Find the length of the confidence interval given the following…
Question Find the length of the confidence interval given the following… Find the length of the confidence interval given the following data. Example 2: Find the length of the confidence interval given the following data:a. ???= 0.25, ?? = 300, ???????????????????? ??????????: 95% b. ???= 0.48, ?? = 210, ???????????????????? ??????????: 90%Solution:a. Step 1: Find ?. Since confidence level: 95%, therefore ? = 5% or 0.05Step 2: Find ??2. ??2=0.052=0.025Step 3: Find the difference between 0.5 and 0.025. 0.5 – 0.025 = 0.4750Step 4: Find the equivalent z value of 0.4750 using the z-table.Step 5: Since the equivalent z-value of 0.4750 is 1.96, then the value of ????2= 1.96Step 6: Find the value of E.Step 7: Since LCI = 2E, then LCI = 2(0.049) = 0.098.Therefore, the Length of the Confidence Interval is 0.098.b. Step 1: Find ?. Since confidence level: 90%, therefore ? = 10% or 0.1Step 2: Find ??2.Step 3: Find the difference between 0.5 and 0.05.Step 4: Find the equivalent z value of 0.4500 using the z-table.Step 5: Since there is no area equivalent to 0.4500 in z-table, consider the nearest area, in this case there are two nearest area 0.4495 and 0.4505, consider the highest nearest area. So, the value of ????2= 1.65Step 6: Find the value of E.Step 7: Since LCI = 2E, then LCI = 2(0.057) = 0.114.Therefore, the Length of the Confidence Interval is 0.114. Math Statistics and Probability Share QuestionEmailCopy link Comments (0)
