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Interpret confidence intervals for population means

The histogram summarizes the measurements a botanist made of the transpiration rates in millimoles of water per square meter per second (mmol/m2s)(\text{mmol/m}^2\text{s}) of several diamondleaf willow plants. In which interval does the median transpiration rate occur? Choose 11 answer:\newlineChoose 11 answer:\newline(Choice A) 0.5−0.70.5-0.7 mmol/m2s\text{mmol/m}^2\text{s} A 0.5−0.70.5-0.7 mmol/m2s\text{mmol/m}^2\text{s}\newline(Choice B) 0.7−0.90.7-0.9 mmol/m2s\text{mmol/m}^2\text{s} B 0.7−0.90.7-0.9 mmol/m2s\text{mmol/m}^2\text{s}\newline(Choice C) 1.1−1.31.1-1.3 mmol/m2s\text{mmol/m}^2\text{s} C 1.1−1.31.1-1.3 mmol/m2s\text{mmol/m}^2\text{s}\newline(Choice D) 1.3−1.51.3-1.5 mmol/m2s\text{mmol/m}^2\text{s} D 1.3−1.51.3-1.5 mmol/m2s\text{mmol/m}^2\text{s}
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This is the graph of function ff. Dashed lines represent asymptotes. Function ff is graphed. The xx-axis goes from negative 88 to 88. The graph consists of 33 curves. The first curve starts at about (−8,5)( -8, 5 ), moves downward and ends at a closed circle at (−2,0)( -2, 0 ). The second curve starts at an open circle at (−2,−3)( -2, -3 ) and moves upward toward a vertical asymptote at x=4x = 4. The third curve moves downward, away from a vertical asymptote at x=4x = 4 and ends at about (8,−3)( 8, -3 ). \newline1 2 3 4 5 6 7 −2 −3 −4 −5 −6 −7 1 2 3 4 5 6 7 −2 −3 −4 −5 −6 −7 y x f1 \ 2 \ 3 \ 4 \ 5 \ 6 \ 7 \ -2 \ -3 \ -4 \ -5 \ -6 \ -7 \ 1 \ 2 \ 3 \ 4 \ 5 \ 6 \ 7 \ -2 \ -3 \ -4 \ -5 \ -6 \ -7 \ y \ x \ f \newlineOver which intervals is ff continuous? Choose all answers that apply: \newlineChoose all answers that apply: \newline(Choice A) [−5,2][-5,2] \newlineA [−5,2][-5,2] \newline(Choice B) [−2,3][-2,3] \newlineB [−2,3][-2,3] \newline(Choice C) None of the above \newlineC None of the above
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www.khanacademy.org\newlineCourses\newlineSearch\newlineKhan Academy\newlineDonate πi \underset{i}{\pi} \newlinejosemanuel.zubieta\newlineYou're on fire, that's a 44 week streak!\newlineweek\newlineLevel 77\newlinestreak\newlineDigital SAT Math\newlineCOURSE: DIGITAL SAT MATH > UNIT 66\newlineUnit test\newlineTest prep > > Digital SAT Math > > Medium:\newlineAlgebra > Unit test ‾ >\underline{\text { Unit test }} \newline(c) 20242024 Khan Academy\newlineTerms of use\newlinePrivacy Policy\newlineCookie Notice y≥−1 y \geq-1 y≤4x+1 y \leq 4 x+1 \newlineWhich of the following ordered pairs (x,y) (x, y) satisfies the system of inequalities?\newlineChoose 11 answer:\newline(a) (−4,2) (-4,2) \newline(B) (0,4) (0,4) \newline(c) (2,−2) (2,-2) \newline(00) (2,4) (2,4) \newlineShow calculator\newlineS′ S^{\prime} \newline55 of 1010\newlineSkip\newlineCheck
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They randomly assigned a group of 500500 children, 77- 1111 years old, to two groups. After randomization, each child was asked to watch a cartoon in a private room, containing a large bowl of goldfish crackers. The cartoon included 22 commercial breaks. The first group watched food commercials (mostly snacks), while the second group watched non-food commercials (games and entertainment products). Once the child finished watching the cartoon, the psychologists weighed the crackers bowl to measure how many grams of crackers the child ate. Then, they compared the average amount of crackers eaten by each group. What type of statistical study did the psychologists use? Choose 11 answer: Choose 11 answer: (Choice A) Sample study A Sample study (Choice B) Experiment B Experiment (Choice C) Observational study C Observational study The psychologists found that the mean amount of crackers eaten by the children who watched food commercials is 1010 grams greater than the mean amount of crackers eaten by the children who watched non-food commercials. Based on some re-randomization simulations, they concluded that the result is significant and not due to the randomization of the groups. What valid conclusions can be made from this result? Mark the most suitable choice. Choose 11 answer: Choose 11 answer: (Choice A) The result suggests that a 77- 1111 year old child would eat 1010 grams of crackers more while watching food commercials than he would have if he watched other commercials. A The result suggests that a 77- 1111 year old child would eat 1010 grams of crackers more while watching food commercials than he would have if he watched other commercials. (Choice B) The result suggests that food commercials make the people watching them eat more crackers than other types of commercials. B The result suggests that food commercials make the people watching them eat more crackers than other types of commercials. (Choice C) The result suggests a positive correlation between the number of food commercials and the amount of crackers eaten by 77- 1111 year old children while watching them. C The result suggests a positive correlation between the number of food commercials and the amount of crackers eaten by 77- 1111 year old children while watching them. (Choice D) The result suggests that food commercials can have an influence on the amount of crackers consumed by a 77- 1111 year old child watching them. D The result suggests that food commercials can have an influence on the amount of crackers consumed by a 77- 1111 year old child watching them. Related content
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They randomly assigned a group of 500500 children, 77- 1111 years old, to two groups. After randomization, each child was asked to watch a cartoon in a private room, containing a large bowl of goldfish crackers. The cartoon included 22 commercial breaks. The first group watched food commercials (mostly snacks), while the second group watched non-food commercials (games and entertainment products). Once the child finished watching the cartoon, the psychologists weighed the crackers bowl to measure how many grams of crackers the child ate. Then, they compared the average amount of crackers eaten by each group. What type of statistical study did the psychologists use? Choose 11 answer: Choose 11 answer: (Choice A) Sample study A Sample study (Choice B) Experiment B Experiment (Choice C) Observational study C Observational study The psychologists found that the mean amount of crackers eaten by the children who watched food commercials is 1010 grams greater than the mean amount of crackers eaten by the children who watched non-food commercials. Based on some re-randomization simulations, they concluded that the result is significant and not due to the randomization of the groups. What valid conclusions can be made from this result? Mark the most suitable choice. Choose 11 answer: Choose 11 answer: (Choice A) The result suggests that a 77- 1111 year old child would eat 1010 grams of crackers more while watching food commercials than he would have if he watched other commercials. A The result suggests that a 77- 1111 year old child would eat 1010 grams of crackers more while watching food commercials than he would have if he watched other commercials. (Choice B) The result suggests that food commercials make the people watching them eat more crackers than other types of commercials. B The result suggests that food commercials make the people watching them eat more crackers than other types of commercials. (Choice C) The result suggests a positive correlation between the number of food commercials and the amount of crackers eaten by 77- 1111 year old children while watching them. C The result suggests a positive correlation between the number of food commercials and the amount of crackers eaten by 77- 1111 year old children while watching them. (Choice D) The result suggests that food commercials can have an influence on the amount of crackers consumed by a 77- 1111 year old child watching them. D The result suggests that food commercials can have an influence on the amount of crackers consumed by a 77- 1111 year old child watching them. Related content
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What is the constant of proportionality, yx\dfrac{y}{x} ? A graph on a Cartesian coordinate system with x and y-axes. The x-axis is marked with evenly spaced ticks in increments of 11, ranging from 11 to 88. The y-axis is marked with evenly spaced ticks in increments of 22, ranging from 22 to 3030. The graph displays a single slant line starting from (00,00) with an arrowhead at its end. The line passes through a point marked with a filled dot at (11,44). The point (00,00) is marked with a filled dot as well. 1\small{1} 2\small{2} 3\small{3} 4\small{4} 5\small{5} 6\small{6} 7\small{7} 8\small{8} 2\small{2} 4\small{4} 6\small{6} 8\small{8} 1\small{1}33 1\small{1}44 1\small{1}55 1\small{1}66 1\small{1}77 1\small{1}88 1\small{1}99 2\small{2}00 2\small{2}11 2\small{2}22 2\small{2}33 2\small{2}44 2\small{2}55 55 of 77
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In a random survey of US adults, a political scientist found that \\[\(56\)\%\\] of the survey respondents are confident in the current administration's ability to make good foreign policy decisions. The margin of error for this estimation is \\[\(1\)\%\\]. Based on this information, which of the following is the most appropriate conclusion?\(\newline\)A) The true proportion of US adults who are confident in the current administration's ability to make good foreign policy decisions is between \(55\)% and \(57\)%.\(\newline\)B) The true proportion of US adults who are confident in the current administration's ability to make good foreign policy decisions is exactly \(56\)%.\(\newline\)C) The margin of error is too small to make any meaningful conclusions.\(\newline\)D) More than half of the US adults are not confident in the current administration's ability to make good foreign policy decisions.
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Ming has a standard 5252-card deck. A standard 5252-card deck has 44 suits ♡\heartsuit, ♢\diamondsuit, ♣\clubsuit, and ♠\spadesuit and an equal number of cards of each suit. She is going to randomly draw a card from the deck 100100 times, putting the card back in the deck after each draw. Complete the following statement with the best prediction. Ming will draw something other than a ♡\heartsuit…\newlineChoose 11 answer:\newlineChoose 11 answer:\newline(Choice A) Exactly 2525 times\newlineA Exactly 2525 times\newline(Choice B) Close to 525211 times but probably not exactly 525211 times\newlineB Close to 525211 times but probably not exactly 525211 times\newline(Choice C) Exactly 525211 times\newlineC Exactly 525211 times\newline(Choice D) Close to 2525 times but probably not exactly 2525 times\newlineD Close to 2525 times but probably not exactly 2525 times
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The following frequency table summarizes yesterday's orders at Sizzlin' Skillets. Type of stir fry\quadNumber of orders Vegetable\quadChicken\quadPork\quadBeef\quadShrimp\quad Based on this data, what is a reasonable estimate of the probability that the next type of stir fry ordered is shrimp?
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To investigate the history of plate subduction—when one of Earth’s tectonic plates slides beneath another—Sarah M. Aarons and colleagues compared ancient rocks from the Acasta Gneiss Complex in Canada to modern rocks. Using isotope analysis, the researchers found that Acasta rocks dating to about 4.024.02 billion years ago (bya) most strongly resemble modern rocks formed in a plume setting (an area in which hot rocks from Earth’s mantle flow upward into the crust). By contrast, they found that Acasta rocks dating to about 3.753.75 bya and 3.63.6 bya have an isotope composition that is similar to that of modern rocks formed in a subduction setting. Aarons’s team therefore concluded that \newlineWhich choice most logically completes the text? Choose 11 answer: \newline(Choice A, Checked) the majority of the rocks in the Acasta Gneiss Complex formed through subduction. \newline(Choice B) subduction-like processes began occurring in some locations no later than 3.753.75 bya. \newline(Choice C) the rocks in the Acasta Gneiss Complex are of a more recent origin than scientists previously thought. \newline(Choice D) subduction replaced mantle plume formation as the most common geological process by about 4.024.02 bya.
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On her way out of the toy store, Janelle stops to get 22 gumballs from the giant gumball machine. Her favorite flavor is blue raspberry, but only about 30%30\% of the gumballs in the machine are blue. How likely is it that both of the gumballs Janelle gets will be blue? Janelle simulates the situation by putting 33 blue marbles and 77 yellow marbles in a bag. She picks a marble, then returns it to the bag, 22 times. Each time a blue marble appears, it represents a blue gumball. Janelle records the results by writing ＂B＂ for a blue marble and ＂Y＂ for a yellow marble. Here are the results of 2020 trials: \newlineYY, YB, YY, YY, BY, YB, YY, BB, BY, YY, YY, YB, YY, YY, BY, YY, BY, YY, BY, YY\newline Based on Janelle's results, what is the probability that both of the gumballs will be blue?
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Omar tried to evaluate an expression. Here is his work:\newline3×23÷2×4−1+23 \times 2^3 \div 2 \times 4 - 1 + 2\newline3×8÷2×4−1+23 \times 8 \div 2 \times 4 - 1 + 2 {Step 11}\newline24÷2×4−1+224 \div 2 \times 4 - 1 + 2 {Step 22}\newline24÷8−1+224 \div 8 - 1 + 2 {Step 33}\newline3−1+23 - 1 + 2 {Step 44}\newline2+22 + 2 {Step 55}\newline44 {Step 66}\newlineIs Omar's work correct?\newline(A)No, Omar made a mistake going from Step 22 to Step 33. Omar should have divided 2424 by 22 before multiplying. The order of operations says to multiply and divide from left to right.\newline(B)No, Omar made a mistake going from Step 44 to Step 55. Omar should have added 11 and 22 before subtracting. The order of operations says to add before you subtract.\newline(C)Yes, Omar's work is correct.
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Leroy tried to evaluate an expression. Here is his work:\newline42+22−4×6÷3×24^2 + 2^2 - 4 \times 6 \div 3 \times 2\newline62−4×6÷3×26^2 - 4 \times 6 \div 3 \times 2 {Step 11}\newline36−4×6÷3×236 - 4 \times 6 \div 3 \times 2 {Step 22}\newline36−24÷3×236 - 24 \div 3 \times 2 {Step 33}\newline36−8×236 - 8 \times 2 {Step 44}\newline36−1636 - 16 {Step 55}\newline2020 {Step 66}\newlineIs Leroy's work correct?\newline(A)No, Leroy made a mistake going from the given expression to Step 11. Leroy should have squared 44 and 22 instead of adding. The order of operations says to evaluate exponents before you add.\newline(B)No, Leroy made a mistake going from Step 33 to Step 44. Leroy should have multiplied 33 and 22 before dividing. The order of operations says to multiply before you divide.\newline(C)Yes, Leroy's work is correct.
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Joey tried to evaluate an expression. Here is his work:\newline97−3+53÷25×2×3297 - 3 + 5^3 \div 25 \times 2 \times 3^2\newline97−3+125÷25×2×997 - 3 + 125 \div 25 \times 2 \times 9 {Step 11}\newline97−3+5×2×997 - 3 + 5 \times 2 \times 9 {Step 22}\newline97−3+10×997 - 3 + 10 \times 9 {Step 33}\newline97−3+9097 - 3 + 90 {Step 44}\newline97−9397 - 93 {Step 55}\newline44 {Step 66}\newlineIs Joey's work correct?\newline(A)No, Joey made a mistake going from the given expression to Step 11. Joey should have multiplied 22 and 33 instead of evaluating exponents. The order of operations says to multiply before you evaluate exponents.\newline(B)No, Joey made a mistake going from Step 44 to Step 55. Joey should have subtracted 33 from 97−3+125÷25×2×997 - 3 + 125 \div 25 \times 2 \times 900 before adding. The order of operations says to add and subtract from left to right.\newline(C)Yes, Joey's work is correct.
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A school district has n n schools located in different neighborhoods of City Y. A researcher for the school district believes that teacher job satisfaction varies greatly from school to school. Which of the following sampling methods is most appropriate to estimate the proportion of all teachers in the school district who are satisfied with their jobs?\newline Choose 11 answer: \newline(Choice A) Surveying the n n teachers who have taught for the school district the longest\newline(Choice B) Using the first n n responses from an optional online survey for the teachers\newline(Choice C) Selecting one of the n n schools at random and then surveying each teacher at the school\newline(Choice D) Selecting n n teachers from each school at random and then surveying each teacher selected
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There are some red counters and some white counters in a bag. At the start, 77 of the counters are red and the rest of the counters are white. Woody takes two counters from the bag. First he takes at random a counter from the bag. He does not put the counter back in the bag. Woody then takes at random another counter from the bag.\newline(a) Let the number of white counters in the bag be x x ,\newlineDraw a tree diagram that represents the above scenario, showing all relevant information.
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Toby rides his bike to school every day and to his best friend's house regularly. One week, he rode to and from school 55 times and to and from his best friend's house 33 times. He rode a total of 14.414.4 miles that week. The next week, he rode to and from school 44 times and to and from his best friend's house 66 times. He rode a total of 14.414.4 miles that week, too.\newlineThis system of equations can be used to represent the situation:\newline5x+3y=14.45x + 3y = 14.4\newline4x+6y=14.44x + 6y = 14.4\newlineWhich statement is correct?\newlineChoices:\newline(A)In the system of equations, xx represents the total distance Toby traveled to and from school each week, and yy represents the total distance he traveled to and from his best friend's house each week.\newline(B)In the system of equations, xx represents the round-trip distance to and from Toby's best friend's house, and yy represents the round-trip distance to and from Toby's school.\newline(C)In the system of equations, xx represents the round-trip distance to and from Toby's school, and yy represents the round-trip distance to and from his best friend's house.\newline(D)In the system of equations, xx represents the total distance Toby traveled to and from his best friend's house each week, and yy represents the total distance he traveled to and from his school each week.\newlineWhat was the total distance Toby traveled to and from school the first week?\newline____ miles\newline
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Suppose that an airplane is asked to stay in a holding pattern near an airport. The distance of the plane to the airport is described by the following.\newlined(t)=132+66sin⁡(2π11t)d(t)=132+66 \sin\left(\frac{2\pi}{11}t\right)\newlineIn this equation, d(t)d(t) is the distance of the plane to the airport (in miles), and tt is the time (in minutes) after the plane enters the holding pattern.\newlineDuring the first 1111 minutes after the plane enters the holding pattern, when will the plane be 170170 miles from the airport?\newlineDo not round any intermediate computations, and round your answer(s) to the nearest hundredth of a minute. (If there is more than one answer, enter additional answers with the ＂or＂ button.)\newlinet=t=◻＂ minutes ＂◻＂ or ＂
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A local package delivery service wants to improve the efficiency of its deliveries. As a first step, the management team decides to conduct a study to determine the average length of time from the arrival of a package at the company's mail center until its delivery at a home. Which of the following methods is most likely to produce valid results?\newlineChoose 11 answer:\newline(A) The team selects the 11,000000 heaviest packages in a one-week, non-holiday period and records how long it takes for each package to reach its destination.\newline(B) The team calls 11,000000 residents in their delivery area and asks them whether they have received a package from their service in the past week. They will then record how long it took for those packages to reach their destination.\newline(C) The team selects a random sample of 11,000000 packages arriving at the center over a one-week, non-holiday period and records how long it takes for each package to reach its destination.\newline(D) None of the above
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In a study of 4040 randomly selected captive Octopus vulgaris, researchers found that the octopuses could learn to integrate visual and tactile information to find food after a mean of 119119 trials. The estimate had a margin of error of 1818 trials at a 95% 95 \% confidence level. Which of the following is the most reasonable conclusion about the number of trials it would take all captive Octopus vulgaris in general to learn to find the food?\newlineChoose 11 answer:\newline(A) The evidence suggests that half of them would require 119119 or fewer trials.\newline(B) The evidence suggests that the mean number of trials would be 119119 trials.\newline(C) The evidence suggests that the mean number of trials would be between 119119 and 137137 trials.\newline(D) The evidence suggests that the mean number of trials would be between 101101 and 137137 trials.
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In a random survey of US adults, a political scientist found that 56% 56 \% of the survey respondents are confident in the current administration's ability to make good foreign policy decisions. The margin of error for this estimation is 1% 1 \% . Based on this information, which of the following is the most appropriate conclusion?\newlineChoose 11 answer:\newline(A) Exactly 56% 56 \% of US adults are confident that 99% 99 \% of the foreign policy decisions made by the current administration will be good.\newline(B) The political scientist is 99% 99 \% sure that 56% 56 \% of the foreign policy decisions made by the current administration will be good ones.\newline(C) Most US adults believe that 55% 55 \% to 57% 57 \% of the foreign policy decisions made by the current administration will be good ones.\newline(D) It is likely that 55% 55 \% to 57% 57 \% of all US adults are confident in the current administration's ability to make good foreign policy decisions.
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In a survey of smartphone owners, 64% 64 \% of a random sample of younger adults aged 1818−29-29 used their phones to listen to music or podcasts, compared to 21% 21 \% of a random sample of older users who did so. Based on the results of this survey, which of the following conclusions are valid?\newlineI : Younger adults are more likely to listen to music or podcasts on their smartphones than are older adults.\newlineII : Older adults like music less than younger adults.\newlineIII : Older adults do not listen to music on their smartphones because they find it inconvenient.\newlineIV : Younger adults are more likely than older adults to own smartphones.\newlineChoose 11 answer:\newline(A) I only\newline(B) I and II\newline(C) II only\newline(D) I, II, III, and IV
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A study was conducted to compare two biology study aids: a new online game and physical flashcards. 8080 middle school biology students were selected at random, and their parent(s) chose which study aid their child used. The results showed that the students who used flashcards had significantly better outcomes than students who used the online game. Based on this information, which of the following statements is true?\newlineChoose 11 answer:\newline(A) Flashcards are a more effective study aid than the online game for all middle school biology students.\newline(B) The lack of random assignment means there could be other explanations for the study results.\newline(C) The lack of a control group makes comparing flashcards and the online game impossible.\newline(D) None of the statements are true.
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A study was conducted on an elementary school's extracurricular programs. The study divided the students into two groups, those who attended after school electives and those who did not. The results of the study showed that students who attended after school electives were more likely to attend summer camp than students who did not attend these electives. Based on the information provided, which of the following is an appropriate conclusion?\newlineChoose 11 answer:\newline(A) Attending after school electives is a requirement for attending summer camp.\newline(B) After school elective attendance is the strongest predictor of whether a student will attend summer camp.\newline(C) There is a positive association between after school electives attendance and summer camp attendance.\newline(D) If a student stops attending after school electives, then they will not attend summer camp.
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