Question

A statistician calculates a 95% confidence interval for Mean when Standard Deviation is known. The confidence interval is Rs.18000 to Rs.22000, the amount of the sample mean is

Answer 1

In this question we will use the concept of interval estimation to get the sample mean.

Since standard deviation is known the Variance is also know since from the standard deviation we can get the Variance.

We use the formulae for getting intervals for the mean when Variance is known.

Since we have the lower and upper interval we can easily get the sample mean by forming two Equations for the sample mean and equating them.

When we do this we get :

Rs 20000 as the mean.

Find working in the image below.

Answer 2

Thank you for asking this question.

In order to find the mean we will use the interval estimation.

In this question we have the lower as well as upper intervals and with the help of this we can get the sample mean.

x̅ +- 8/vn Z∝/2

x = sample mean

z = standard normal distribution

(1-∝) 100% = The % probability that the mean lies between interval C₁  and C₂

C₁ is the lower interval

C₂ is the upper interval

C₁ = x̅ - S/Vn Z∝/2 = Rs 18000

C₂ = x̅ + S/Vn Z∝/2 = Rs 22000

Let S/Vn +- Z∝/2 = Y

x̅ +Y = 22000

x̅ - Y = 18000

x̅ = 22000 - Y

x̅ = 18000 + Y

Equating the two

22000 - Y = 18000 + Y

- 2Y = - 4000

Y = 2000

x̅ = 18000 + 2000 = 20000

Sample mean = x̅ = 20000 is the answer