math test 1

b

Which of the following statements is true about variation? a. Variation indicates that there is a problem with the data. b. Variation is common in data sets. c. All of the answer options are correct. d. There is usually only one source of variation.

a

Which of the statements is true? a. We can never be 100% confidentin the conclusions of a statistical study. b. Errors and lurking variables are the only sources of variation in data. c. A good statistical study will account for all sources of variability, so that we can be 100% confident in our conclusions.

500, 492.898, 507.102, 14.204, a

A new version of the Medical College Admissions Test (MCAT) was introduced in spring 2015 and is intended to shift the focus from what applicants know to how well they can use what they know. One result of the change is that the scale on which the exam is graded was modified, with the total score of the four sections on the test ranging from 472472 to 528.528. In spring 2015, the mean score was 500.0500.0 with a standard deviation of 10.6.10.6. (a) Assuming that the MCAT scores are normally distributed, use Table A to find the median and the first and third quartiles of the MCAT scores. Find the median of the MCAT scores. (Enter your answer rounded to a whole number.) median= Find the first quartile of the MCAT scores. (Enter your answer rounded to three decimal places.) 𝑄1= Find the third quartile of the MCAT scores. (Enter your answer rounded to three decimal places.) 𝑄3= Find the interquartile range of the MCAT scores. (Enter your answer rounded to three decimal places.) 𝐼𝑄𝑅= (b) Which interval contains the central 80%80% of the MCAT scores? Select the answer choice that approximates this interval. a. 486.432to 513.568 b. 491.096 to 508.904 c. 472 to 528 d. 480 to 520

8.5

A scale is tested by repeatedly weighing a standard 9.0 kg weight. The weights for 12 measurements are 8.3,9.2,8.3,8.7,8.4,8.3,8.5,8.0,8.4,8.5,8.1,9.3 mean?

3.59, 4.84

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). A new version of the exam was introduced in spring 20152015 and is intended to shift the focus from what applicants know to how well they can use what they know. One result of the change is that the scale on which the exam is graded has been modified, with the total score of the four sections on the test ranging from 472472 to 528528 . In spring 20152015 the mean score was 500.0500.0 with a standard deviation of 10.610.6 . Use Table A to find the answers to the two questions. (a) What proportion of students taking the MCAT had a score over 519519 ? Compute the proportion and then enter the answer as a percentage rounded to two decimal places. percentage over 519 = (b) What proportion of students taking the MCAT had scores between 515 and 520? Compute the proportion and then enter the answer as a percentage rounded to two decimal places. percentage between 515 and 520=

d

Drawing conclusions about the greater world based on examining patterns in variation within a sample of data is called: a. None of the answer options is correct. b. data production. c. data analysis. d. statistical inference.

17

Paleontology students went on a dig for fossils. The following data set contains the number of fossils found by a sample of 12 students. 12,15,11,52,18,15,24,20,22,16,21,14 median:

1.59, 1.47, c

Suppose that Jason recently landed job offers at two companies. Company A reports an average salary of $51,500 with a standard deviation of $2,200. Company B reports an average salary of $46,820 with a standard deviation of $5,560. Assume that salaries at each company are normally distributed. Jason's goal is to secure a position that pays $55,000 per year. What are the 𝑧z‑scores for Jason's desired salary at Company A and Company B? Please round your answers to two decimal places. company a= company b= At which company is Jason more likely to obtain his desired salary of $55,000 per year? a. Company B, because the 𝑧z‑score for $55,000 at Company B is greater than the 𝑧z‑score for $55,000 at Company A. b. Company A, because the 𝑧z‑score for $55,000 at Company A is greater than the 𝑧z‑score for $55,000 at Company B. c. Company B, because the 𝑧z‑score for $55,000 at Company B is less than the 𝑧z‑score for $55,000 at Company A. d. Company A, because the 𝑧z‑score for $55,000 at Company A is less than the 𝑧z‑score for $55,000 at Company B.

a, c

The summer monsoon rains in India follow approximately a Normal distribution with mean 852852 millimeters (mm) of rainfall and standard deviation 8282 mm. (a) In the drought year 19871987 , 697697 mm of rain fell. In what percent of all years will India have 697697 mm or less of monsoon rain? a. 2.94% b. 2.5% c. 97.06% d. 47.06% (b) "Normal rainfall" means within 20%20% of the long‑term average, or between 682682 mm and 10221022 mm. In what percent of all years is the rainfall normal? a. 20% b. 99.18% c. 96.16% d. 3.84%

b

The three numbers 8,9,138,9,13 have a sum of 30 and therefore a mean of 10. Use software to determine the standard deviation. Use the function for sample standard deviation. Give your answer precise to two decimal places standard deviation= Now suppose a fourth value equal to the mean, 10, were added to the data set. What would happen to the standard deviation? Choose the correct statement. a. The standard deviation would remain the same because the fourth value is equal to the mean. b. The standard deviation would decrease because the data get less spread out relative to the mean. c. The standard deviation would increase because the data get more spread out relative to the mean.

0.47, 0.88

Use Table A to find the value 𝑧z of a standard Normal variable that satisfies each of the following conditions. Use the value of 𝑧z from Table A that comes closest to satisfying the condition. In each case, sketch a standard Normal curve with your value of 𝑧z marked on the axis. (a) Find the point 𝑧z with 68%68% of the observations falling below it. Enter your answer rounded to two decimal places. 𝑧= (b) Find the point 𝑧z with 19%19% of the observations falling above it. Enter your answer rounded to two decimal places. 𝑧=

a

Which statement best characterizes the definitions of categorical and quantitative data? a. Quantitative data consist of numbers representing measurements or counts, whereas categorical data consist of names or labels. b. Quantitative data consist of values that can be arranged in order, whereas categorical data consist of values that cannot be arranged in order. c. Quantitative data have an uncountable number of possible values, whereas categorical data have a countable number of possible values. d. Quantitative data consist of numbers, whereas categorical data consist of names and labels that are not numeric.

67, 8, 5, -13, 64, 25, 169, 129, 11.4

Calculate the sample standard deviation for this data set: 75, 72, 54. Calculate the sample mean. Calculate the deviations and the squares of the deviations. Calculate the sample variance and the sample standard deviation. Provide your sample standard deviation answer precise to one decimal place.

10, -3, -1, 4, 9, 1, 16, 13

Calculate the sample variance, 𝑠2,s2, of the set of numbers. 7,9,14 𝑥--= deviation of value 1 = deviation of value 2 = deviation of value 3 = square of the deviation of value 1 = square of the deviation of value 2 = square of the deviation of value 3 = variance =

bar chart, pie chart, pie chart, bar chart, parts of a whole

Complete the sentences to form correct statements about the usage of bar charts and pie charts for displaying data. A ______________________ can always do the same thing as a ______________, but a __________________ cannot always replace a _____________. Pie charts must represent _________________ that add up to 100%.

a, c, 0.1875, 0.75

Examining the location of accidents on a level, 88 ‑mile bike path shows that they occur uniformly along the length of the path. The figure displays the density curve that describes the distribution of accidents. (a) Choose the explanation for why this curve satisfies the two requirements for a density curve. a. It is on or above the horizontal axis everywhere and the area beneath the curve is 11 . b. It is on the nonnegative part of the 𝑥x ‑axis and the area beneath the curve is 88 . c. It is a smooth curve on or above the horizontal axis. d. It is symmetrical with respect to the vertical line at 𝑥=4x=4 and the area beneath the curve is less than or equal to 11 . (b) The proportion of accidents that occur in the first 33 miles of the path is the area under the density curve between 00 miles and 33 miles. What is this area? a. 8/3 b. 0.3 c. 3/8 d. 3/16 (c) There is a stream alongside the bike path between the 1.51.5 ‑mile mark and the 3.03.0 ‑mile mark. What proportion of accidents happen on the bike path alongside the stream? (Enter your answer rounded to four decimal places.) proportion = (d) There are small towns at the two ends of the bike path, but the remainder of the paved bike path goes through the woods. What proportion of accidents happen more than 11 mile from either town? Hint: First determine where on the bike path the accident needs to occur to be more than 11 mile from either town, and then find the area. (Enter your answer rounded to two decimal places.) proportion =

d

Given a set of data sorted from smallest to largest, define the first, second, and third quartiles. a. The first quartile is the area that contains the 25%25% of all values that are closest to the mean. The second quartile is the area that contains the 50%50% of all values that are closest to the mean. The third quartile is the area that contains the 75%75% of all values that are closest to the mean. b. The first quartile is the area within one standard deviation of the mean.The second quartile is the area within two standard deviations of the mean.The third quartile is the area within three standard deviations of the mean. c. The first quartile is the mean of the lower half of the data below the median.The second quartile is the median.The third quartile is the mean of the upper half of the data above the median. d. The first quartile is the median of the lower half of the data below the overall median.The second quartile is the overall median.The third quartile is the median of the upper half of the data above the overall median. e. The first quartile is the minimum value.The second quartile is the median.The third quartile is the maximum value.

d, b

Once every three years, the Board of Governors of the Federal Reserve System collects data on household assets and liabilities through the Survey of Consumer Finances (SCF). Some results from the 2013 survey are provided. (a) Transaction accounts, which include checking, savings, and money market accounts, are the most commonly held type of financial asset. The mean value of transaction accounts per household was $270,000$270,000 , and the median value was $94,500$94,500 . Which statement explains the differences between the two measures of center? a. The distribution of the value of transaction accounts is a uniform distribution. b. The distribution of the value of transaction accounts is an approximately symmetrical distribution. c. The distribution of the value of transaction accounts is a left‑skewed distribution. d. The distribution of the value of transaction accounts is a right‑skewed distribution. (b) The mean value of retirement accounts per household, which includes Individual Retirement Account (IRA) balances and certain employer‑sponsored accounts, was $94,500$94,500 , but the median value was $0$0 . What does a median of $0$0 say about the percentage of households with retirement accounts? a. There is not enough information to make any reliable estimate on the percentage of households with retirement accounts. b. At least 50%50% of households do not have a retirement account. c. Approximately 50%50% of households have a retirement account. d. At least 75%75% of households have a retirement account.

c,c

Once every three years, the Board of Governors of the Federal Reserve System collects data on household assets and liabilities through the Survey of Consumer Finances (SCF). Some results from the 2013 survey are provided. (a) Transaction accounts, which include checking, savings, and money market accounts, are the most commonly held type of financial asset. The mean value of transaction accounts per household was $270,000$270,000 , and the median value was $94,500$94,500 . Which statement explains the differences between the two measures of center? a. The distribution of the value of transaction accounts is an approximately symmetrical distribution. b. The distribution of the value of transaction accounts is a left‑skewed distribution. c. The distribution of the value of transaction accounts is a right‑skewed distribution. d. The distribution of the value of transaction accounts is a uniform distribution. (b) The mean value of retirement accounts per household, which includes Individual Retirement Account (IRA) balances and certain employer‑sponsored accounts, was $94,500$94,500 , but the median value was $0$0 . What does a median of $0$0 say about the percentage of households with retirement accounts? a. At least 75%75% of households have a retirement account. b. Approximately 50%50% of households have a retirement account. c. At least 50%50% of households do not have a retirement account. d. There is not enough information to make any reliable estimate on the percentage of households with retirement accounts.

c,d,f

Select all of the true statements about the standard deviation of a quantitative variable. a. If a set of values has a mean of 00 and a standard deviation that is not 0,0, then removing a data point with a value of 00 will have no effect on the standard deviation. b. Changing the units of a set of values (e.g., converting from inches to feet) does not affect its standard deviation. c. Standard deviation is never negative. c. The standard deviation of a set of values is equal to 00 if and only if all of the values are the same. d. Standard deviation is resistive to unusual values. e. Standard deviation represents how far a group of values are from the mean of those values, on average.

24, 28, 4

Suppose a biologist studying the mechanical limitations of growth among different species of tulips monitors a national preserve. He collects data on the heights of 10 different types of tulips in the reserve and rounds each height to the nearest centimeter. 25,21,26,24,28,31,29,25,17,2425,21,26,24,28,31,29,25,17,24 Compute the first quartile (𝑄1Q1), the third quartile (𝑄3Q3), and the interquartile range (IQR) of the data set.

a

The 2013-2014 roster of the Seattle Seahawks, winners of the 20142014 NFL Super Bowl, included 1010 defensive linemen and nine offensive linemen. The weights in pounds of the 1010 defensive linemen are shown in the table. 311, 254, 297, 260, 323, 242, 300, 252, 303, 274 The correct units for the standard deviation are a. pounds. a. not listed-none of the other choices are correct. c. pounds squared. d. no units-it is just a number.

0.64, -1.13, a

The heights of women aged 2020 - 2929 in the United States are approximately Normal with mean 64.264.2 inches and standard deviation 2.82.8 inches. The heights of men aged 2020 - 2929 in the United States are approximately Normal with mean 69.469.4 inches and standard deviation 3.03.0 inches. What is the 𝑧z‑score for a woman 5.55.5 feet tall? (Enter your answer rounded to two decimal places.) z= What is the 𝑧z‑score for a man 5.55.5 feet tall? (Enter your answer rounded to two decimal places.) z= What information do the 𝑧z‑scores give that the original non‑standardized heights do not? a. The 𝑧z‑scores show us that the woman is slightly taller than average, while the man is much shorter than average. b. The 𝑧z‑scores show us that the woman is slightly shorter than average, while the man is much taller than average. c. The 𝑧z‑scores do not give us any additional information, since we already know that the man and woman have equal heights. d. The 𝑧z‑scores show that the woman is slightly different from the average, while the man is very different from the average.

a,a

The left‑most bar has a height of 53.53. Explain what this means. a. There are 5353 countries in which there are between 00 and 0.020.02 fatalities per confirmed case of COVID‑19. b. In 00 to 2%2% (0.02)(0.02) of countries, the ratio of fatalities to cases of COVID‑19 is 53%.53%. c. In 53%53% of the countries in the world, there are between 00 and 0.020.02 fatalities per confirmed case of COVID‑19. d. There is not enough information because we do not know if this is a frequency or a relative frequency histogram. Describe the shape of the distribution and interpret what that means in terms of case‑fatalities. a. The distribution is skewed to the right. Most of the countries have relatively low case‑fatality rates and there are comparatively few countries with high case‑fatality rates. b. The distribution is skewed to the right. Most of the countries have relatively high case‑fatality rates and there are comparatively few countries with low case‑fatality rates. c. The distribution is skewed to the left. Most of the countries have relatively low case‑fatality rates and there are comparatively few countries with high case‑fatality rates. d. The distribution is skewed to the left. Most of the countries have relatively high case‑fatality rates and there are comparatively few countries with low case‑fatality rates.

56.28, 3, c

To investigate water quality, the Columbus Dispatch took water specimens at 1616 Ohio State Park swimming areas in central Ohio. Those specimens were taken to laboratories and tested for E. coli, which are bacteria that can cause serious gastrointestinal problems. For reference, if a 100100‑milliliter specimen (about 3.33.3 ounces) of water contains more than 130130 E. coli bacteria, it is considered unsafe. The E. coli levels per 100100 milliliters found by the laboratories are presented in the table: 291 10.9 47 86 44 18.9 1 50 190.4 45.7 28.5 18.9 16 34 8.6 9.6 mean: Number of lakes that have E.coli levels greater than the mean: What feature of the data explains the fact that the mean is greater than most of the observations? a. The mean is greater than most of the observations because it is a resistant measure of center. b. The mean is greater than most of the observations because it is greater than the median. c. The mean is greater than most of the observations because of the two outliers (291.0291.0 and 190.4190.4 ). d. The mean is greater than most of the observations because of the two outliers (1.01.0 and 8.68.6 ).

62

graph 2 Carla's Cafe sells five types of beverages. The pie chart displays the relative frequency of beverages sold on a particular month. Determine the combined percentage of beverages sold other than tea and coffee. Percentage of beverage other than tea and coffee =

a,c,d

see graph 1 Suppose a meteorologist is tracking rainfall patterns in Mickton, Florida. This bar graph shows the number of rainy days in Mickton for each month in 2012 and 2013. Select all true statements. a. The month with the greatest difference in the number of rainy days between 2012 and 2013 was December. b. There was only one month with more rainy days in 2013 than 2012. c. Mickton had more rainy days in July than in January, November, and December combined in 2012 and 2013. d. There were 25 rainy days in May 2012. e. Mickton had more rainy days in June 2012 than November 2012, December 2012, and January 2012 combined.

0.3015, 0.9525, 0.9834, 0.6819

𝑧<−0.52= 𝑧>−1.67= 𝑧<2.13= −0.52<𝑧<2.13=−0.52<z<2.13=