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Home Question Bank Math Statistics Archive 2024 November 29

Statistics Questions from Nov 29,2024

Browse the Statistics Q&A Archive for Nov 29,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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1. Which is more likely to produce a representative sample of math texts written in the United States, a college library or the U.S. Library of Congress? Why? 2. Suggest how students at different grades might investigate the length of words in a textbook. 3. What are the Nielsen ratings? How does the survey determine how many people viewed a television show airing last night? 4. How might a sample not be representative of the population in a study? Look through a textbook on statistics or search online for several types of sampling biases. Create a list and compare with your classmates. Gary has discovered a new painting tool to help him in his work. If he can prove to himself that the painting tool reduces the amount of time it takes to paint a room, he has decided to invest in a tool for each of his helpers as well. From records of recent painting jobs that he completed before he got the new tool, Gary collected data for a random sample of 7 medium-sized rooms. He determined that the mean amount of time that it took him to paint each room was 3.6 hours with a standard deviation of 0.2 hours. For a random sample of 8 medium-sized rooms that he painted using the new tool, he found that it took him a mean of 3.5 hours to paint each room with a standard deviation of 0.3 hours. At the 0.01 level, can Gary conclude that his mean time for painting a medium-sized room without using the tool was greater than his mean time when using the tool? Assume that both populations are approximately normal and that the population variances are equal. Let painting times without using the tool be Population 1 and let painting times when using the tool be Population 2 . Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places. Gary has discovered a new painting tool to help him in his work. If he can prove to himself that the painting tool reduces the amount of time it takes to paint a room, he has decided to invest in a tool for each of his helpers as well. From records of recent painting jobs that he completed before he got the new tool, Gary collected data for a random sample of 6 medium-sized rooms. He determined that the mean amount of time that it took him to paint each room was 3.5 hours with a standard deviation of 0.3 hours. For a random sample of 7 medium-sized rooms that he painted using the new tool, he found that it took him a mean of 3.2 hours to paint each room with a standard deviation of 0.2 hours. At the 0.01 level, can Gary conclude that his mean time for painting a medium-sized room without using the tool was greater than his mean time when using the tool? Assume that both populations are approximately normal and that the population variances are equal. Let painting times without using the tool be Population 1 and let painting times when using the tool be Population 2 . Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places. Gary has discovered a new painting tool to help him in his work. If he can prove to himself that the painting tool reduces the amount of time it takes to paint a room, he has decided to invest in a tool for each of his helpers as well. From records of recent painting jobs that he completed before he got the new tool, Gary collected data for a random sample of 6 medium-sized rooms. He determined that the mean amount of time that it took him to paint each room was 4.5 hours with a standard deviation of 0.3 hours. For a random sample of 8 medium-sized rooms that he painted using the new tool, he found that it took him a mean of 4.2 hours to paint each room with a standard deviation of 0.2 hours. At the 0.01 level, can Gary conclude that his mean time for painting a medium-sized room without using the tool was greater than his mean time when using the tool? Assume that both populations are approximately normal and that the population variances are equal. Let painting times without using the tool be Population 1 and let painting times when using the tool be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places. Gary has discovered a new painting tool to help him in his work. If he can prove to himself that the painting tool reduces the amount of time it takes to paint a room, he has decided to invest in a tool for each of his helpers as well. From records of recent painting jobs that he completed before he got the new tool. Gary collected data for a random sample of 6 medium-sized rooms. He determined that the mean amount of time that it took him to paint each room was 4.5 hours with a standard deviation of 0.3 hours. For a random sample of 8 medium-sized rooms that he painted using the new tool, he found that it took him a mean of 4.2 hours to paint each room with a standard deviation of 0.2 hours. At the 0.01 level, can Gary conclude that his mean time for painting a medium-sized room without using the tool was greater than his mean time when using the tool? Assume that both populations are approximately normal and that the population variances are equal. Let painting times without using the tool be Population 1 and let painting times when using the tool be Population 2 . Step 1 of 3 : state the null and alternative hypotheses for the test. Fill in the blank below. \( H_{0}: \mu_{1}=\mu_{2} \) \( H_{a}: \mu_{1} \) A manufacturer fills soda bottles. Periodically the company tests to see if there is a difference between the mean amounts of soda put in bottles of regular cola and diet cola. A random sample of 11 bottles of regular cola has a mean of 501.6 mL of soda with a standard deviation of 3.9 mL . A fandom sample of 14 bottles of diet cola has a mean of 498.9 mL of soda with a standard deviation of 4.5 mL . Test the claim that there is a difference between the mean fill levels for the two types of soda using a 0.10 level of significance. Assume that both populations are approximately normal and that the population variances are not equal since different machines are used to fill bottles of regular cola and diet cola. Let bottles of regular cola be Population 1 and let bottles of diet cola be Population 2 . Step 2 of 3 : Compute the value of the test statistic. Round your answer to three decimal places. A manufacturer fills soda bottles. Periodically the company tests to see if there is a difference between the mean amounts of soda put in bottles of regular cola and diet cola. A random sample of 11 bottles of regular cola has a mean of 501.6 mL of soda with a standard deviation of 3.9 mL . A random sample of 14 bottles of diet cola has a mean of 498.9 mL of soda with a standard deviation of 4.5 mL . Test the claim that there is a difference between the mean fill levels for the two types of soda using a 0.10 level of significance. Assume that both populations are approximately normal and that the population variances are not equal since different machines are used to fill bottles of regular cola and diet cola. Let bottles of regular cola be Population 1 and let bottles of diet cola be Population 2 . Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below. \[ H_{0}: \mu_{1}=\mu_{2} \] \( H_{a}: \mu_{1} \) tienda siguen una distribución normal, con una media aritmética de 500 euros y una desviación estándar de 50 euros. ¿Cuál es la referencia tipificada para una venta de 635 euros? 625 2.71 1.17 2.70 Al centro de la curva de distribución normal encontramos el eje de simetría que corresponde a: Desviación estándar Valor tipificado Media aritmética Desviación media A professor believes that, for the introductory art history classes at his university, the mean test score of students in the evening classes is lower than the mean test score of students in the morning classes. He collects data from a random sample of 150 students in evening classes and finds that they have a mean test score of 88.9 . He knows the population standard deviation for the evening classes to be 2.1 points. A random sample of 200 students from morning classes results in a mean test score of 89.7 . He knows the population standard deviation for the moming classes to be 7.5 points. Test his claim with a \( 90 \% \) level of confidence. Let students in the evening classes be Population 1 and let students in the morning classes be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
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