a fair coin three times? (6.25 points) a. 1/2 b. 1/4 c. 1/8 d. 1/16

c. 1/8 Correct Answer

If a person rolls two dice, what is the probability that the sum of the numbers is equal to 11? a. 1/18 b. 2/6 c. 1/36

a. 1/18 Correct Bonus Answer

If a person tosses three coins what is the probability that he will not have any Tails? a. 1/8 b. 2/8 c. 1/2

a. 1/8 Correct Bonus Answer

14. How many possible combination outcomes are there when you toss a fair coin four times? (6.25 points) a. 8 b. 16 c. 24 d. 32 e. None of these

b. 16 Correct Answer

If a person picks a pair of different Months, what is the probability that both months(different) have 31 days? a. 18/66 b. 21/66 c. 28/66 d. 31/66

b. 21/66 Correct Answer

If one randomly picks two different months from the Tornado data list. What is the probability that their Correlation will be negative? (Hint: Check the correlation table.) a. 2/66 b. 9/66 c. 1/18

b. 9/66 Correct Bonus Answer

. For a linear equation, y = - 4x -2, what is the y-intercept and what is the algebraic definition of it? (5 points) a. The y-intercept = 2. It is the y-coordinate of a point where the graph of y = - 4x -2 cuts across the y-axis at (0,2) b. The y-intercept = - 2. It is the y-coordinate of a point where the graph of y = - 4x -2 cuts across the y-axis at (0,-2) c. The y-intercept = 2. It is the y-coordinate of a point where the graph of y = - 4x -2 cuts across the y-axis at (2,0) d. The y-intercept = - 2. It is the y-coordinate of a point where the graph of y = - 4x -2 cuts across the y-axis at (-2,0)

b. The y-intercept = - 2. It is the y-coordinate of a point where the graph of y = - 4x -2 cuts across the y-axis at (0,-2) Correct Answer

Which of the following is TRUE? a. The mean tells us, roughly, how much the data deviate from the average. b. The mean is the more reliable measure of center because it is not affected by extreme values ( outliers) c. The Mean of Normal Distribution is related to the average of the data set. The Standard deviation is related to data variation. d. The standard deviation is calculated by adding the data values and dividing the total by the number of data values.

c. The Mean of Normal Distribution is related to the average of the data set. The Standard deviation is related to data variation.

For a linear equation, y = - 4x -2, what is the slope and what is the algebraic definition of it? (5 points) a. The slope = -4x. For each unit increase of x, y decreases by -4. b. The slope = -4x. For each unit increase of y, x decreases by -4. c. The slope = -4. For each unit increase of x, y decreases by -4. d. The slope = -4. For each unit increase of y, x decreases by -4

c. The slope = -4. For each unit increase of x, y decreases by -4. Correct Answer

3. Which of the following statement is true? (5 points) a. A line with a positive slope is rising from right to left, a line with a negative slope is falling from right to left, and a horizontal line neither rises nor falls and has no slope. b. A line with a positive slope is rising from left to right, a line with a negative slope is falling from left to right, and a horizontal line neither rises nor falls and has no slope. c. A line with a negative slope is rising from left to right, a line with a positive slope is falling from left to right, and a horizontal line neither rises nor falls and has a slope of zero. d. A line with a positive slope is rising from left to right, a line with a negative slope is falling from left to right, and a horizontal line neither rises nor falls and has a slope of zero.

d. A line with a positive slope is rising from left to right, a line with a negative slope is falling from left to right, and a horizontal line neither rises nor falls and has a slope of zero.

Which of the following is TRUE? a. For a data set with mean = 25 pounds and Standard Deviation = 2 pounds then 95% of the data is between 23 pounds and 27 pounds. b. For a data set with mean = 25 pounds and Standard Deviation = 3 pounds then 95% of the data is between 22 pounds and 28 pounds. c. For a data set with mean = 25 pounds and Standard Deviation = 3 pounds then 65% of the data is between 19 pounds and 31 pounds. d. For a data set with mean = 25 pounds and Standard Deviation = 3 pounds then 95% of the data is between 19 pounds and 31 pounds

d. For a data set with mean = 25 pounds and Standard Deviation = 3 pounds then 95% of the data is between 19 pounds and 31 pounds

Which of the following is FALSE? a. When an outlier is present, the median is probably the best measure of center to represent the data. b. If the number of data values is odd, the median is the number located in the middle of data set when the data values are arranged in order. c. If the number of data values is even, the median is found by calculating the mean of the two middle numbers when the data values are arranged in order. d. The median is very sensitive to extreme values (outliers).

d. The median is very sensitive to extreme values (outliers).

Which of the following statements is FALSE? (5 points) a. The standard deviation is a measure of how far, on average, the data values deviate from the mean. b. The value of the standard deviation can increase dramatically with the inclusion of one or more outliers (data values that are very far away from all of the others). c. If all values of a data set are the same, the standard deviation is zero (because each value is equal to the mean). d. The value of the standard deviation is usually positive. It is only negative when most values in the data set are less than the mean.

d. The value of the standard deviation is usually positive. It is only negative when most values in the data set are less than the mean.

What are the possible combination outcomes when you toss a fair coin three times? (6.25 points) H = Head, T = Tail a. {HHH, TTT} b. {HHH, TTT, HTH, THT} c. {HHH, TTT, HTH, THT, HHT, TTH, THH} d. {HHH, TTT, HTH, THT,HHT, TTH, THH, HTT} e. None of these

d. {HHH, TTT, HTH, THT,HHT, TTH, THH, HTT} Correct Answer