L10 Quiz_ Homework_ Social Science Statistics

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Brigham Young University, Idaho *

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Economics

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Apr 3, 2024

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L10 Quiz: Homework Due Feb 17 at 10:59pm Points 12 Questions 13 Available Feb 7 at 11pm - Feb 17 at 10:59pm Time Limit None Allowed Attempts 2 Instructions This quiz was locked Feb 17 at 10:59pm. Attempt History Attempt Time Score KEPT Attempt 2 3 minutes 12 out of 12 LATEST Attempt 2 3 minutes 12 out of 12 Attempt 1 48 minutes 9.5 out of 12 Score for this attempt: 12 out of 12 Submitted Feb 15 at 1pm This attempt took 3 minutes.  Question 1 1 / 1 pts Preparation Download the L10 Homework Assignment (https://byuistats.github.io/BYUI_M221_Book/hp/L10/10_HW_Assignment_A.html) and answer the questions. Attempt each problem on your own. You are encouraged to collaborate with other students after your first attempt. Download the L10 Homework Answer Key (https://byuistats.github.io/BYUI_M221_Book/hp/L10/10_HW_Answer_Key_A.html) and check your answers. Take the Quiz You may use your notes, but you should complete the quiz without help from others. This quiz is a tool to help you and your instructor gauge your progress.

Using the balances of older homeowners because they will have paid off more of their mortgage. Correct! Using the balances of 50 homeowners rather than 35, because using more data gives a smaller margin of error. Using the balances of only fifteen homeowners rather than 35, because there is likely to be less variation in fifteen balances than 35. Using 99% confidence, because then it's more likely that the true mean is contained in the confidence interval.  Question 2 1 / 1 pts Correct! We are 99% confident that the true mean amount of propionic acid in each 800 mg pill is between 3.2 mg and 6.5 mg. There is a 99% chance that the true mean amount of propionic acid in each 800 mg pill is between 3.2 mg and 6.5 mg. 99% of the pills have between 3.2 mg and 6.5 mg units of propionic acid. There is a 99% chance that the sample mean amount of propionic acid in each 800 mg pill is between 3.2 mg and 6.5 mg.  Question 3 1 / 1 pts A mortgage firm estimates the true mean current debt of local homeowners, using the current outstanding balance of a random sample of 35 homeowners. They find a 95% confidence interval for the true mean current debt to be ($56,000, $120,000). Which of the following would correctly produce a confidence interval with a smaller margin of error than this 95% confidence interval? A health inspector from the Food and Drug Administration was tasked with oversight of a pharmaceutical company in their development of a new medication. He used a 99% confidence interval to estimate the true mean amount of propionic acid in each 800 mg pill. Propionic acid is an important ingredient in several medications, including ibuprofen. His confidence interval was (3.2 mg, 6.5 mg). Which one of the following is the best interpretation of this confidence interval? Marine biologists have been studying the effects of acidification of the oceans on weights of male baluga whales in the Arctic Ocean. One of the studies involves a random sample of 16 baluga whales. The researchers want to create a 95% confidence interval to estimate the true mean weight of male baluga whales. Their data follow a normal distribution. The population standard deviation of weights of male baluga whales is kg, and the researchers feel comfortable using this standard deviation for their confidence interval.

Correct! 61.25 61.25 (with margin: 0.005)  Question 4 1 / 1 pts Correct! Yes. The distribution of sample means is normal because the data are normal. Yes. The distribution of sample means is normal because the sample size is large. No. The distribution of sample means is not normal because the sample size is small. No. The fact that the data are normal does not imply that the distribution of sample means is normal.  Question 5 1 / 1 pts Correct! 30 30 (with margin: 0.5)  Question 6 1 / 1 pts Use this information to answer the next three questions. Assuming the relevant requirements are met, calculate the margin of error in kilograms when estimating the true mean weight of male baluga whales in the Arctic Ocean. Round your answer to 2 decimal places. (Example: 24.74). Are the requirements for the use of a confidence interval met? Explain. Assuming the relevant requirements are met, what sample size would be required if the researchers wanted the margin of error to be 45 kg? The heights of young adult females in the United States are said to have a population standard deviation of inches. A sample was taken of young adult females at BYU-Idaho and the mean was computed to be inches. Use this information to answer the next 9 questions.

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Correct! 65.4 65.4 (with margin: 0.001)   Question 7 0.5 / 0.5 pts Correct! 64.847 64.847 (with margin: 0.001)  Question 8 0.5 / 0.5 pts Correct! 65.953 65.953 (with margin: 0.001)  Question 9 1 / 1 pts Correct! The new confidence interval would be wider. The new confidence interval would be narrower. No change. All 95% confidence intervals are the same width.  Question 10 1 / 1 pts What is the point estimate for the population mean? Round your answer to 1 decimal place. (Example: 24.7) Compute the 95% confidence interval of the mean height. Round your answers to 3 decimal places. You should get an interval of the form (lower bound, upper bound). You'll enter your answers in the next two problems. What is the lower bound of the 95% confidence interval for the mean height? What is the upper bound of the 95% confidence interval for the mean height? Suppose that instead of a sample of , you used a sample of . What would change from the 95% confidence interval you calculated in questions 7-8?

There is a 95% chance that the true mean height of adult females in the United States is in our confidence interval. Correct! We are 95% confident that the true mean height of adult females in the United States is somewhere in our confidence interval. Correct! Approximately 95% of all 95% confidence intervals that could be computed from the population of all adult females in the United States will contain the true mean height. 95% of all of the heights of female adults in the US are in our confidence interval. 95% of the heights of female adults in our sample are in our confidence interval.  Question 11 1 / 1 pts The 90% confidence interval would be wider. Correct! The 90% confidence interval would be narrower. No change.  Question 12 1 / 1 pts Correct! 0.464 0.464 (with margin: 0.001)  Question 13 1 / 1 pts Correct! Which of the following explanations describes the correct way to interpret the 95% confidence interval for this problem? (May be more than one correct answer) Suppose you were also asked to calculate a 90% confidence interval. What would change from the 95% confidence interval you calculated previously? What is the margin of error for a 90% confidence interval of the population mean with inches and a sample of young adult females at BYU-Idaho? Round your answer to 3 decimal places. (Example: 24.735) Suppose a new study is being planned. What sample size would be required to obtain a 95% confidence interval with a margin of error of 0.25 inches and inches?

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