## Answers

10.

Given that,

population mean(u)=1.14

standard deviation, σ =0.25

sample mean, x =1.07

number (n)=36

null, Ho: μ=1.14

alternate, H1: μ<1.14

level of significance, α = 0.05

from standard normal table,left tailed z α/2 =1.645

since our test is left-tailed

reject Ho, if zo < -1.645

we use test statistic (z) = x-u/(s.d/sqrt(n))

zo = 1.07-1.14/(0.25/sqrt(36)

zo = -1.68

| zo | = 1.68

critical value

the value of |z α| at los 5% is 1.645

we got |zo| =1.68 & | z α | = 1.645

make decision

hence value of | zo | > | z α| and here we reject Ho

p-value : left tail - ha : ( p < -1.68 ) = 0.05

hence value of p0.05 < 0.05, here we do not reject Ho

ANSWERS

---------------

a.

null, Ho: μ=1.14

alternate, H1: μ<1.14

test statistic: -1.68

critical value: -1.645

decision: reject Ho

p-value: 0.05

we have enough evidence to support the claim that whether there has been reduction in the

population mean fee charged on such transactions.

b.

type 1 error is possible because it reject the null hypothesis.

type 2 error is not possible.

(if type 2 error is possible only it fails to reject the null hypothesis)

11.

Given that,

population mean(u)=32

sample mean, x =33.8

standard deviation, s =6

number (n)=36

null, Ho: μ=32

alternate, H1: μ!=32

level of significance, α = 0.1

from standard normal table, two tailed t α/2 =1.69

since our test is two-tailed

reject Ho, if to < -1.69 OR if to > 1.69

we use test statistic (t) = x-u/(s.d/sqrt(n))

to =33.8-32/(6/sqrt(36))

to =1.8

| to | =1.8

critical value

the value of |t α| with n-1 = 35 d.f is 1.69

we got |to| =1.8 & | t α | =1.69

make decision

hence value of | to | > | t α| and here we reject Ho

p-value :two tailed ( double the one tail ) - Ha : ( p != 1.8 ) = 0.0805

hence value of p0.1 > 0.0805,here we reject Ho

ANSWERS

---------------

a.

null, Ho: μ=32

alternate, H1: μ!=32

test statistic: 1.8

critical value: -1.69 , 1.69

decision: reject Ho

p-value: 0.0805

b.

we have enough evidence to support the claim that whether the population mean years of life

lost has changed