Assume that a simple random sample has been selected from a normally distributed

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 simple random sample of 25 filtered 100 mm cigarettes is obtained, and the tar content of each cigarette is measured. The sample has a mean of 19.2 mg and a standard deviation of 3.48 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is the mean for unfiltered king size cigarettes. What do the results suggest, if anything, about the effectiveness of the filters?

A.

Upper H 0H0:

muequals=21.121.1

mg

Upper H 1H1:

mugreater than or equals21.121.1

mg

B.

Upper H 0H0:

muequals=21.121.1

mg

Upper H 1H1:

muless than<21.121.1

mg

C.

Upper H 0H0:

mugreater than>21.121.1

mg

Upper H 1H1:

muless than<21.121.1

mg

D.

Upper H 0H0:

muless than<21.121.1

mg

Upper H 1H1:

mugreater than or equals21.121.1

mg

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 support the claim that the mean tar content of filtered 100 mm cigarettes is less than

21.121.1

mg.

B.

Fail to rejectFail to reject

Upper H 0H0.

There is

sufficientsufficient

evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than

21.121.1

mg.

C.

RejectReject

Upper H 0H0.

There is

sufficientsufficient

evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than

21.121.1

mg.

D.

Fail to rejectFail to reject

Upper H 0H0.

There is

insufficientinsufficient

evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than

21.121.1

mg.

What do the results suggest, if anything, about the effectiveness of the filters?

Explanation / Answer

Set Up Hypothesis
Null, H0: U=21.1
Alternate, H1: U<21.1
Test Statistic
Population Mean(U)=21.1
Sample X(Mean)=19.2
Standard Deviation(S.D)=3.48
Number (n)=25
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =19.2-21.1/(3.48/Sqrt(25))
to =-2.73
| to | =2.73
Critical Value
The Value of |t | with n-1 = 24 d.f is 1.711
We got |to| =2.73 & | t | =1.711
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Left Tail -Ha : ( P < -2.7299 ) = 0.00584
Hence Value of P0.05 > 0.00584,Here we Reject Ho

[ANSWERS]

H0: U=21.1 , H1: U<21.1
There is sufficient
evidence to support the claim that the mean tar content of
filtered 100 mm cigarettes is less than 21.1
Reject Ho

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