Quantitative Methods Exam 2
The FDA is testing whether a new medication is effective in preventing strep throat. During a three-month period, the 100 randomly selected people in a treatment group take the medication while the 100 randomly selected people in a control group take a placebo. The results show that 10 people in the treatment group get strep throat, compared to 85 people in the control group. Can we conclude that the medication is effective in preventing strep? a) No, we cannot conclude this medication as being statistically significant enough to work b) There is not enough information to determine if we can conclude if the medication works c) Yes, we can conclude that the medication works as this is statistically significant d) It is statistically insignificant and needs further experimentation
6 [do you mean b?] is correct because there are much fewer cases of strep throat in the experimental group, showing statistical significance which helps conclude that the medication works.
What is the null hypothesis? a) the starting assumption for a hypothesis test b) a claim that the population parameter has a value different from that claimed c) A set of measurements or observations in a statistical study that is unlikely to have occurred by chance. d) All of the above
Correct answer: A, The null hypothesis is the starting assumption for a hypothesis test. Although other forms are possible, in this book we consider only null hypotheses that claim a specific value for a population parameter.
What does a z-score tell you? a) The standardized distance from the mean b) How far above the mean a number is c) How far below the mean a number is d) All of these could be considered correct
D is the correct answer because a z score describes a number by the standardized distance above or below the mean
) When trying to find symmetry in normal distribution, what are you trying to understand? a) Range b) Variable c) Mean d) Mode
The Correct Answer is C. Mean. Normal Distribution calculates the standard deviation from the mean
A survey of 600 people finds 70% believe in global warming. What is the margin of error? a) 4.7% b) 4.1% c) 3.5% d) 4.3%
The correct answer is B because if you divide 1 by the square root of 600 you get 0.041 or 4.1%.
Which answer best defines the purpose of the null hypothesis? a) A statement that sees if the data is statistically significant b) Describes the disparities in data points. c) Displays a lack of significant differences in data. d) Is a prediction about data.
The correct answer is c. The student would just need to know what the null hypothesis stands for in general statistics and c is the best answer.
3) What is the range of a data set? a) The maximum value minus the minimum value. b) The sum of all elements of the dataset divided by the total of elements in the dataset. c) The middle point of a data set. d) The most frequently occurring number in the data set.
a
What is the formula for range? a) Range= max-min b) Range= min-max c) Range =min x max d) Max = range- min
Answer: A
A set of measurements or observations in a statistical study is said to be _______________ if it is unlikely to have occurred by chance. a) Statistically significant b) Skewed Significantly c) Statistically Insignificant d) Least Significant
The answer is A, statistically significant.
A sample statistic is taken from...? a) A random sample of the true population b) Surveying the whole population you are studying c) The population parameter d) Margin of error
The answer is A. Page 411 says "Because it was measured from a sample, 64% is a sample statistic..."
What kind of shape does normal distribution have? a) Parallel line b) O-shape c) Bell shape d) Triangular shape
The answer is C. This is true because if there is a normal distribution, there will be a gradual increase and decrease which shows the "average" spread of data appropriately.
What is the third step in drawing a boxplot? a) add whiskers extending to the lowest and the highest values b) draw a vertical line through the box at the median c) draw a number line that spans all the values in the data set d) enclose the values from the lower to the upper quartile in a box
The correct answer is b).
Oncw [Once] we know the standard score of a data value, the properties of the ________ allow us to find the data value's percentile in the distribution. a) False distribution b) Positive distribution c) Negative distribution d) Correct distribution
The correct answer is b, positive distribution
If the likelihood (probability) of an outcome as extreme as the one observed is 0.03 or less, the difference is statistically significant at the what level? a) 0.01 b) 0.03 c) 0.02 d) 0.04
Answer: B
) Which of the following describes the term population parameter? a) a number that describes something about an entire group or population. b) the starting assumption for a hypothesis test. c) a theoretically defined, complete group of objects or people d) a representative group from the population under study
the correct answer is A, because it is the definition.
Which of the following variables would you expect to have a normal or nearly normal distribution? a) Scores on a very easy test b) Foot lengths of a random sample of adult women c) scores on a very hard test d) all of the above
Correct answer: b because Foot length is a human trait determined by many genetic and Environmental factor. We therefore expect lengths of women's feet to cluster near a mean and become 1 common farther from the mean in both directions, giving the distribution the bell shape of a normal distribution.
Ashley wants to compute the standard deviation for a set of data. She finds the deviations of the means, squares them, and adds all these values up. She then plugs her numbers into the formula and is left with her quotient. How does she finalize to get her standard deviation? a) Subtract her quotient by 1 b) Divide this value by 1 c) Square root this value (correct) d) Add this value by 1
The correct answer is c. The student would need to know the steps of finding standard deviation. They would follow the example and understand that standard deviation is found by finding the square root of the quotient Ashley had computed. With this, they would select letter c as the correct answer.
Which of these is the correct formula to find the range? a) Maximum value - minimum value (correct) b) Minimum value + maximum value c) Maximum value / minimum value d) Minimum value*maximum value
A is the correct answer because when finding the range, one must subtract the minimum value (lowest) from the maximum value (highest)
Which data set would you expect to have the highest standard deviation? a) The height of basketball players b) The weight of sumo wrestlers and non-athletes c) The weight of football linebackers d) The height of female high school seniors
Answer is B. Trying to compare the weight of a sumo wrestler, compared to the weight of an average person will be widely spread due to their not being a cluster near the mean. There will be outliers due to obesity.
What is the percentile of a data value? a) The percentage of all data values in a data set that are less than or equal to it. b) The categories of the subject. c) The data itself. d) The percentage of all data values in a data set that are less to it.
Answer: (a) the percentile of a data value is the percentage of all data values in a data set that are less than or equal to it.
What is the formula for standard deviation? a) The total number of data values minus one over the sum of the deviations from the mean squared. b) The square root of, the total number of data values minus one over the sum of the deviations from the mean squared. c) The square root of, the sum of the deviations from the mean over the total number of data values minus one. d) The square root of, the sum of the deviations from the mean squared over the total number of data values minus one.
Answer: D
The lowest score on an exam was 51, the median score was 80, and the high score was 98. The range was a) 34 b) 62 c) C. 75 d) 47
Answer: d, 47 because the high score (98) minus the low score (51) is 47.
What percentage of data points lie within 3 standard deviations of the mean? a) 93.5% b) 99.7% c) 68.3% d) 95.3%
B is the correct answer as the others answers either only account for the data points that are in the first or second standard deviation or are not an accurate percentage of the data points in the third standard deviation.
Which of these would be considered statistically significant? a) Something that occurred by chance b) Something that occurred on purpose c) Something that unlikely occurred by chance d) Something that unlikely occurred on purpose
C is the correct answer because the definition of statistical significance is "a statistical study if said to be significant if it is unlikely to have occurred by chance"
Using this set of grades on quizzes for students determine the set with greater ranger and variation. Quiz 1: 1 2 5 7 10 12 15 Quiz 2: 3 4 4 4 5 5 5 a) Quiz 1 has a greater variation and range. b) Quiz 2 has a greater variation and range. c) Quiz 1 has a greater variation and Quiz 2 has a greater range d) Quiz 2 has a greater variation and Quiz 1 has a greater range.
Correct Answer: A.
Using the range rule of thumb, determine the standard deviation wait times between doctors appointment A and B. Doctors Appointment A: 16 to 13 minutes Doctors Appointment B: 7 to 5 minutes a) Doctors Appointments A and B: .25 and .5 b) Doctors Appointment A and B: .75 and .5 c) Doctors Appointment A and B: .1 and .6 d) Doctors Appointment A and B: .3 and .5
Correct Answer: B
What rule is applied to finding the standard deviations in a normal distribution? a) 68-95-99.7 b) 67-95-99.8 c) 68-99.7-95 d) 69-98-97.9
The answer and correct rule is A, 68-95-99.7
A group of researchers aim to find out if texting affects English grades in highschoolers. They asked 70 high school aged kids how much time they spend texting, and their English grade. The results showed that there is no correlation. The researchers originally thought there was a correlation. What is the null hypothesis for this survey? a) Texting and English grades are correlated. b) Texting and English grades are not correlated. c) Texting and English grades have a linear correlation. d) Texting and English grades are useless.
The answer is A [B], since the original hypothesis led researchers to believe there was a correlation.
) If a set of data is said to have occurred by chance it is....? a) Statistically significant b) A part of the 90th percentile c) 2 standard deviations above the mean d) Not accurate data
The answer is A. Page 409 defines statistically significant data as "A set of measurements or observations in a statistical study [that] is said to be statistically significant if it is unlikely to have occurred by chance."
If a set of data is said to have occurred by chance it is....? a) Statistically significant b) A part of the 90th percentile c) 2 standard deviations above the mean d) Not accurate data
The answer is A. Page 409 defines statistically significant data as "A set of measurements or observations in a statistical study [that] is said to be statistically significant if it is unlikely to have occurred by chance."
Ashley wants to compute the standard deviation for a set of data. She finds the deviations of the means, squares them, and adds all these values up. She then plugs her numbers into the formula and is left with her quotient. How does she finalize to get her standard deviation? a) Subtract her quotient by 1 b) Divide this value by 1 c) Square root this value d) Add this value by 1
The correct answer is c. The student would need to know the steps of finding standard deviation. They would follow the example and understand that standard deviation is found by finding the square root of the quotient Ashley had computed. With this, they would select letter c as the correct answer.
Which of the following is true about the 68-95-99.7 rule? a) 68% of values fall within 1 standard deviation of the mean, 95% of values fall within 3 standard deviations, & 99.7% fall within 2 standard deviations b) 68% of values fall within 3 standard deviations of the mean, 95% of values fall within 2 standard deviations, & 99.7% fall within 1 standard deviation c) 68% of values fall within 2 standard deviations of the mean, 95% of values fall within 3 standard deviations, & 99.7% fall within 1 standard deviation d) 68% of values fall within 1 standard deviation of the mean, 95% of values fall within 2 standard deviations, & 99.7% fall within 3 standard deviations
The correct answer is d).
The five-number summary characterizes a data set's variation well, but statisticians often prefer to describe variation with a single number. The single number most commonly used to describe variation is called the _______________, which is a measure of how far data values are spread around the mean of a data set. a) Mean b) Standard deviation c) Relative frequency d) Right skewed
The answer is B
What is the range of a data set? a) When you add all the numbers together and divide by the number of data entries b) When you list the numbers in order of largest to smallest and find the middle value c) When you find the difference between the highest and the lowest points in the data d) When you count how many times each number appears
The answer is B.
How do we consider quantifiable data as statistically significant? a) If the likelihood (probability) of an outcome is as extreme as the one observed is .05 (1 in 20 or 5%) or less, the difference is statistically significant at the .05 level b) Both A and C c) If the likelihood (probability) of an outcome as extreme as the one observed is .01 (1 in 100 or 1%) or less, the difference is statistically significant at the .01 level. d) Neither A or C
The answer is B. This is true because there needs to be a difference that is significant enough. These two answers are the rule of thumb when quantifying statistical significance.
The 68-95-99.7 rule gives approximate guidelines for percentages of data values within how many standard deviations of the mean? a) 4, 5, 6 b) 3, 4, 5 c) 1, 2, 3 d) 7, 8, 9
The answer is C. Page 399 defines the 68-95-99.7 rule as giving "approximate guidelines for the percentages of data values that lie within, 1, 2, and 3 standard deviations of the mean for any normal distribution."
What kind of distribution would you expect the test scores of a large class to have? a) Right skewed b) Left skewed c) Abnormal d) Normal
The answer is D because there is a greater variety of scores in the data
What is the formula for margin of error? a) =1/√n b) ≈ 1/√n c) = √n /1 d) ≈ √n /1
Answer: B
Consider a survey with a margin of error of 4%. If you want to reduce the margin of error to 2%, you should repeat the survey with a) half as many people. b) twice as many people. c) four times as many people. d) three times as many people.
Answer: C four times as many people.
1) What is the range of the following data? 21 27 34 43 38 53 48 72 a) 72 b) 21 c) 51 d) 63
Answer: C. 51; Reason : The range is the highest number (72) - the lowest number (21) = 51.
) Pick the statement that best describes normal distribution. a) Bell-shape and symmetric b) Left skewed c) Right skewed A pie chart
Correct answer- A.
A survey of 200 people finds that 45% plan to vote for Greg for governor. What is the margin of error and is there a 95% confidence interval for the following surveys? a) The margin of error is .07 and there is a 95% confidence interval for the survey. b) The margin of error is .04 and there is not a 95% confidence interval for the survey. c) The margin of error is .05 and there is a 95% confidence interval for the survey. d) The margin of error is .07 and there is not a 95% confidence interval for the survey.
Correct answer: A.
The PSAT test is scaled so that its scores are normally distributed with a mean of 100 and a standard deviation of 15. What are the standard scores for IQ scores of 85, 95, and 115? a) 0.5 below the mean, 0.3 above the mean, 1.00 below the mean b) 1.00 below the mean, 0.3 below the mean, 1.00 above the mean c) 1.00 above the mean, 0.3 above the mean, 1.00 above the mean d) 0.8 below the mean, 0.9 below the mean, 1.00 above the mean
Correct answer: B
A friend tells you that his IQ is in the 102nd percentile. You can conclude that a) he is smarter than 102% of all people. b) he is smarter than 2% of all people. c) he doesn't understand percentiles. d) he is not smarter than 2% of all people
Correct answer: he does not understand percentiles
The number of standard deviations a data value lies above or below the mean is called its standard score, the standard score is ___________ for data values above the mean and ____________ for data values below the mean. a) Positive, negative b) Negative positive c) Standard, equal to d) 4, 5
The correct answer Is a because above the mean would be positive values and below the mean would be negative.
The percentile of a data value is the percentage of all data values in a data set that are ________ it. a) Greater than b) Less than c) Less than or equal to Equal to
Answer: C
The percentile of a data value is the percentage of all data values in a data set that are: a) More than b) Less than c) Less than or equal to d) Equal to
Answer: C; Reason: The percentile of a data value is the percentage of all data values in a data set that are less than or equal to it
At the 0.05 level of significance the probability of an observed difference occurring by chance is what? a) 1 in 10 b) 1 in 5 c) 1 in 2 d) 1 in 20
Answer: D
Which of the following is true about standard deviation? a) The standard score of the mean is z = 0 because the mean is 0 standard deviations from the mean. b) The standard score of a data value 1.5 standard deviations above the mean is z = 3.0. c) The standard score of a data value 2.4 standard deviations below the mean is z = -7.2. d) None of the above. [try to avoid this option]
Correct Answer: A; Reasoning: A is correct because no matter what the z-score is, that same number is also how many standard deviations away from the mean. A says 0 is the z-score, so that means it is zero standard deviations away from the mean. B is incorrect because the z-score is doubled to account for the standard deviations away from the means. C is incorrect for the same reason except the value was tripled.
Pick the statement that sounds the truest? a) The median of basketball players height was 5"4in b) The girl on the swim team on average could hold their breathe longer than girls in the art club c) Boys who run long distance has a high correlation to having divorced parents. d) Chess players on average had the lowest scores of patience.
Correct answer- B.
There is a 50/130 chance for rain todays what's the percentage of chance? a) 50% b) 7% c) 38.4% d) 33.7%
Correct answer- C.
What's the median of these values? 4,6,8,2,7,6 a) 2 b) 5.5 c) 6 d) 7
Correct answer- C. 6
Studies on weight within the US are constantly being observed by researchers. The average weight for a for females is has a normal distribution with the mean being 130 with a standard deviation measure at 50. Find the z score for a female weighing 155 pounds. a) 0.22 b) 0.50 c) 0.34 d) 0.39
The correct answer is b. The student would just need knowledge of the z score formula. They would subtract the data value (155) by the mean (130) and divide this by the standard deviation (50). After plugging these into the formula, the student will get a z score of 0.5, making the correct answer as b.
A professor has two classes that she gave exams to in the past week. Each exam has varying ranges. Which classes mean is misleading? Class 1: 100, 80, 40, 60, 70, 80, 80, 90 Class 2: 100, 100, 20, 30, 20, 100, 80, 90 a) Class 1 b) Class 2 c) Neither classes have misleading means d) Both classes have misleading means
Answer: (b) Class 2 has a misleading mean because each score is to one far end of the scale or another.
"The claim that Gender Choice does not work, and the proportion of baby girls born to women who used the product is unchanged from its normal value of about 50%" is the definition of what term? a) Alternative hypothesis b) Null hypothesis c) Margin of error d) Sample distribution
Answer: (b) The answer is null hypothesis because alternative hypothesis is the opposite, and the other two options are not related.
The range rule of thumb works reasonably well only for data sets in which... a) Varey widely. b) Are distributed fairly evenly. c) Grouped at each end of the spectrum. d) Are only on one end.
Answer: (b) they need to be distributed fairly evenly in order for the range rule of thumb to work because otherwise the range will not apply well to the data.
Abigail and her friend Hannah are throwing water straight up into the air and each time it falls exactly straight back down. Both take turns trying it and see no different each time, in this case what is the statistical significance? a) 80% b) 70% c) 100% d) 50%
Answer: (c) the answer is 100% because every time they threw the water up into the air the results where the same meaning statistically it would continue that way.
What is the correct equation to use when using the range rule of thumb? a) Range = standard deviation/4 b) Standard deviation = range/4 c) 4 = standard deviation/range d) Standard deviation = 4/range
The correct answer is B. This is true because if you know the range of a data set, you can use this rule to figure out the standard deviation.
A Survey finds that the prices paid for two-year-old Ford Fusion cars are normally dis- tributed with a mean of $20,500 and a standard deviation of $900. Consider a sample of 10,000 people who bought two-year-old Ford Fusions.How many people paid more than $20,000? a) Half of these people paid more than 20,000 b) Less than half of these people paid more than 20,000 c) More than half of these people paid more than 20,000 d) There's no way of knowing
Answer: A
Which of the following situations state a symmetric distribution of skewness? a) Height of kindergarten students. b) Number of books kindergarten students read during the school year. c) Number of cognitive based activities a kindergarten class does. d) Speed of kindergarten students running to the playground.
Answer: A; Explanation: Kindergartener's height would mostly be somewhere in between the shortest and tallest kindergarten students because it's a rare case.
A dozen of college students were asked to complete rate their Student Center food court places. From 1-10, with 1 being least satisfied and 10 as most satisfied. Answer was two each from 5 to 10. Evaluate the standard deviation. a) 1.22 b) 1.40 c) 1.50 d) 1.60
Answer: A; Explanation: To find the Standard Deviation, you must find the mean then apply the Standard Deviation formula: square (x-x)^2/ n-1.
BMI scores of professional athletic women 24-28 are normally distributed between 18.5 to 24.5 with mean of 21.2 and a standard deviation of 5. In what percentile is a 26-year-old woman athlete with a BMI of 23.5? a) 0.46 b) 0.90 c) 0.10 d) 0.30
Answer: A; Explanation: To find the Standard Score, you must use the equation z= date value - mean/ standard deviation. Plugging the information from above, (23.5-21.2)/5 = 0.46
What is the shape of the normal distribution? a) Skewed right b) Bell shaped c) Skewed left d) bimodal shaped
Answer: B
What is the first step in calculating the standard deviation? a) Find the squares (second power) of all the deviations from the mean. b) Compute the mean of the data set. Then find the deviation from the mean for every data value by subtracting the mean from the data value. That is, for every data value: deviation from mean = data value - mean c) Divide this sum by the total number of data values minus 1. d) Find soiree root of quotient
Answer: B Reason you need the mean to calculate the standard deviation
Correct answer- A. 18) What is the middle quartile? a) divides the lowest three-fourths of a data set from the upper fourth. It is the median of the data values in the upper half of a data set. b) it is the median of the entire data set. c) divides the lowest fourth of a data set from the upper three-fourths. It is the median of the data values in the lower half of a data set d) The range of a data set is the difference between its highest and lowest data values
Answer: B. A is upper quartile, C is lower quartile, and D is the definition of range. Therefore, the correct answer is B.
For the Primary election season, the Democratic challenger claimed they gained an additional 30% increase in votes from newly registered Democrats, compared to last election. The County Commissioners representing the county that the challenger is claiming the boost in votes record that there was only a 15% boost in newly registered Democrats from last election. Does this make since [sense]? State the Null and Alternative Hypothesis a) Null: 15%, Alternative: 30%, YES b) Null: 30%, Alternative 15%, NO [It appears your decision is to reject the null hypothesis] c) Null: 15%, Alternative: 30%, NO d) Null: 30%, Alternative: 15%, YES
Answer: B. The Null hypothesis is what is believed (The politician believes they gained a 30% increase). The Alternative hypothesis is contradictory to the Null hypothesis, whether it is greater or less than. County Commissioners proved that there was only a 15% increase, not the politicians claimed 30%. [If so, your decision probably will be correct because the votes record was only a 15% boost in newly registered Democrats, not 30% as claimed.]
Which is not an example of a normal or nearly normal distribution? a) Random hair length samples of women taking public transportation. b) Facial features of blood related family members. c) Nail length of women who do and do not get nail extensions d) Height of women basketball players and soccer players
Answer: B; A normal or nearly normal distribution means results would be expected. In the case of facial features of blood related family members and the other mentioning, it's the only one with possible results varying around the sample tested.
What does a 'null' hypothesis refer to ? a) Little effect or difference b) No effect or difference c) Large effect or different Many portions of effects
Answer: B; Reason: " A null hypothesis often states that there is no special effect or difference.
How many 'peaks' are in a normal distribution? a) 2 b) 1 c) 3 d) 0
Answer: B; Reason: normal distribution is a symmetric, bell-shaped distribution with a single peak.
Which of the following is not a part of the conditions for normal distribution? a) Most data values are clustered far away from the center of the data, and don't have a peak. b) Data values are spread evenly around the mean, making the distribution symmetric. c) Large deviations from the mean become increasingly rare, producing the ymm tric tapering tails of the distribution. d) Individual data values result from a combination of many different factors , such as genetic and environmental factors.
Correct Answer: A; Reasoning: A is not a condition for normal distribution because it lacks all the qualities it needs. Instead of the values clustering away from the center, it actually has to be clustered towards the mean. Also, the graph needs to have a peak, option A states there is no peak.
Which of the following is an example of a normal curve distribution? a) Age of deaths b) Height c) Incomes d) Possibilities of heads or tails
Correct Answer: B
Which of the following is the formula to find the margin of error? a) μ = ΣX / N b) 1/√n c) x = Σx / n d) s2 = Σ ( xi - x )2 / ( n - 1 )
Correct Answer: B
Find the range in this data set: 4.5, 6.7, 2.2, 4.2, 7.5, 5.6, 3.4 a) 2.4 b) 4.2 c) 5.3 d) 3.5
The correct answer is C because 7.5 is the highest data value, and 2.2 is the lowest data value and when you subtract them, you get 5.3
The mean of a set of test scores is 90 and the standard deviation is 10. What is the standard score for 60? a) 1 b) -2.06 c) -3 d) -1.01
The correct answer is C because when you subtract 60 from the mean and divide it by the standard deviation you get -3.
Which of these scenarios show a statistically significant study? a) A doctor wanted to know if a herbal remedy could help with colds. 100 sick people take a herbal remedy for a cold and only 20 people begin to feel better b) It is said that baseball pitchers can throw a ball as far as 120 ft, so Tom recorded [how far pitchers can throw baseball and see if they can throw the ball around 120 ft] [he can throw 150ft] and all the pitchers threw the ball around 120 ft c) Demy wanted to find out if one player got injured more often than another. She compared two players John and Ron found that more injuries occurred with Ron than John d) Kayla wanted to see which side people prefer to walk on when they are in a hallway. When she asked random people 50 people said left and 30 people said right.
Correct Answer: B, because the rest of the options are controlled by chance
Suppose you want to know if your study responses follows has the same ratio of yes/no answers as the population, you would use a confidence interval for standard deviation. What is the rule? a) 72-95-98.2 b) 68-95-99.7 c) 70.5-88-95 d) 68-80-99.7
Correct Answer: B; Reasoning: It is known to us through reading our text book and listening in class, the rule is 68-95-99.7
The range rule of thumb works reasonably well only for data sets that... a) Have outliers b) Are distributed fairly evenly c) Have no correlation d) None of the Above [try to avoid this option]
Correct Answer: B; Reasoning: The range rule of thumb does not work well when the highest or lowest value is an outlier. It must be distributed fairly evenly.Correlation does not matter when working on range rule of them
6) Which of the following is not an example of central tendency? a) Mode b) Median c) Standard Deviation d) Mean
Correct Answer: C
The ages of the Brown children are 8, 11, 17, 7, 19. What is the standard deviation of the children? a) 2.7 b) 3.0 c) 4.8 d) 5.7
Correct Answer: C
Which of the following is an example of a statistically significant study? a) The average amount of points a basketball player makes is between 10-15 a game b) Homes in a neighborhood gets mail delivered at six pm, homes in a different neighborhood gets mail delivered ed at five pm c) [The top three classes] [In a departmental introductory statistics test, one section has] with the highest test scores (M = 91.17), [also had the most students fail the course] [and one section has the lowest test scores (M = 72.69)]. d) Having five out of five cold winters where the lowest temperature was 12 degrees
Correct Answer: C
Which of the following is the equation to find the standard score? a) Mean = Sample size x probability b) Data Value - Mean/Standard Deviation c) Highest Value - Lowest Value d) Highest Value + Lowest Value/2
Correct Answer: C
Standard deviation is the measure of how far data values are spread around the mean of a data set. What is the purpose of finding the standard deviation? a) To pair together similar statistics b) To overwrite the idea of others when they make mistakes c) to represent an average of the individual deviations without regard to their signs (positive or negative) d) to represent a median of multiple deviations
Correct Answer: C This is the definition of standard deviation
A group of researchers conducted a study in Calama, Chile, in which they surveyed a group of participants to compare their salaries with United States Salaries. The lowest salary recorded was 25,000 USD with the most frequent salary being 68,000 USD, and the highest paid salary being 345,500 USD. What is the range of the salaries? a) $243,500 b) $245,500 c) $320,500 d) $315,500
Correct Answer: C, because 345,500 - 25,000 = 32,500 [$320,500] and the range is the difference between two data points on a graph.
4) The five-number summary can be displayed best in... a) Quartiles b) The range c) A boxplot d) A graph
Correct Answer: C; Reasoning: A box plot is the only option that includes all of the five number summary, which is a data set that consists of the following five numbers: lowest value, lower quartile, median, upper quartile, highest value.
A test is done to determine if a coin is equally likely to land on either side. The coin is flipped 100 times. It lands on heads 47 times and tails 53 times. Is this statistically significant a) Yes, it is about equal b) No, it is not 50-50 so it can not be equally likely. c) Yes, we expect small deviations to occur by chance d) No, the gap is too large.
Correct Answer: C; Reasoning: There is always a chance a test like this will deviate from the idea that it is equal. It could be the way coin is tossed, or anything else that could simply occur by chance.
John is working through a big set of data concerning the varying home prices in Pennsylvania. He has ten numbers, $100,000, $110,000, $125,000, $150,000, $180,000, $190,000, $210,000, $250,000, $260,000, $310,000. What is the range of this data? a) $1,885,000 b) $942,500 c) $210,000 d) $275,000
Correct Answer: C; The first answer is wrong because it represents all the numbers totaled. The second is wrong because it represents the mean. The third is correct, as it shows the max-min of the data given. The fourth is wrong because it represents the median.
2) The five number summary of a data set consists of the following five numbers: lowest value, lower quartile, median, upper quartile, and the highest value. What is best for this information? a) Bar graph b) Pictograph c) Line graph d) Box and whisker plot
Correct Answer: D, because the box and whisker plot has the proper format in order to showcase all the specific data from the five number summary
Sarah finds 4000 people in a sample of 50,000 people that own a scooter. What is the approximate margin of error? 95% confidence interval. a) 4.5% [0.45%] b) 8.5% c) 5% d) 95%
Correct Answer: a) 1%; When you calculate the margin of error using the data provided, you get 4.5%. ; 8% ± 0.45%
What is the first step you have to follow when completing a calculation using standard deviation? a) First, you have to compute the mean of whatever data set you are working with, and then find the deviation. b) First, you find the deviation by taking the data value and subtracting the mean. c) First, you have to add all the squares of the deviations of the mean. d) First, you have to compute the mean from the data and find the range, and find the deviation from the range and mean.
Correct Answer: a) This is the correct answer because it is the way to begin calculating standard deviation. You compute the mean and then take your data value, subtract the mean, and get the deviation.
When looking at the graph of test scores, Bob notices that most of the values are clustered near the mean, data values are spread evenly around the mean, rare deviations from the mean, and individual data values from combined different factor. With this information, what can he conclude? a) It has a low standard deviation. b) The data has a normal distribution with a single peak bell-shape. c) Under two-thirds of the data points fall within 1 standard deviation. d) The data has a clustered distribution with two peaks both resemble bell-shapes
Correct Answer: b); The reason is that hall the information Bob gathers from the data describes a normal distribution, which means the data would show in a single bell shape. [The seventh edition APA Style manual identifies "datum" as the singular form and "data" as the plural form]
Which option below is a statistically significant event? a) A basketball team with the best record of win-loss gets defeated by a team with the worst record. b) The poll results show a change in percentage from 61%-60%. c) The lowest temperature in Delaware last year was 6, and this year's low was 8. d) You flip a coin 100 times and it lands heads-up 95 times and tails up 5 times.
Correct Answer: d) The difference between 5 and 95 for 100 flips is a statistically significant. That does not seem like something that happens by chance.
When Nate is looking at the percentage of all his data values, his data set shows that a data value is lying between 2 percentiles. What does this mean for the data value? a) It has an average percentile. b) It has an unimportant percentile. c) It has a higher percentile. It has a lower percentile.
Correct Answer: d) When a data value lies between two percentiles, it is said to be in the lower percentile.
Which is the correct definition of distribution. a) a variable that refers to the way its values are spread over all possible values. b) Warm weather c) A variable that changes all possible values d) Cold weather
Correct answer- A.
A soccer team with a consistent losing streak wins one game against an undefeated team. Is this statistically significant? a) No, this is not statistically significant as one or two wins are expected. b) Yes, because it is against an undefeated team it is statistically significant. c) There is no way of knowing if it's statistically significant. d) Yes, because it is statistically significant for the undefeated team.
Correct answer: a
In a set of data, 35% of have a standard score of .45. Which percentile would the score .45 lie in? a) 50th percentile b) 45th percentile c) 35th percentile d) 55th percentile
The answer is C. Page 403 gives a similar example which can help to understand this question. "55.96% of the values in a normal distribution have a standard score less than or equal to 0.15. In other words if we are looking for an integer percentile, a data value with a standard score of 0.15 lies in the 55th percentile."
An experiment is being conducted on the use of a new drug that increases hair growth. A randomly selected sample of 50 people are given the actual drug, and another group of 50 randomly selected people are given the placebo. Most participants in the groups had nearly the same hair length and the average hair growth was 1.5 inches more in the treatment group. What is the significance of this study? a) Not statistically significant b) Statistically significant c) Likely significant d) Unlikely significant
The correct answer is B because the results for the group that took the actual drug were higher than the group who took the placebo.
What is the correct term for the percentile of a data value that is the percentage of all data values in a data set that are less than or equal to it? a) Quartile b) Percentile c) Standard deviation d) Percentage
The correct answer is B, percentile.
Which answer choice best explains the importance of statistical significance? a) The variables have no relationship, and everything is most likely wrong. b) There is a relationship between the variables measured, and the margin of error is small. c) Validates that the statistics are correct. d) Presents the data was correctly presented.
The correct answer is B. The best explanation for what statistical significance does and its importance is answer choice B. Answer choice C and D can contribute to the importance of statistical significance, but B is the best answer choice.
In a study conducted to determine the color blindness of employees working in King of Prussia 4 out of the 25 employees taken as a sample population were reported to be color blind. Assuming this study were conducted 3 more times with 3 different sample [sizes?] populations which number of participants being colorblind is not proportional to the original sample? a) 2 out of 25 b) 5 out of 25 c) 6 out of 25 d) 8 out of 25
The correct answer is D because it's nearly double the original population thought to be colorblind. This would change from the original conclusion that about 16% of employees are colorblind to about 32% which drastically can change the conclusions toward the population of colorblind employees at King of Prussia.
Find the standard deviation of the data set: 4.7, 5.2, 6.5, 7.0, 7.5, 8.2, 8.4, 9.2, 11.0 a) 1.23 b) 0.55 c) 1.9 d) 1.55
The correct answer is D, if you follow the steps on page 390, you can calculate the standard deviation. Step 1. Compute the mean of the data set. Then find the deviation from the mean for every data value by subtracting the mean from the data value. That is, for every data value: deviation from mean = data value - mean Step 2. Find the squares (second power) of all the deviations from the mean. Step 3. Add all the squares of the deviations from the mean. Step 4. Divide this sum by the total number of data values minus 1. Step 5. Th standard deviation is the square root of this quotient.
What measure in chapter 6 was described to possibly be used to approximate, or estimate the standard deviation of a set of data? a) Mean b) Median c) Mode d) Range
The correct answer is D, range. This is because the range can be used in the 'range rule of thumb', in which you utilize the equation range= highest-lowest, in the range rule of thumb equation, standard deviation = (range/4).
In the book we learned about the example of variation, of which there are two banks: big bank and best bank. Using this example and understanding the difference between a single line and a multiple line scenario. Based on your understanding of a box and whiskers plot, what does the below figure tell you about the waiting times of big bank? a) greater variation of waiting times b) Smaller variation of waiting times c) Equivalent waiting times to best bank d) They're between 5.6 and 7.2 minutes
The correct answer is a because the figure shows a longer box and whisker meaning the variation is greater, it doesn't mean that the waiting times are longer or shorter. Although we know by reading the chapter that the waiting times are similar to best bank but the best answer would be a not c.
7) Compute the mean, median, and mode of the following data set. {40.5, 46.7, 54.8, 56.9, 61.3} a) mean = 52.04; median = 54.8; mode = none b) mean = 52.04; median = 54.8; mode = 61.3 c) mean = 51.06; median = 54.8; mode = 46.7 d) mean = 48.6; median = 56.9; mode = none
The correct answer is a). Calculating the mean: (40.5+46.7+54.8+56.9+61.3) = 260.2 260.2 / 5 = 52.04
Researchers are gathering data on a study that has research relating to college students. As they collected data, they found that a lot of the data they were getting was so similar to the mean. When graphed, what kind of shape might make the most sense for this data? a) Bell curve b) Skewed left c) Skewed right d) Normal distribution
The correct answer is d. The student needs to know that a common characteristic of data that froms [from] a normal distribution is when data is close to the mean. Due to this being stated in the example, normal distribution is the best answer choice, making d the best answer.
