A simple random sample of26filtered 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 of0.18Use a0.01significance level to test the claim that the tar content of filtered100-mm cigarettes has a standard deviation different from0.25mg, which is the standard deviation for unfiltered king-size cigarettes. Complete parts (a) through (d) below.What are the null and alternative hypotheses?A.H0:σ≠0.25mgH1: σ=0.25mgB.H0:σ=0.25mgH1: σ≠0.25mgC.H0:σ=0.25mgH1: σ<0.25mgD.H0:σ>0.25mgH1: σ≤0.25mgFind the test statistic.χ2=nothing(Round to three decimal places as needed.)Find the P-value of the test statistic.The P-value of the test statistic isnothing.(Round to three decimal places as needed.)State the conclusion.▼ Fail to rejectReject H0.There▼ isis not sufficient evidence to conclude that the tar content of filtered 100-mm cigarettes has a standard deviation different from0.25mg.

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Author:Amos Gilat

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A simple random sample of

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

Use a

0.01

significance level to test the claim that the tar content of filtered100-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.

What are the null and alternative hypotheses?

H0:

σ≠0.25

H1: σ=0.25

H0:

σ=0.25

H1: σ≠0.25

H0:

σ=0.25

H1: σ<0.25

H0:

σ>0.25

H1: σ≤0.25

Find the test statistic.

χ2=nothing

(Round to three decimal places as needed.)

Find the P-value of the test statistic.

The P-value of the test statistic is

nothing.

(Round to three decimal places as needed.)

State the conclusion.

▼

Fail to reject

Reject

H0.

There

▼

is not

sufficient evidence to conclude that the tar content of filtered 100-mm cigarettes has a standard deviation different from

0.25

mg.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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