2. 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? 820 798 1352 628 621 479 What are the hypotheses? OA. Ho: μ<1000 hic H₁: μz 1000 hic O C. Ho: μ = 1000 hic H₁: μz 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. (1) O Reject (1). Ho. 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? O A. The requirement is met since most sample measurements are less than 1000 hic. O B. The results are inconclusive regarding whether one of the booster seats could have a measurement that is greater than 1000 hic. O C. 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. O D. 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. Fail to reject (2) OB. Ho: > 1000 hic H₂₁:μ< 1000 hic insufficient sufficient O D. H₂: μ = 1000 hic H₁: μ< 1000 hic

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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

820, 798, 1352, 628, 621, 479

32. 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?
820 798 1352 628 621 479
What are the hypotheses?
O A. Ho: μ<1000 hic
H₁: μz 1000 hic
O C. Ho: μ = 1000 hic
H₁: μ z 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.
(1) O Reject
(1).
Ho. 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 requirement is met since most sample measurements are less than 1000 hic.
O B. The results are inconclusive regarding whether one of the booster seats could have a measurement that is greater than 1000 hic.
OC. 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.
O D. 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.
Fail to reject
(2)
OB. Ho: > 1000 hic
H₁: μ< 1000 hic
insufficient
sufficient
O D. Ho: μ = 1000 hic
H₁: μ< 1000 hic

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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