4) Existe un medicamento para aliviar la tensión nerviosa, el cual es efectivo en el \( 60 \% \) de los casos. Se han realizado experimentos con un nuevo medicamento en 100 sujetos, que sufren tensión nerviosa y el medicamento ha proporcionado alivio en un \( 70 \% \) de los casos. Con un nivel de significación del \( 5 \% \) ¿es esto suficiente evidencia para concluir que el nuevo medicamento es mejor? ( 2.50 p)

5. Read about basic ideas of statistics in Common Core Standards for grades \( 3-5 \), and discuss why students at these grade levels should be studying data analysis. 6. Choose a grade and design a grade-appropriate question that students could investigate using statistics. 7. A student asks if the precision with which manufacturers must calibrate their tools is at all related to statistics. How do you respond? 8. Lucas asks what an exit poll is and whether exit polls are effective at predicting results in an election. What do you tell him? kric asks about the taste-testers a popular pizza restaurant chain employs. He wants to related to statistics. How do you respond?

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 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.

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. \[ H_{0}: \mu_{1}=\mu_{2} \] \( H_{a}: \mu_{1} \)

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.