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Interpret confidence intervals for population means

A research study was conducted to determine if a gene therapy is successful in treating color blindness in mice. From a large population of mice with color blindness, 200200 were selected at random. Half of the mice were randomly assigned to receive the therapy, and the other half did not. The results showed that 80% 80 \% of the mice that received therapy had some of their ability to see color restored. Based on the design and results of the study, which of the following is an appropriate conclusion?\newlineChoose 11 answer:\newline(A) The gene therapy is better at treating color blindness than other available treatments.\newline(B) The gene therapy is likely to fully restore the ability to see color for mice with color blindness.\newline(C) The gene therapy is likely to improve the ability to see color for mice with color blindness.\newline(D) The gene therapy will improve the ability to see color for humans with color blindness.
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A study was conducted on the effect of classical music on puzzle solving. 500500 randomly selected college students were asked to solve a jigsaw puzzle. Half of them were randomly assigned to listen to classical music while solving, and the other half were not. On average, it took participants who were listening to classical music 2525 seconds longer to solve their puzzles. Based on the information provided, which of the following is an appropriate conclusion for college students?\newlineChoose 11 answer:\newline(A) Listening to classical music is likely to lengthen puzzle solving time.\newline(B) Listening to classical music is likely to shorten puzzle solving time.\newline(C) Listening to classical music is likely to lengthen the time needed for any activity.\newline(D) Classical music is the best genre of music to listen to for shortening puzzle solving time.
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Chapter 1111 Review WS\newline11. Determine whether the question is a statistical question. How much do new cell phones cost?\newline22. The table shows the distances of students' homes from a school. Display the data in a dot plot.\newline\begin{tabular}{|c|c|c|c|c|c|}\newline\hline \multicolumn{77}{|c|}{ Distances (miles) } \\\newline\hline 88 & 11 & 66 & 33 & 22 & 44 \\\newline\hline 44 & 22 & 22 & 77 & 88 & 88 \\\newline\hline 11 & 77 & 88 & 66 & 66 & 33 \\\newline\hline\newline\end{tabular}\newline33. A group of five sixth-graders measure and reeord their heights. The heights (in inches) are 5959,5757,6262,5858, and 5959. Find the mean and the median of the heights.\newline44. Find the mode of the data.\newline22,25,25,20,17,21,24,25,21,18 22,25,25,20,17,21,24,25,21,18 \newline55. Find the range of the data.\newline32,33,99,76,35,62 32,33,99,76,35,62 \newline66. Identify the outlier(s) in the data set.\newline89,85,88,83,87,89,81,87,85,88,83,133 89,85,88,83,87,89,81,87,85,88,83,133 \newline77. Each backpack in a store is on sale for $5 \$ 5 off the original price. How does this affect the mean, median, and mode of the prices?\newline1212. Make a box-and-whisker plot of the data values 63,65,79,60,69,73 63,65,79,60,69,73 , 7878,6767 , and 7474 .\newlineName:\newline99. The frequency table shows the numbers of books read by students in a elass over sunamer vacation. Display the data in a histogram. Identify any gaps, clusters, or outlicrs.\newline\begin{tabular}{|l|c|c|c|c|c|}\newline\hline Books & 0−1 0-1 & 2−3 2-3 & 4−5 4-5 & 6−7 6-7 & 8−9 8-9 \\\newline\hline Frequency & 11 & 77 & 88 & 66 & 44 \\\newline\hline\newline\end{tabular}\newline1919. The histogram shows the weights of gams in a bin. Which interval contains the most data values?\newline1111. The hisegrams show the ages of prople riding two rides at an amusertikent park. Deseribe the shape of each distribution. Which ride has older riders?\newline1313. The box-and-whisker plot shows the lengths of caterpillars at an exhibit. What fraction of the caterpillars has a length of at least 4545 millimeters?
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44) Testing conducted by Consumer Reports evaluated the costs of various toaster ovens. The results and the partial Excel output are as follows:\newline\begin{tabular}{|c|c|}\newline\hline Product & Cost \\\newline\hline X22 Power & 350350 \\\newline\hline Napa Legend & 130130 \\\newline\hline Odyssey Extreme & 380380 \\\newline\hline Bosch & 125125 \\\newline\hline Odyssey Performance & 255255 \\\newline\hline Exide & 180180 \\\newline\hline Duracell 5151R & 105105 \\\newline\hline Optima & 260260 \\\newline\hline\newline\end{tabular}\newline\begin{tabular}{|l|r|}\newline\hline Level of Significance & 00.0505 \\\newline\hline Sample Size & 88 \\\newline\hline Sample Mean & 223223 \\\newline\hline \begin{tabular}{l} \newlineSample Standard \\\newlineDeviation\newline\end{tabular} & 105105 \\\newline\hline p-value & 00.24532453 \\\newline\hline\newline\end{tabular}\newlineSource: Consumer Reports,
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Suppose 11%11\% of student veterans at a college are involved in sports. A random sample of 135135 student veterans is taken. What is the mean of the sampling distribution for the proportion of veterans in sports at this college? 1111. σ(@)\sigma^{(@)} When working with samples of size 135135, what is the standard error of the sampling distribution for the proportion of veterans in sports at this college? .027.027 Round answer to 33 decimal places. Is it unusual that no more than 2020 veterans in the sample are involved in sports? (hint: 2020 of 135135 is about 13513500) ◻ Round answer to 13513511 decimal places. Enter an integer or decimal number, with 13513511 decimal places [more..] Is this result unusual? Yes, there is a less than 13513533 chance of this happening by random variation. No, there is at least a 13513533 chance of this happening by random variation.\newline13513555\newlineSubmit Question
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Suppose 11% 11 \% of student veterans at a college are involed in sports. A random sample of 135135 student veterans is taken.\newlineWhat is the mean of the sampling distribution for the proportion of veterans in sports at this college?\newline□ \square σ∘ \sigma^{\circ} \newlineWhen working with samples of size 135135, what is the standard error of the sampling distribution for the proportion of veterans in sports at this college? .027027 □ \square σ4 \sigma^{4} Round answer to 33 decimal places.\newlineIs it unusual that no more than 2020 veterans in the sample are involved in sports? (hint: 2020 of 135135 is about 0.148) 0.148) □ \square Round answer to 44 decimal places.\newlineEnter an inteycr or decimal number, with 44 decimal places [more.−1-1]\newlineIs this result unusual?\newlineYes, there is a less than 5% 5 \% chance of this happening by random variation.\newlineNo, there is at least a 5% 5 \% chance of this happening by random variation.\newlineσ \sigma \newlineSubmit Question
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deltamath.com\newlineA group of students at a high school took a standardized test. The number of students who passed or failed the exam is broken down by those who did or did not eat breakfast in the following table. Determine whether eating breakfast and passing the test are independent by filling out the blanks in the sentence below, rounding all probabilities to the nearest thousandth.\newline\begin{tabular}{|c|c|c|}\newline\hline & Passed & Failed \\\newline\hline Did Eat Breakfast & 123123 & 2626 \\\newline\hline Didn't Eat Breakfast & 66 & 7777 \\\newline\hline\newline\end{tabular}\newlineAnswer Attempt 22 out of 22\newlineSince P(didn't eat breakfast | fail )=□ )=\square and P( P( didn't eat breakfast ) ) =□ =\square , the two results are unequal ∨ \vee so the events are\newlineindependent
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Suppose a bowler claims that her bowling score is not equal to 150150 points, on average. Several of her teammates do not believe her, so the bowler decides to do a hypothesis test, at a 5% 5 \% significance level, to persuade them. She bowls 2222 games. The mean score of the sample games is 157157 points. The bowler knows from experience that the standard deviation for her bowling score is 1818 points.\newline- H0:μ=150;Ha:μ≠150 H_{0}: \mu=150 ; H_{a}: \mu \neq 150 \newline- α=0.05 \alpha=0.05 (significance level)\newlineWhat is the test statistic (z-score) of this one-mean hypothesis test?\newlineSelect the correct answer belov:\newline71822≈1.82 \frac{7}{\frac{18}{\sqrt{22}}} \approx 1.82 \newline7182323≈1.87 \frac{\frac{7}{18}}{\frac{\sqrt{23}}{\sqrt{23}}} \approx 1.87
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Practice | Siyavula\newlinesiyavula.com/activity/44b77fa11aa−1-1f6868−4-4f88c-b77b00-cf5959c99d00f5353b/response/f66c653653d11-dd2121−4-4a5858-b11eb−558-558af33a00f11a11/00\#now\newlineHome\newlineSIYAVULA\newlinePractice\newlinePast papers\newlineTextbooks Measurements\newlineRIGHT PYRAMIDS, RIGHT CONES AND SPHERES\newlineThe diagram below shows a cone. The slant height is 19 cm 19 \mathrm{~cm} and the radius of the base is 5 cm 5 \mathrm{~cm} . The figure is not necessarily drawn to scale.\newlineCalculate the surface area and the volume of the cone.\newlineINSTRUCTION: Round each of your answers to the nearest integer.\newlineKutlwano Tema\newlineNotifications\newlineLog out\newlineAnswer:\newline- The surface area = = □ \square cm2 \mathrm{cm}^{2} \newline- The volume = = □ \square cm3 \mathrm{cm}^{3} cm3 \mathrm{cm}^{3} \newlineReport error in question\newlineType here to search
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Practice | Siyavula\newlinesiyavula.com/activity/b1616df5252e-e308308−43-43bb−848-848a−7-7a4242edfbe77fc/response/19311931e88b55-a875875−459-459e−8521-8521-fe903903f88be178178/complete\#now\newlineHome\newlinePractice\newlinePast papers\newlineSIYAVULA\newlineTHCOMNOLOGY-POWFRTO LIARNING\newlineThe three facts above tell us everything we need to know about how the trigonometric ratios are defined on the Cartesian plane! We already know how the trigonometric ratios are related to the opposite, adjacent, and hypotenuse sides of a triangle. And now we know how the opposite, adjacent, and hypotenuse sides are related to x,y x, y , and r r . So we can tie it all together:\newlineTextbooks\newlineLeaderboards\newlineCampaigns\newlineLearner opportunities\newlinePricing\newlineSupport\newlineKutlwano Tema\newlineNOTE: In the diagram above, the point (x;y) (x ; y) does not have to be in Quadrant I. It will move around the circle depending on the value of θ \theta . When the point rotates around the circle, the triangle will change shape and the values of x x and y y will change. But the relationships above stay the same.\newlineThe definition of the cosine ratio on the Cartesian plane is xr \frac{x}{r} .\newlineNotifications\newlineSubmit your answer as: □ \square \newline□ \square \newlineLog out
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Practice | Siyavula\newlineMath Al\newlinesiyavula.com/activity/aa55d55205520-f2525b−410-410a−82-82ca-d66c428428ba00b2525/response/157157bc77c00−2-2bce−4136-4136-be99f-cc66f77c11dc1818b/00\#now\newlineSIYAVULA\newlineReading mode\newlinePoppins\newlineA- A+ A+ \newlinec\newlineThe figure below shows a histogram which summarises a set of data values. The data values are real numbers. The data are grouped into 55 intervals. Answer the two questions below about the histogram.\newlineHighlight the text you want to open in reading mode\newlineReading mode can't find the main content on this page\newlinehttps://www.siyavula.com/practice/isolated_image/37213721/405565405565/00?region=ZA\&activity_type=practice\&language=en\newlineType here to search\newlineLinks\newline16∘C 16^{\circ} \mathrm{C} Partly sunny\newline0808:1818\newline20242024/0404/0303
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Sarah and David agree to a friendly game of darts. Sarah has some skill as a carpenter and makes a fancy dartboard, as show below:\newlineEach of the green and yellow squares is 4 cm×4 cm 4 \mathrm{~cm} \times 4 \mathrm{~cm} . The pink, dark blue, and light blue circles are exactly in the centre of the dartboard and have radii of 1 cm,3 cm 1 \mathrm{~cm}, 3 \mathrm{~cm} and 5 cm 5 \mathrm{~cm} respectively. When you include the grey teardrops in each corner, the whole dartboard is 32 cm 32 \mathrm{~cm} across.\newlineAs inquisitive mathematicians, they are of course interested in the probabilities of certain outcomes, ie what is her chance of landing the dart in a yellow section, etc. They haven't had much practice with playing darts, and 10% 10 \% of the time they don't hit the dartboard at all (ie they only hit it 90% 90 \% of the time). Of the shots that land on the dartboard, they are randomly distributed except that 70% 70 \% land within the region containing the red square and the centre circles, and 40% 40 \% land within the region containing the centre circles.\newlineIn deciding on a fair scoring system for this dartboard, they agree that the points awarded for hitting a certain colour should be inversely proportional to the chance of hitting that colour (ie: something twice as rare should be worth twice as much). As a starting point, they decide that striking yellow should be worth 88 points.\newlineYour task is to find the probability distribution of hitting each colour, and thus determine how many points each colour is worth. The game is not played with half-points, so if the correct proportional answer is not a whole number, round it to the nearest whole number.\newlineFor full marks your answers must include:\newline- an introductory explanation of your overall strategy\newline- full details including brief explanations of all calculations used\newline- tables where appropriate to summarise your results (these may include relevant calculations)
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The accompanying data set lists full IQ scores for a random sample of subjects with medium lead levels in their blood and another random sample of subjects with high lead levels in their blood. Use a 00.0101 significance level to test the claim that IQ scores of subjects with medium lead levels vary more than IQ scores of subjects with high lead levels.\newlineLet sample 11 be the sample with the larger sample variance, and let sample 22 be the sample with the smaller sample variance. What are the null and alternative hypotheses?\newlineA. H0:σ12=σ22 H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \newlineB. H0:σ12=σ22 H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \newlineH1:σ12<σ22 \mathrm{H}_{1}: \sigma_{1}^{2}<\sigma_{2}^{2} \newlineH1:σ12≠σ22 \mathrm{H}_{1}: \sigma_{1}^{2} \neq \sigma_{2}^{2} \newlineC. H0:σ12=σ22 H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \newlineD. H0:σ12≠σ22 H_{0}: \sigma_{1}^{2} \neq \sigma_{2}^{2} \newlineH1:σ12>σ22 \mathrm{H}_{1}: \sigma_{1}^{2}>\sigma_{2}^{2} \newlineH1:σ12=σ22 \mathrm{H}_{1}: \sigma_{1}^{2}=\sigma_{2}^{2} \newlineIdentify the test statistic.\newlineThe test statistic is 22.5757 .\newline(Round to two decimal places as needed.)\newlineIdentify the P-value.\newlineThe P-value is □ \square \newline(Round to three decimal places as needed.)
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The accompanying data set lists full IQ scores for a random sample of subjects with medium lead levels in their blood and another random sample of subjects with high lead levels in their blood. Use a 00.0101 significance level to test the claim that IQ scores of subjects with medium lead levels vary more than IQ scores of subjects with high lead levels.\newline\begin{tabular}{|c|c|c|c|c|c|c|c|c|}\newline\hline \multirow{22}{*}{ Medium } & \multicolumn{88}{|c|}{\begin{tabular}{llllllll}\newline9090 & 111111 & 9292 & 9797 & 8585 & 9191 & 9191 & 100100\newline\end{tabular}} \\\newline\hline & 8383 & 8686 & 9292 & 7272 & 7777 & 9191 & 8282 & 7878 \\\newline\hline & 9393 & 7575 & 8080 & 9696 & 8383 & 8888 & 8888 & 88 \\\newline\hline & 101101 & 8585 & 8585 & 8282 & 7979 & 7676 & 104104 & \\\newline\hline\newline\end{tabular}\newlineLet sample I ve ule sample winl ule ranyer sample vananice, anlu let sample < < ve ule sample winl ule smaller sample variance. What are the null and alternative hypotheses?\newlineA. H0:σ12=σ22 H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \newlineB. H0:σ12≠σ22 H_{0}: \sigma_{1}^{2} \neq \sigma_{2}^{2} \newlineH1:σ12<σ22H1:σ12=σ22 \mathrm{H}_{1}: \sigma_{1}^{2}<\sigma_{2}^{2} \quad \mathrm{H}_{1}: \sigma_{1}^{2}=\sigma_{2}^{2} \newlineC. H0:σ12=σ22 H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \newlineD.\newlineH1:σ12≠σ22 \mathrm{H}_{1}: \sigma_{1}^{2} \neq \sigma_{2}^{2} \newlineH0:σ12=σ22H1:σ12>σ22 \begin{array}{l} H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \\ H_{1}: \sigma_{1}^{2}>\sigma_{2}^{2} \end{array} \newlineIdentify the test statistic.\newlineThe test statistic is □ \square \newline(Round to two decimal places as needed.)
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The accompanying data set lists full IQ scores for a random sample of subjects with medium lead levels in their blood and another random sample of subjects with high lead levels in their blood. Use a 00.0101 significance level to test the claim that IQ scores of subjects with medium lead levels vary more than IQ scores of subjects with high lead levels. smaller sample variance. What are the null and alternative hypotheses?\newlineA. H0:σ12=σ22 H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \newlineB.\newlineH0:σ12≠σ22H1:σ12=σ22 \begin{array}{l} H_{0}: \sigma_{1}^{2} \neq \sigma_{2}^{2} \\ H_{1}: \sigma_{1}^{2}=\sigma_{2}^{2} \end{array} \newlineH1:σ12<σ22 \mathrm{H}_{1}: \sigma_{1}^{2}<\sigma_{2}^{2} \newlineC. H0:σ12=σ22 H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \newlineH0:σ12=σ22H1:σ12>σ22 \begin{array}{l} H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \\ H_{1}: \sigma_{1}^{2}>\sigma_{2}^{2} \end{array} \newlineH1:σ12≠σ22 \mathrm{H}_{1}: \sigma_{1}^{2} \neq \sigma_{2}^{2} \newlineIdentify the test statistic.\newlineThe test statistic is □ \square \newline(Round to two decimal places as needed.)
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Words were displayed on a computer screen with background colors of red and blue. Results from scores on a test of word recall are given below. Use a 00.0505 significance level to test the claim that the samples are from populations with the same standard deviation. Assume that both samples are independent simple random samples from populations having normal distributions. Does the background color appear to have an effect on the variation of word recall scores?\newline\begin{tabular}{lccc} \newline& n \mathbf{n} & x‾ \overline{\mathbf{x}} & s \mathbf{s} \\\newlineRed Background & 3434 & 1515.5353 & 55.9595 \\\newlineBlue Background & 3737 & 1212.3535 & 55.4747\newline\end{tabular}\newlineC. H0:σ12=σ22 H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \newlineD. H0:σ12=σ22 H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \newlineH1:σ12≥σ22 \mathrm{H}_{1}: \sigma_{1}^{2} \geq \sigma_{2}^{2} \newlineH1:σ12<σ22 \mathrm{H}_{1}: \sigma_{1}^{2}<\sigma_{2}^{2} \newlineIdentify the test statistic.\newlineF=1.18 \mathrm{F}=1.18 (Round to two decimal places as needed.)\newlineUse technology to identify the P-value.\newlineThe P-value is 00.620620 . (Round to three decimal places as needed.)\newlineWhat is the conclusion for this hypothesis test?
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Words were displayed on a computer screen with background colors of red and blue. Results from scores on a test of word recall are given below. Use a 00.0505 significance level to test the claim that the samples are from populations with the same standard deviation. Assume that both samples are independent simple random samples from populations having normal distributions. Does the background color appear to have an effect on the variation of word recall scores?\newline\begin{tabular}{lccc} \newline& n \mathbf{n} & x‾ \overline{\mathbf{x}} & s \mathbf{s} \\\newlineRed Background & 3434 & 1515.5353 & 55.9595 \\\newlineBlue Background & 3737 & 1212.3535 & 55.4747\newline\end{tabular}\newlinepopulations with the same standard deviation.\newlineD. Reject H0 \mathrm{H}_{0} . There is insufficient evidence to warrant rejection of the claim that the samples are from populations with the same standard deviation.\newlineDoes the background color appear to have an effect on the variation of word recall scores?\newlineA. Yes, the variation of word recall scores appears to be different when the color is changed.\newlineB. No, the variation of word recall scores appears to be the same when the color is changed.\newlineC. Yes, the variation of word recall scores appears to be the same when the color is changed.\newlineD. No, the variation of word recall scores appears to be different when the color is changed.
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Words were displayed on a computer screen with background colors of red and blue. Results from scores on a test of word recall are given below. Use a 00.0505 significance level to test the claim that the samples are from populations with the same standard deviation. Assume that both samples are independent simple random samples from populations having normal distributions. Does the background color appear to have an effect on the variation of word recall scores?\newline\begin{tabular}{lccc} \newline& n \mathbf{n} & x‾ \overline{\mathbf{x}} & s \mathbf{s} \\\newlineRed Background & 3434 & 1515.5353 & 55.9595 \\\newlineBlue Background & 3737 & 1212.3535 & 55.4747\newline\end{tabular}\newlineH1:σ12≠σ22 \mathrm{H}_{1}: \sigma_{1}^{2} \neq \sigma_{2}^{2} \newlineC.\newlineH0:σ12=σ22H1:σ12≥σ22 \begin{array}{l} H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \\ H_{1}: \sigma_{1}^{2} \geq \sigma_{2}^{2} \end{array} \newlineH1:σ12=σ22 H_{1}: \sigma_{1}^{2}=\sigma_{2}^{2} \newlineD.\newlineH0:σ12=σ22H1:σ12<σ22 \begin{array}{l} H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \\ H_{1}: \sigma_{1}^{2}<\sigma_{2}^{2} \end{array} \newlineIdentify the test statistic.\newlineF=1.18 \mathrm{F}=1.18 (Round to two decimal places as needed.)\newlineUse technology to identify the P-value.\newlineThe P \mathrm{P} -value is □ \square . (Round to three decimal places as needed.)
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PSSA MATHEMATICS GRADE 66\newline1616. Franco asked his soccer team how many glasses of milk and how many glasses of water each player drinks per day. The line plots below show his data.\newlineAmount of Milk Each Player Drinks\newlineAmount of Water Each Player Drinks\newlineWhich statement correctly describes the number of glasses of milk and the number of glasses of water each player drinks per day?\newlineA. The mean would be a better measure of center than the median for the number of glasses of milk the players drink.\newlineB. There is less variability in the number of glasses of milk the players drink than the number of glasses of water they drink.\newlineC. The median number of glasses of milk the players drink is greater than the mean number of glasses of milk the players drink.\newlineD. The range for the number of glasses of milk and the range for the number of glasses of water the players drink are the same.
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