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 0.05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified requirement? 679 714 1099 605 536 567 What are the hypotheses? A. H0:μ>1000hic H1:μ<1000hic B. H0:μ<1000hic H1:μ≥1000hic C. H0:μ=1000hic H1:μ<1000hic D. H0:μ=1000hic H1:μ≥1000hic 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. (1) __________H0. There is (2) __________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? A. The results are inconclusive regarding whether one of the booster seats could have a measurement that is greater than 1000 hic. B. 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. C. The requirement is met since most sample measurements are less than 1000 hic. D. 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. (1) Reject OR Fail to reject (2) insufficient OR sufficient

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 0.05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified requirement? 679 714 1099 605 536 567 What are the hypotheses? A. H0:μ>1000hic H1:μ<1000hic B. H0:μ<1000hic H1:μ≥1000hic C. H0:μ=1000hic H1:μ<1000hic D. H0:μ=1000hic H1:μ≥1000hic 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. (1) H0. There is (2) ____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? A. The results are inconclusive regarding whether one of the booster seats could have a measurement that is greater than 1000 hic. B. 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. C. The requirement is met since most sample measurements are less than 1000 hic. D. 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. (1) Reject OR Fail to reject (2) insufficient OR sufficient

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Description: 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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section: Chapter Questions

Problem 8SGR

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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

0.05

significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified requirement?

679

714

1099

605

536

567

What are the hypotheses?

H0:μ>1000hic

H1:μ<1000hic

H0:μ<1000hic

H1:μ≥1000hic

H0:μ=1000hic

H1:μ<1000hic

H0:μ=1000hic

H1:μ≥1000hic

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.

(1) __________H0. There is (2) __________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 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.

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

There

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.

(1)

Reject OR

Fail to reject

(2)

insufficient OR

sufficient

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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