MATH302 WK5 HMWK QUESTIONS AND ANSWERS | LATEST VERSION | GRADED A+

MATH302 WK5 HMWK QUESTIONS AND ANSWERS | LATEST VERSION | GRADED A+ 1. **Which of the following statements correctly describes the relationship between sample size and confidence level to achieve the same margin of error?** - a. Sample size decreases as confidence level increases. - b. Sample size remains constant regardless of confidence level. - c. Sample size fluctuates based on the margin of error. - d. Sample size increases as confidence level increases. - e. None of the above - d. Sample size increases as confidence level increases. **Explanation:** Increasing the confidence level requires a larger sample size to maintain the same margin of error. 2. **In a study estimating the proportion of Americans supporting gun control in 2018 with no prior information, a 92% confidence interval and 0.2 margin of error are desired. How many randomly selected Americans must be surveyed?** - a. 18 - b. 20 - c. 22 - d. 24 - e. None of the above - b. 20 **Explanation:** To estimate with a 92% confidence interval and 0.2 margin of error, approximately 20 Americans need to be surveyed. 3. **A researcher aims to estimate the proportion of children diagnosed with Autism Spectrum Disorder (ASD) in their county with a 95% confidence level and a margin of error within 2%. Using the CDC national estimate of 1 in 68 children diagnosed with ASD, what sample size should the researcher use?** - a. 128 - b. 135 - c. 140 - d. 145 - e. None of the above - c. 140 **Explanation:** To achieve a margin of error within 2% at a 95% confidence level, a sample size of approximately 140 is recommended. 4. **Which statement accurately describes the relationship between sample size and confidence level to achieve the same margin of error?** - a. Sample size decreases as confidence level decreases. - b. Sample size remains constant regardless of confidence level. - c. Sample size fluctuates based on the margin of error. - d. Sample size increases as confidence level decreases. - e. None of the above - a. Sample size decreases as confidence level decreases. **Explanation:** Lower confidence levels require a smaller sample size to achieve the same margin of error. 5. **In a survey aiming to estimate the proportion of Americans supporting gun control in 2018 with a 95% confidence interval and 0.36 margin of error, how many randomly selected Americans must be surveyed?** - a. 7 - b. 8 - c. 9 - d. 10 - e. None of the above