Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

A coin mint has a specification that a particular coin has a mean weight of

2.52.5

g. A sample of

3737

coins was collected. Those coins have a mean weight of

2.494372.49437

g and a standard deviation of

0.014810.01481

g. Use a

0.050.05

significance level to test the claim that this sample is from a population with a mean weight equal to

2.52.5

g. Do the coins appear to conform to the specifications of the coin mint?

What are the hypotheses?

A.

Upper H 0H0 :

muμequals=2.52.5

g

Upper H 1H1 :

muμgreater than or equals≥2.52.5

g

B.

Upper H 0H0 :

muμnot equals≠2.52.5

g

Upper H 1H1 :

muμequals=2.52.5

g

C.

Upper H 0H0 :

muμequals=2.52.5

g

Upper H 1H1 :

muμless than<2.52.5

g

D.

Upper H 0H0 :

muμequals=2.52.5

g

Upper H 1H1 :

muμnot equals≠2.52.5

g

Identify the test statistic.

tequals=nothing

(Round to three decimal places as needed.)

Identify the P-value.

The P-value is

nothing.

(Round to four decimal places as needed.)

State the final conclusion that addresses the original claim. Choose the correct answer below.

A.

RejectReject

Upper H 0H0.

There is

insufficientinsufficient

evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to

2.52.5

g.

B.

Fail to rejectFail to reject

Upper H 0H0.

There is

sufficientsufficient

evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to

2.52.5

g.

C.

Fail to rejectFail to reject

Upper H 0H0.

There is

insufficientinsufficient

evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to

2.52.5

g.

D.

RejectReject

Upper H 0H0.

There is

sufficientsufficient

evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to

2.52.5

g.

Do the coins appear to conform to the specifications of the coin mint?

A.

No comma since the coins seemNo, since the coins seem

to come from a population with a mean weight different from

2.52.5

g.

B. Yes, since the coins do not seem to come from a population with a mean weight different from

2.494372.49437

g.

C.

Yes comma since the coins do not seemYes, since the coins do not seem

to come from a population with a mean weight different from

2.52.5

g.

D. No, since the coins seem to come from a population with a mean weight different from

2.494372.49437

g.

E.

The results are inconclusive because individual differences in coin weights need to be analyzed further.

Click to select your answer(s).

Answer 1

Ans:

2.5

$H_1:\mu\neq 2.5$

Option D is correct.

Test statistic:

t=(2.49437-2.5)/(0.01481/SQRT(37))

t=-2.312

df=37-1=36

p-value=tdist(2.312,36,2)=0.0266

Reject H0.There is sufficient evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to 2.5 g.

(Option D is correct)

No, since the coins seem to come from a population with a mean weight different from 2.5g

(Option A is correct)