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 25 filtered 100 mm cigarettes is obtained, and the tar content of each cigarette is measured. The sample has a mean of 18.8 mg and a standard deviation of 3.38 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1mg, which is the mean for unfiltered king size cigarettes. What are the hypotheses?A.H0: μ<21.1 mg H1: μ≥21.1 mg B.H0: μ=21.1 mgH1: μ≥21.1 mg C.H0: μ>21.1 mgH1: μ<21.1 mg D.H0: μ=21.1 mgH1: μ<21.1 mg Identify the test statistic.t=(Round to three decimal places as needed.) Identify the P-value.The P-value ?(Round to four decimal places as needed.) State the final conclusion that addresses the original claim. Choose the correct answer below.A.Fail to reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. B.Reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. C.Fail to reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. D.Reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. What do the results suggest, if anything, about the effectiveness of the filters?A.The results do not suggest that the filters are effective. B.The results are inconclusive because the sample size is less than 30. C.The results suggest that the filters increase the tar content. D.The results suggest that the filters are effective. E.The results suggest that the filtered cigarettes have the same tar content as unfiltered king size cigarettes.

Given that Sample size n = 25 Sample mean = 18.8 Sample SD = 3.38 Level of significance = 0.05

Answered: Identify the null and alternative…

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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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 25 filtered 100 mm cigarettes is obtained, and the tar content of each cigarette is measured. The sample has a mean of 18.8 mg and a standard deviation of 3.38 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1mg, which is the mean for unfiltered king size cigarettes.

What are the hypotheses?

H0: μ<21.1 mg

H1: μ≥21.1 mg

H0: μ=21.1 mg

H1: μ≥21.1 mg

H0: μ>21.1 mg

H1: μ<21.1 mg

H0: μ=21.1 mg

H1: μ<21.1 mg

Identify the test statistic.

(Round to three decimal places as needed.)

Identify the P-value.

The P-value ?
(Round to four decimal places as needed.)

State the final conclusion that addresses the original claim. Choose the correct answer below.

Fail to reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

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

Fail to reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

Reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

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

The results do not suggest that the filters are effective.

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

The results suggest that the filters increase the tar content.

The results suggest that the filters are effective.

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

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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