HW3_STAT302

docx

School

American University *

*We aren’t endorsed by this school

Course

302

Subject

Statistics

Date

Jan 9, 2024

Type

docx

Pages

2

Uploaded by DeaconMoonPorcupine36

Report
HW3: Due Thursday Feb 17 via blackboard 100 points Find Z* and T* critical values (10 points) What is the Zcritical value for a confidence interval with C = 0.9? 1.2815516 What is the Tcritical value for a confidence interval with C = 0.9 and sample size = 15 0.80882893 What is the Tcritical value for a confidence interval with C = 0.9 and sample size= 100? 0.81485876 What happens to the Tcritical value (assuming confidence level stays the same) when you increase the sample size? The Tcritical value also increases. Estimating the sample size (30 points) Let’s assume that you want to estimate the sample size for a survey of American University students to determine their mean height. What is the sample size of your random sample to achieve a margin of error = 0.25 inches at a confidence level = 0.95? Assume that the population standard deviation is 2.5 inches. 1537 Confidence Interval for a population mean (30) In ER of a hospital, a patient was taken 7 consecutive blood pressure measurements at random. Assume that the measurements are normally distributed. Form a confidence interval for the true blood pressure of the patient when the sample mean blood pressure is 135 and the sample standard deviation is 10. Confidence level is 0.90 a) What is the T-critical value corresponding to C = 0.9 and n = 7? a. 1.4149239 b) What is the standard error? a. 10/sqrt(135) = 0.86 c) What is the margin of error?
a. 2.8313292 d) What is the confidence interval? a. 0.9 Confidence Interval for a population proportion (30 points): Three independently taken recent polls of likely voters were asked if they would vote for Biden. Poll nr 1: sample size = 500, sample proportion = 52 % Poll nr 2: sample size = 1000, sample proportion = 50 % Poll nr 3: sample size = 2500, sample proportion = 48% a. Build a 95% confidence interval for the proportion of all likely voters who would vote for Biden in a general election for poll nr1, poll nr. 2 and poll nr3. a. Margin errors: i. Poll nr1 = 0.087582104 ii. Poll nr2 = 0.061979503 iii. Poll nr3 = 0.039167908 b. Compare and comment on their margins of error! a. Poll nr1 has the largest margin or error, while poll nr3 has the lowest. I tried testing poll nr1 with sample proportion of 48% and I still got a similar (if not same) margin of error. This shows that the margin of error inversely proportional to the sample size. The larger the sample size is, the smaller the margin of error is.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help