Q4 A contest is held on campus to decide if people like the taste of 3 novel drinks to different degrees. 18 students were selected as representative judges. Each judge Q7 tastes one drink and rates it on a scale of \( 0-10 \) where a 0 means disgusting and a 10 means heavenly tasting. Below are the 18 students' ratings of the three drinks. \begin{tabular}{|c|c|c|c|c|c|c|c|} \hline Sprite Coffee & 3 & 5 & 8 & 9 & 3 & 2 \\ \hline Ginger Coconut Juice & 6 & 4 & 4 & 5 & 2 & 6 \\ \hline Hazelnut Vodka & 4 & 8 & 9 & 7 & 9 & 5 \\ \hline \end{tabular} Q4 Which of the following equations represents the between-group variability? A. \( (3-4.3)^{2}+(5-5.6)^{2}+\ldots+(6-4.3)^{2}+(4-5.6)^{2}+\ldots+(9-4.6)^{2}+(5-4.3)^{2} \) B. \( (3-5.5)^{2}+(5-5.5)^{2}+\ldots+(6-5.5)^{2}+(4-5.5)^{2}+\ldots+(9-5.5)^{2}+(5-5.5)^{2} \) C. \( (5-5.5)^{2}+(5-5.5)^{2}+\ldots+(4.5-5.5)^{2}+(4.5-5.5)^{2}+\ldots+(7-5.5)^{2}+(7-5.5)^{2} \) D. \( (3-5)^{2}+(5-5)^{2}+\ldots+(6-4.5)^{2}+(4-4.5)^{2}+\ldots+(9-7)^{2}+(5-7)^{2} \) Q5 Which of the following equations represents the within-group variability? A. \( (3-4.3)^{2}+(5-5.6)^{2}+\ldots+(6-4.3)^{2}+(4-5.6)^{2}+\ldots+(9-4.6)^{2}+(5-4.3)^{2} \) B. \( (3-5.5)^{2}+(5-5.5)^{2}+\ldots+(6-5.5)^{2}+(4-5.5)^{2}+\ldots+(9-5.5)^{2}+(5-5.5)^{2} \) C. \( (5-5.5)^{2}+(5-5.5)^{2}+\ldots+(4.5-5.5)^{2}+(4.5-5.5)^{2}+\ldots+(7-5.5)^{2}+(7-5.5)^{2} \) D. \( (3-5)^{2}+(5-5)^{2}+\ldots+(6-4.5)^{2}+(4-4.5)^{2}+\ldots+(9-7)^{2}+(5-7)^{2} \)
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Between-group variability measures how different the groups are from each other, while within-group variability measures how spread out the values are within each group. Show more…
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A college food court surveyed students to gather information about the types of drinks they like. Here are the results. • 692 students were surveyed in all • 311 of the students drink milk • 356 of the students drink tea • 225 of the students drink both tea and milk • 119 of the students drink both milk and soda • 191 of the students drink both tea and soda • 97 of the students drink all three types of drinks (tea, milk, soda) • 101 of the students don't drink any of these three types of drinks (tea, milk, soda) Construct a Venn diagram illustrating these results. Then answer the question. All students in the survey How many of the students drink both milk and tea, but don't drink soda? students Drink tea Drink milk Drink soda
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Refer to the following setting. The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the following school year. She wants to know if each type of food will be equally popular so she can start ordering supplies and making other plans. To find out, she selects a random sample of 100 students and asks them, "Which type of food do you prefer: Asian food, Mexican food, pizza, or hamburgers?" Here are her data: $$ \begin{array}{lcccc} \hline \text { Type of Food: } & \text { Asian } & \text { Mexican } & \text { Pizza } & \text { Hamburgers } \\ \text { Count: } & 18 & 22 & 39 & 21 \\ \hline \end{array} $$ (a) $\frac{(18-25)^{2}}{25}+\frac{(22-25)^{2}}{25}+\frac{(39-25)^{2}}{25}+\frac{(21-25)^{2}}{25}$ (b) $\frac{(25-18)^{2}}{18}+\frac{(25-22)^{2}}{22}+\frac{(25-39)^{2}}{39}+\frac{(25-21)^{2}}{21}$ (c) $\frac{(18-25)}{25}+\frac{(22-25)}{25}+\frac{(39-25)}{25}+\frac{(21-25)}{25}$ (d) $\frac{(18-25)^{2}}{100}+\frac{(22-25)^{2}}{100}+\frac{(39-25)^{2}}{100}+\frac{(21-25)^{2}}{100}$ (e) $\frac{(0.18-0.25)^{2}}{0.25}+\frac{(0.22-0.25)^{2}}{0.25}+\frac{(0.39-0.25)^{2}}{0.25}$ $+\frac{(0.21-0.25)^{2}}{0.25}$ The chi-square statistic is
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