Question

You want to estimate the mean salary of people in a country, so you take a random sample of 49 people from around the country. The sample had an average salary of 8450 00 dollars with population standard deviation of 50000 dollars. Calculate the Lower Limit of the 95% confidence interval for the mean salary of the people in the country. Reminder: You only need to calculate the Lower Limit of the confidence interval

Answer 1

The confidence interval for sample mean is calculated as:

μ = M ± Z(s_M)

where:

M = sample mean
Z = Z statistic determined by confidence level

$\sigma$ = population standard deviation
s_M = standard error = √($\sigma$²/n)

M = 8450
Z = 1.96 calculated using the excel formula for normal distribution which is =NORM.S.INV(0.975)
s_M = √(500²/49) = 71.43

μ = M ± Z(s_M)
μ = 8450 ± 1.96*71.43

μ = 8450 ± 140

thus the confidence inteval is computed as:

Lower limit = 8310,

Upper limit = 8590

Note: Feel free to ask if query remains,