Find the level of confidence assigned to an interval estimat

Find the level of confidence assigned to an interval estimate of the mean formed using the following intervals. (Give your answers correct to three decimal places.)

(a) x - 0.93·_x to x + 0.93·_x


(b) x - 1.65·_x to  x + 1.65·_x


(c) x - 2.29·_x to x + 2.29·_x


(d) x - 2.68·_x to x + 2.68·_x

Solution

Find the level of confidence assigned to an interval estimate of the mean formed using the following intervals.

Confidence interval for mean is,

Xbar - E < mu < Xbar + E

where, Xbar is sample mean.

E is margin of error.

mu is population mean.

Error can be written as,

E = critical value * standard error

So we are given critical values from that we can find confidence level.

(a) x - 0.93· x to x + 0.93· x

critical value is 0.93.

We are given critical value from that we get probability value that is confidence level.

syntax in EXCEL to find test statistics or confidence level is,

=NORMSDIST(z)

where z is the test statistic value.

for first example z is 0.93.

confidence level = 0.951

but confidence level we can write in percentage.

confidence level = 0.951 * 100 = 95.1%

Similarly do for remaining examples.

(b) x - 1.65· x to  x + 1.65· x

confidence level = 0.824

confidence level = 0.824 * 100 = 82.4%

(c) x - 2.29· x to x + 2.29· x

confidence level = 0.989

confidence level = 0.989 * 100 = 98.9%

(d) x - 2.68· x to x + 2.68· x

confidence level = 0.996

confidence level = 0.996 * 100 = 99.6%