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

2525

filtered 100 mm cigarettes is​ obtained, and the tar content of each cigarette is measured. The sample has a mean of

19.019.0

mg and a standard deviation of

3.233.23

mg. Use a

0.050.05

significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than

21.121.1

​mg, which is the mean for unfiltered king size cigarettes. What do the results​ suggest, if​ anything, about the effectiveness of the​ filters?

What are the​ hypotheses?

A.

Upper H 0H0​:

muμequals=21.121.1

mg

Upper H 1H1​:

muμgreater than or equals≥21.121.1

mg

B.

Upper H 0H0​:

muμequals=21.121.1

mg

Upper H 1H1​:

muμless than<21.121.1

mg

C.

Upper H 0H0​:

muμgreater than>21.121.1

mg

Upper H 1H1​:

muμless than<21.121.1

mg

D.

Upper H 0H0​:

muμless than<21.121.1

mg

Upper H 1H1​:

muμgreater than or equals≥21.121.1

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.

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.

B.

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.

C.

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.

D.

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.

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

A.

The results are inconclusive because the sample size is less than 30.

B.The results

suggestsuggest

that the filters are effective.

C.

The results suggest that the filtered cigarettes have the same tar content as unfiltered king size cigarettes.

D.The results

do not suggestdo not suggest

that the filters are effective.

E.

The results suggest that the filters increase the tar content.

Click to select your answer(s).

Answer 1

n = 25

S = 3.23

claim : The mean tar content of filtered 100 mm cigarettes is less than 21.1

Null and alternative hypothesis is

option B is correct

upper H0 : u = 21.1

upper H1 : u < 21.1

Level of significance = 0.05

Here population standard deviation is not known so we use t-test statistic.

Test statistic is

Degrees of freedom = n - 1 = 25 - 1 = 24

P-value = 0.0017 ( using t table)

P-value , Reject H0

conclusion : D. Reject Upper H0.There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1

suggetion

option B is correct

B.The results suggest that the filters are effective.