Question

Determine the point estimate of the population mean and margin of error for the confidence interval. Lower bound is 19, upper bound is 31. The point estimate of the population mean is

Answer 1

Solution :

Lower bound and upper bound of the confidence interval of population mean is given as follows:

Lower bound = x̅ - E

Upper bound = x̅ + E

Where, x̅ is point estimate of population mean and E is margin of error.

We have, lower bound = 19 and upper bound = 31

i.e.

x̅ - E = 19 .......................(1)

x̅ + E = 31 ........................(2)

Adding (1) and (2) we get,

(x̅ - E) + (x̅ + E) = 19 + 31

2x̅ = 50

x̅ = 50/2

x̅ = 25

Hence, the point estimate of the population mean is 25.

Now, putting the value of x̅ in equation (2) we get,

25 + E = 31

E = 31 - 25

E = 6

The margin of error is 6.

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