As we prepare to take a sample and compute a 95% confidence interval we know tha

Question

As we prepare to take a sample and compute a 95% confidence interval we know that the probability that the interval we compute will cover the parameter is 0.95. That's the meaning of 95% confidence. If we use several such intervals, however, our confidence that all of them give correct results is less than 95%. Suppose we take independent samples each month for five months and report a 95% confidence interval for each set of data. What is the probability that all five intervals cover the true means? This probability is our overall confidence level for the five simultaneous statements. Give your answer to 4 decimal places. Fill in the blank: The probability is: _____ As we prepare to take a sample and compute a 95% confidence interval we know that the probability that the interval we compute will cover the parameter is 0.95. That's the meaning of 95% confidence. If we use several such intervals, however, our confidence that all of them give correct results is less than 95%. Suppose we take independent samples each month for five months and report a 95% confidence interval for each set of data. What is the probability that at least four of the five intervals cover the true means? Give your answer to 4 decimal places. Fill in the blank: The probability is: _____.

Explanation / Answer

Solution:- formula =P(X=x) = (nCx) px (1-p)n-x

given values :-   n= 5, p= 0.95, x = 5

Step 1:   P(x=5) = 5C5 (0.95)^5 = 1 * 0.7738 = 0.7738

Step 2:   P( x >= 4) = P(x=4)+P(x=5)
P(x=5) = 0.7738
P(x = 4) = 5C4 (0.95)^4 (0.05) = 5 * 0.8145 * 0.05 = 0.2036
P( at least 4) = 0.7738 + 0.2036 = 0.9774

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.