Question

As part of your work for an environmental awareness​ group, you want to test the claim that the mean waste generated by adults in the country is more than

33

pounds per person per day. In a random sample of

1515

adults in the​ country, you find that the mean waste generated per person per day is

3.23.2

pounds and the standard deviation is

1.31.3

pounds. At

alpha equals 0.05α=0.05​,

can you support the​ claim? Assume the population is normally distributed.​(a) Write the claim mathematically and identify

Upper H 0H0

and

Upper H Subscript aHa.

Which of the following correctly states

Upper H 0H0

and

Upper H Subscript aHa​?

A.

Upper H 0H0​:

muμless than or equals≤33

Upper H Subscript aHa​:

muμgreater than>33

B.

Upper H 0H0​:

muμgreater than or equals≥33

Upper H Subscript aHa​:

muμless than<33

C.

Upper H 0H0​:

muμgreater than>33

Upper H Subscript aHa​:

muμless than or equals≤33

D.

Upper H 0H0​:

muμequals=33

Upper H Subscript aHa​:

muμless than<33

E.

Upper H 0H0​:

muμequals=33

Upper H Subscript aHa​:

muμgreater than>33

F.

Upper H 0H0​:

muμequals=33

Upper H Subscript aHa​:

muμnot equals≠33

​(b) Find the critical​ value(s) and identify the rejection​ region(s).

What​ is(are) the critical​ value(s),

t 0t0​?

t 0t0equals=nothing

​(Use a comma to separate answers as needed. Round to three decimal places as​ needed.)

Which of the following graphs best depicts the rejection region for this​ problem?

A.

0

nbsp t 0  t0

x y graph

B.

0

nbsp t 0  t0

x y graph

C.

0

nbsp t 0  t0

negative t 0−t0

x y graph

​(c) Find the standardized test statistic.

tequals=nothing

​(Round to two decimal places as​ needed.)

​(d) Decide whether to reject or fail to reject the null hypothesis.

A.

RejectReject

Upper H 0H0

because the standardized test statistic

isis

in the rejection region.

B.

RejectReject

Upper H 0H0

because the standardized test statistic

is notis not

in the rejection region.

C.

Fail to rejectFail to reject

Upper H 0H0

because the standardized test statistic

is notis not

in the rejection region.

D.

Fail to rejectFail to reject

Upper H 0H0

because the standardized test statistic

isis

in the rejection region.

​(e) Interpret the decision in the context of the original claim.

A.

There

is notis not

sufficient evidence to support the claim that the mean waste generated is more than

33

pounds per person per day.

B.

There

isis

sufficient evidence to support the claim that the mean waste generated is less than

33

pounds per person per day.

C.

There

isis

sufficient evidence to support the claim that the mean waste generated is more than

33

pounds per person per day.

D.

There

is notis not

sufficient evidence to support the claim that the mean waste generated is less than

33

pounds per person per day.

Answer 1

Solution: .​(a) Write the claim mathematically and identify and

Answer: The null and the alternative hypotheses are given below:

Therefore option A is correct.

​(b) Find the critical​ value(s) and identify the rejection​ region(s).

What​ is(are) the critical​ value(s),

Answer: The critical value is:

Which of the following graphs best depicts the rejection region for this​ problem?

Answer:

​(c) Find the standardized test statistic.

Answer: The standardized test statistic is:

  

  

Therefore the standardized test statistic is

​(d) Decide whether to reject or fail to reject the null hypothesis.

Answer: C. Fail to reject because the standardized test statistic is not in the rejection region.

​(e) Interpret the decision in the context of the original claim.

Answer: A. There is not sufficient evidence to support the claim that the mean waste generated is more than 3 pounds per person per day.

A.

There

is notis not

sufficient evidence to support the claim that the mean waste generated is more than

33

pounds per person per day.