Question

A  confidence interval for a population mean was reported to be  to . If , what sample size was used in this study? (Round your answer to next whole number.)

Answer 1

Note :- you have not provided the values of confidence interval , level and standard deviation

Steps:-

Suppose we consider

95% confidence level

Alpha = 0.05 , Z critical = 1.96 (two tailed)

95% confidence interval of population mean

Mu +/- Z * [ sigma / sqrt (n) ]

Lower bound = mu - Z * [ sigma / sqrt (n) ]

Upper bound = mu + Z*[sigma/sqrt(n)]

Let us find mu

We will be provided with upper and lower bound in the given question.

Mu = (lower bound + upper bound) / 2

Consider Sigma is given

Take any equation and simplify it

Upper bound - mu = (Z * sigma ) / sqrt (n)

Sqrt ( n ) = Z*sigma / (upper - mu )

Sample size = n = { (Z*sigma) / (upper - mu) }²

We will get the sample size by solving the equation.