Question

A random sample of size 775 is drawn from a large population. The population standard deviation is 8.7. The sample mean is 81.5. Find a 99% confidence interval for the population mean, . Round your answers to the nearest tenth.

Answer 1

Step-by-step explanation:

Given A random sample of size 775 is drawn from a large population. The population standard deviation is 8.7. The sample mean is 81.5. Find a 99% confidence interval for the population mean

• So for C % confidence interval,
• n will be the sample size
• So σ will be the population standard deviation.
• So X bar is the sample mean
• Now  
• Sample size is n = 775
• So population standard deviation σ = 8.7
• Sample Mean is X bar = 81.5
• So the critical value for a 99% confidence level is z = 2.576
• So we need to find 99% confidence level for the population mean.
• So we have μ = X bar + - Z . σ / √n
•                       = 81.5 + - 2.576 x 8.7 / √775
•                      = 81.5 + - 0.8052
• So we have two values.
•        One is 81.5 - 0.8052
•                    = 80.6948
•                     = 80.7
•     Another is 81.5 + 0.8052
•                      = 82.3052
•                      = 82.3
• So the 99% confidence for the population mean will be
•             80.7 < μ < 82.3

Reference link will be

https://brainly.in/question/7260437