Question

For the following experiments, compute the 95% confidence intervals and determine whether the data comes from the stated population:

(a) X= (3, 2.3, 4.5, 1.2, 5.6, 2.3, 4.5). =3.

(b) i = 4.2, ở = 1.2, n= 100, u= 3.

(c) ji = 0.2, ở = 5, n= 10, u= 3.

(d) å = 1.5, n=10, a=5.

Answer 1

a)

$\mu=3.34, \sigma=1.45$

$t=\frac{x-\mu}{\sigma/\sqrt n}=\frac{x-3.34}{1.45/\sqrt 7}$

$df=n-1=6$

critical values:

$t_{crit}=\pm 2.447$

$-2.447<\frac{x-3.34}{1.45/\sqrt 7}<2.447$

$-1.34<x-3.34<1.34$

$2<x<4.68$

$x=3$ comes from the stated population

b)

$t=\frac{i-u}{\sigma/\sqrt n}=\frac{i-3}{1.2/\sqrt {100}}$

$df=n-1=99$

critical values:

$t_{crit}=\pm 1.984$

$-1.984<\frac{i-3}{1.2/\sqrt {100}}<1.984$

$-0.02<i-3<0.02$

$2.98<i<3.02$

$i=4.2$ does not come from the stated population

c)

$t=\frac{ji-u}{\sigma/\sqrt n}=\frac{ji-3}{5/\sqrt {10}}$

$df=n-1=9$

critical values:

$t_{crit}=\pm 2.262$

$-2.262<\frac{ji-3}{5/\sqrt {10}}<2.262$

$-3.58<ji-3<3.58$

$-0.58<ji<6.58$

$ji=0.2$ comes from the stated population

d)

$t=\frac{x-a}{\sigma/\sqrt n}=\frac{x-5}{1.5/\sqrt {10}}$

$df=n-1=9$

critical values:

$t_{crit}=\pm 2.262$

$-2.262<\frac{x-5}{1.5/\sqrt {10}}<2.262$

$-1.07<x-5<1.07$

$3.93<x<6.07$

$a=5$ ​comes from the stated population