A simple random sample of 26 filtered​ 100-mm cigarettes is obtained from a normally distributed​ population, and the tar content of each cigarette is measured. The sample has a standard deviation of 0.18 mg. Use a 0.01 significance level to test the claim that the tar content of filtered​ 100-mm cigarettes has a standard deviation different from 0.25 ​mg, which is the standard deviation for unfiltered​ king-size cigarettes. Complete parts​ (a) through​ (d) below. a. What are the null and alternative​ hypotheses?     A. H0​: σ≠0.25 mg H1: σ=0.25 mg   B. H0​: σ=0.25 mg H1: σ≠0.25 mg   C. H0​: σ=0.25 mg H1: σ<0.25 mg   D. H0​: σ>0.25 mg H1: σ≤0.25 mg           b. Find the test statistic.   χ2=_____ ​(Round to three decimal places as​ needed.)         c. Find the​ P-value of the test statistic.   The​ P-value of the test statistic is ______ ​(Round to three decimal places as​ needed.)         d. State the conclusion.   (Fail to reject OR Reject )H0. There (is not OR is) sufficient evidence to conclude that the tar content of filtered​ 100-mm cigarettes has a standard deviation different from 0.25 mg.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 13PPS
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A simple random sample of
26
filtered​ 100-mm cigarettes is obtained from a normally distributed​ population, and the tar content of each cigarette is measured. The sample has a standard deviation of
0.18
mg. Use a
0.01
significance level to test the claim that the tar content of filtered​ 100-mm cigarettes has a standard deviation different from
0.25
​mg, which is the standard deviation for unfiltered​ king-size cigarettes. Complete parts​ (a) through​ (d) below.
a. What are the null and alternative​ hypotheses?
 
 
A.
H0​:
σ≠0.25
mg
H1: σ=0.25
mg
 
B.
H0​:
σ=0.25
mg
H1: σ≠0.25
mg
 
C.
H0​:
σ=0.25
mg
H1: σ<0.25
mg
 
D.
H0​:
σ>0.25
mg
H1: σ≤0.25
mg
 
 
 
 
 
b. Find the test statistic.
 
χ2=_____
​(Round to three decimal places as​ needed.)
 
 
 
 
c. Find the​ P-value of the test statistic.
 
The​ P-value of the test statistic is ______
​(Round to three decimal places as​ needed.)
 
 
 
 
d. State the conclusion.
 
(Fail to reject OR Reject )H0.
There
(is not OR is)
sufficient evidence to conclude that the tar content of filtered​ 100-mm cigarettes has a standard deviation different from
0.25
mg.
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