Question

A simple random sample of 29 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 0.22 mg. Use a 0.05 significance level to test the claim that the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.35 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? O A. H: 0= 0.35 mg H: 04 0.35 mg OB. Ho: 6+0.35 mg H: 3 = 0.35 mg OD. Ho: 6=0.35 mg H: 0 < 0.35 mg 0C. He s> 0.35 mg H: 650.35 mg b. Find the test statistic. x2 = 11.06 (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 Ho. There is not sufficient evidence to conclude that the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.35 mg.

Answer 1

i am using minitab to solve the problem.

steps :-

stat $1596138130869_blob.png$basic statistics $1596138130782_blob.png$ 1 variance $1596138130909_blob.png$select sample standard deviation from the drop down menu$1596138130773_blob.png$type 29 in sample size and 0.22 in sample standard deviation $1596138130993_blob.png$tick perform hypothesis test $1596138131067_blob.png$select hypotheized standard deviation from the drop down menu $1596138131081_blob.png$in value type 0.35$1596138130850_blob.png$options$1596138130755_blob.png$in confidence level type 95$1596138130763_blob.png$select the alternative hypothesis as standard deviation $\neq$ hypothesizedstandard deviation$1596138131078_blob.png$ok$1596138131121_blob.png$ok.

*** SOLUTION ***

hypothesis:-

$H_{0}:\sigma=0.35$

$H_{1}:\sigma\neq0.35$

the test statistic be:-

$\chi^2=\mathbf{11.06}$

the p value of the test statistic is = 0.004

decision:-

Fail to reject H₀. There is sufficient evidence to conclude that the tar content of filtered 100 mm cigarettes has a standard deviation different than 0.35 mg.

[ p value =0.004 < 0.05 (alpha) ]

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