Question

Calculate the following:

a. lower limit

b. upper limit

c. error bound

Short answer

a. limit limit = 0.7217.

b. Upper limit = 0.87830.

c. Error bound = 0.07830.

Step-by-step solution

Given Information

Formula:

$CIP\text{'}\pm z_c\sqrt{\frac{pq}{n}}$

A value that is less than or equal to every element of a set of data is called a lower bound.

A value that is larger than or equal to every element of a set of data is called an upper bound.

The error bound for a population mean is the margin of error when estimating a population mean ( EBM). The following is the general shape of a confidence interval: (point estimate – EBM, point estimate + EBM) = (lower bound, higher bound)

Solution of A

Lower limit formula is given by,

Lower limit=P'- $z_{aI2}$$\sqrt{\frac{p\text{'}q\text{'}}{n}}$

Lower limit = 0.8 - $z_{0.04}$$\sqrt{\frac{0.8(1-0.8)}{80}}$

Lower limit = 0.8-0.07830472

Lower limit = 0.7217

Solution of B

Upper limit formula is given by,

Upper limit =P' + $z_{aI2}$$\sqrt{\frac{p\text{'}q\text{'}}{n}}$

Upper limit-0.8 + $z_{0.04}$$\sqrt{\frac{0.8(1-0.8)}{80}}$

Upper limit=0.8 + 1.751 x 004472

Upper limit = 0.8 + 0.07830472

Upper limit = 0.87830

Solution of C

Error bound formula is given by,

Error bound=$z_{aI2}$$\sqrt{\frac{p\text{'}q\text{'}}{n}}$

Error bound = $z_{0.04}$$\sqrt{\frac{0.8(1-0.8)}{80}}$

Error bound = 1.751 x 0.04472

Error hound= 0.07830