STATS HW

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Peru State College *

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MISC

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Statistics

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Feb 20, 2024

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You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately o = 35.6. You would like to be 95% confident that your estimate is within 5 of the true population mean. How large of a sample size is required? n= Do not round mid-calculation. However, you are encouraged to use a critical value accurate to three decimal places — this is important for the system to be able to give hints for incorrect answers. 6) You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately o = 28.8. You would like to be 95% confident that your estimate is within 4 of the true population mean. How large of a sample size is required? - Do not round mid-calculation. However, you are encouraged to use a critical value accurate to three decimal places — this is important for the system to be able to give hints for incorrect answers. 7) In a survey, 21 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $30 and standard deviation of $2. Find the margin of error at a 99% confidence level. Give your answer to two decimal places. | 8) If n=14, T (x-bar)=46, and s=19, construct a confidence interval at a 95% confidence level. Assume the data came from a normally distributed population. Give your answers to one decimal place. n
9) In a survey, 32 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $35 and standard deviation of $20. Construct a confidence interval at a 90% confidence level. Give your answers to one decimal place. | J*| 10) Assume that a sample is used to estimate a population mean u. Find the 90% confidence interval for a sample of size 38 with a mean of 37.3 and a standard deviation of 6.4. Enter your answer as an open- interval (i.e., parentheses) accurate to one decimal place (because the sample statistics are reported accurate to one decimal place). 90% C.I. = Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. 11) You intend to estimate a population mean p with the following sample. 52.9 74.3 77.4 94.4 79.3 83.9 72.2 114.3 95.5 100.5 97.7 You believe the population is normally distributed. Find the 95% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place). 95% C.1. = Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
14) A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 3% margin of error at a 99% confidence level, what size of sample is needed? Give your answer in whole people. | 16) Express the confidence interval 49.2% = 3.6% in the form of a trilinear inequality. 18) Assume that a sample is used to estimate a population proportion p. Find the 80% confidence interval for a sample of size 291 with 27.1% successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places. 80% C.I. =[ Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. 19) Assume that a sample is used to estimate a population proportion p. Find the 90% confidence interval for a sample of size 348 with 66 successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places. el Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
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20) Assume that a sample is used to estimate a population proportion p. Find the 90% confidence interval for a sample of size 230 with 69.1% successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places. e Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. 21) Assume that a sample is used to estimate a population proportion p. Find the 90% confidence interval for a sample of size 230 with 69.1% successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places. el Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. 22) You want to obtain a sample to estimate a population proportion. At this point in time, you have no reasonable estimate for the population proportion. You would like to be 99% confident that your estimate is within 2% of the true population proportion. How large of a sample size is required? S Do not round mid-calculation. However, use of a critical value rounded to three decimal places will suffice. 23) Out of 300 people sampled, 150 preferred Candidate A. Based on this, estimate what proportion of the voting population () prefers Candidate A. Use a 95% confidence level, and give your answers as decimals, to three places. [<m<|
24) We wish to estimate what percent of adult residents in a certain county are parents. Out of 400 adult residents sampled, 56 had kids. Based on this, construct a 99% confidence interval for the proportion 7 of adult residents who are parents in this county. Give your answers as decimals, to three places. | < T < 25) We wish to estimate what percent of adult residents in a certain county are parents. Out of 500 adult residents sampled, 55 had kids. Based on this, construct a 90% confidence interval for the proportion 7 of adult residents who are parents in this county. Provide the point estimate and margin of error. Give your answers as decimals, to three places. = ]i[

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