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 safety administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in hic (standard head injury condition units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.01 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. 828 735 1198 677 593 589 What are the hypotheses? A. H0: μ=1000 hic H1: μ≥1000 hic B. H0: μ<1000 hic H1: μ≥1000 hic C. H0: μ>1000 hic H1: μ<1000 hic D. H0: μ=1000 hic H1: μ<1000 hic Identify the test statistic. t=? (Round to three decimal places as needed.) Identify the P-value. The P-value is? (Round to four decimal places as needed.) State the final conclusion that addresses the original claim. (Reject?,Fail to reject?)H0. There is (sufficient?,insufficient?)evidence to support the claim that the sample is from a population with a mean less than 1000 hic.

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 safety administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in hic (standard head injury condition units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a

0.01 significance level to test the claim that the sample is from a population with a mean less than 1000 hic.

828 735 1198 677 593 589

What are the hypotheses?

H0: μ=1000 hic

H1: μ≥1000 hic

H0: μ<1000 hic

H1: μ≥1000 hic

H0: μ>1000 hic

H1: μ<1000 hic

H0: μ=1000 hic

H1: μ<1000 hic

Identify the test statistic.

t=?

(Round to three decimal places as needed.)

Identify the P-value.

The P-value is?

(Round to four decimal places as needed.)

State the final conclusion that addresses the original claim. (Reject?,Fail to reject?)H0.

There is (sufficient?,insufficient?)evidence to support the claim that the sample is from a population with a mean less than 1000 hic.

What do the results suggest about the child booster seats meeting the specified requirement?

The requirement is met since most sample measurements are less than 1000 hic.

There is strong evidence that the mean is less than 1000 hic, but one of the booster seats has a measurement that is greater than 1000 hic.

The results are inconclusive regarding whether one of the booster seats could have a measurement that is greater than 1000 hic.

There is not strong evidence that the mean is less than 1000 hic, and one of the booster seats has a measurement that is greater than 1000 hic.

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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