A simple random sample of2828filtered 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 of0.220.22mg. Use a0.050.05significance level to test the claim that the tar content of filtered 100-mm cigarettes has a standard deviation different from0.350.35mg, 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:sigmaσnot equals≠0.350.35mgUpper H 1 : sigma equals 0.35H1: σ=0.35mg B.H0:sigmaσequals=0.350.35mgUpper H 1 : sigma not equals 0.35H1: σ≠0.35mgYour answer is correct. C.H0:sigmaσequals=0.350.35mgUpper H 1 : sigma less than 0.35H1: σ<0.35mg D.H0:sigmaσgreater than>0.350.35mgUpper H 1 : sigma less than or equals 0.35H1: σ≤0.35mgb. Find the test statistic. chi squaredχ2equals=10.66810.668(Round to three decimal places as needed.)c. Find the P-value of the test statistic. The P-value of the test statistic is

Given information Sample size, n = 28 Sample standard deviation, s = 0.22 Significance level, α =…

Answered: A simple random sample of 2828…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A simple random sample of

2828

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

0.220.22

mg. Use a

0.050.05

significance level to test the claim that the tar content of filtered 100-mm cigarettes has a standard deviation different from

0.350.35

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?

H0:

sigmaσnot equals≠0.350.35

Upper H 1 : sigma equals 0.35H1: σ=0.35

H0:

sigmaσequals=0.350.35

Upper H 1 : sigma not equals 0.35H1: σ≠0.35

Your answer is correct.

H0:

sigmaσequals=0.350.35

Upper H 1 : sigma less than 0.35H1: σ<0.35

H0:

sigmaσgreater than>0.350.35

Upper H 1 : sigma less than or equals 0.35H1: σ≤0.35

b. Find the test statistic.

chi squaredχ2equals=10.66810.668

(Round to three decimal places as needed.)

c. Find the P-value of the test statistic.

The P-value of the test statistic is

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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