A simple random sample of 30 items was selected. The sample mean it was 20 and t

Question

A simple random sample of 30 items was selected. The sample mean it was 20 and the population standard deviation is known to be 4. What is a 99% confidence interval for the population mean? A simple random sample of 30 items was selected. The sample mean it was 20 and the population standard deviation is known to be 4. What is a 99% confidence interval for the population mean? A simple random sample of 30 items was selected. The sample mean it was 20 and the population standard deviation is known to be 4. What is a 99% confidence interval for the population mean?

Explanation / Answer

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.005          
X = sample mean =    20          
z(alpha/2) = critical z for the confidence interval =    2.575829304          
s = sample standard deviation =    4          
n = sample size =    30          
              
Thus,              
              
Lower bound =    18.11888025          
Upper bound =    21.88111975          
              
Thus, the confidence interval is              
              
(   18.11888025   ,   21.88111975   ) [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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