Question

According to a​ report, the

standardstandard

deviation ofdeviation of

monthly cell phone

billbills

was

​$48.4248.42

three years ago. A researcher suspects that the

standardstandard

deviation ofdeviation of

monthly cell phone

billbills

is

higherhigher

today.

​(a)	Determine the null and alternative hypotheses.
​(b)	Explain what it would mean to make a Type I error.
​(c)	Explain what it would mean to make a Type II error.

​(a) State the hypotheses.

Upper H 0H0​:

▼

muμ

sigmaσ

pp

▼

equals=

greater than>

not equals≠

less than<

nothing

Upper H 1H1​:

▼

sigmaσ

muμ

pp

▼

not equals≠

equals=

less than<

greater than>

nothing

​(Type integers or decimals. Do not​ round.)

​(b) Explain what it would mean to make a Type I error. Choose the correct answer below.

A.

The sample evidence did not lead the researcher to believe the

standardstandard

deviation ofdeviation of

the monthly cell phone

billbill

is

higher thanhigher than

​$48.4248.42​,

when in fact the

standardstandard

deviation ofdeviation of

the

billbill

is

higher thanhigher than

​$48.4248.42.

B.

The sample evidence led the researcher to believe the

standardstandard

deviation ofdeviation of

the monthly cell phone

billbill

is

less thanless than

​$48.4248.42​,

when in fact the

standardstandard

deviation ofdeviation of

the

billbill

is $ 48.42 .$48.42.

C.

The sample evidence led the researcher to believe the

standardstandard

deviation ofdeviation of

the monthly cell phone

billbill

is

higher thanhigher than

​$48.4248.42​,

when in fact the

standardstandard

deviation ofdeviation of

the

billbill

is

​$48.4248.42.

D.

The sample evidence did not lead the researcher to believe the

standardstandard

deviation ofdeviation of

the monthly cell phone

billbill

is

less thanless than

​$48.4248.42​,

when in fact the

standardstandard

deviation ofdeviation of

the

billbill

is

less thanless than

​$48.4248.42.

​(c) Explain what it would mean to make a Type II error. Choose the correct answer below.

A.

The sample evidence led the researcher to believe the

standardstandard

deviation ofdeviation of

the monthly cell phone bill is

higher thanhigher than

​$48.4248.42​,

when in fact the

standardstandard

deviation ofdeviation of

the

billbill

is

higher thanhigher than

​$48.4248.42.

B.

The sample evidence did not lead the researcher to believe the

standardstandard

deviation ofdeviation of

the monthly cell phone

billbill

is

higher thanhigher than

​$48.4248.42​,

when in fact the

standardstandard

deviation ofdeviation of

the

billbill

is

higher thanhigher than

​$48.4248.42.

C.

The sample evidence did not lead the researcher to believe the

standardstandard

deviation ofdeviation of

the monthly cell phone

billbill

is

less thanless than

​$48.4248.42​,

when in fact the

standardstandard

deviation ofdeviation of

the

billbill

is

less thanless than

​$48.4248.42.

D.

The sample evidence led the researcher to believe the

standardstandard

deviation ofdeviation of

the monthly cell phone

billbill

is

higher thanhigher than

​$48.4248.42​,

when in fact the

standardstandard

deviation ofdeviation of

the

billbill

is

​$48.4248.42.

Answer 1

(A) it is given that the researcher suspects that the standard deviation of monthly cell phone is higher today

So, we have to test whether it is higher or not

(B) Type I error is rejection of true null hypothesis

So, type I error in this case would be “the standard deviation of monthly cell phone is higher today, when in fact, it is not higher ”

option C

(C) type II error is the failure to reject the false null hypothesis

So, type II error in this case would be “the standard deviation is equal to 48.42, when in fact, it is higher than 48.42”

option B