A pool supply company sells 50-pound buckets of chlorine tablets. A customer believes that the company may be underfilling the buckets. To investigate, an inspector is hired. The inspector randomly selects 30 of these buckets of chlorine tablets and weighs the contents of each bucket. The sample mean is 49.4 pounds with a standard deviation of 1.2 pounds. The inspector would like to know if this provides convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds, so he plans to test the hypotheses H0: μ = 50 versus Ha: μ < 50, where μ = the true mean weight of all 50-pound buckets of chlorine tablets. The conditions for inference are met. The test statistic is t = –2.74 and the P-value is between 0.005 and 0.01. What conclusion should be made at the significance level, ?Reject H0. There is convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.Reject H0. There is not convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.Fail to reject H0. There is convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.Fail to reject H0. There is not convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds. An engineer would like to design a parking garage in the most cost-effective manner. He reads that the averageheight of pickup trucks, which is the largest type of vehicle that should be expected to fit into the parking garage,is 76.4 inches. To double-check this figure, the engineer employs a statistician. The statistician selects a randomsample of 100 trucks and finds the mean height of the sample to be 77.1 inches with a standard deviation of 5.2inches. The statistician will determine if these data provide convincing evidence that the true mean height of alltrucks is greater than 76.4 inches. The statistician plans to test the hypotheses, Ho: µ = 76.4 versus H₂: µ > 76.4,where μ = the true mean height of all trucks. The conditions for inference are met. The test statistic is t = 1.35 andthe P-value is between 0.05 and 0.10. What conclusion should be made at the significance level, x = 0.05?Reject Ho. There is convincing evidence that the true mean height of all trucks is greater than 76.4 inches.Reject Ho. There is not convincing evidence that the true mean height of all trucks is greater than 76.4 inches.Fail to reject Ho. There is convincing evidence that the true mean height of all trucks is greater than 76.4 inches.O Fail to reject Ho. There is not convincing evidence that the true mean height of all trucks is greater than 76.4inches.Ο Ο Ο

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A pool supply company sells 50-pound buckets of chlorine tablets. A customer believes that the company may be underfilling the buckets. To investigate, an inspector is hired. The inspector randomly selects 30 of these buckets of chlorine tablets and weighs the contents of each bucket. The sample mean is 49.4 pounds with a standard deviation of 1.2 pounds. The inspector would like to know if this provides convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds, so he plans to test the hypotheses H0: μ = 50 versus Ha: μ < 50, where μ = the true mean weight of all 50-pound buckets of chlorine tablets. The conditions for inference are met. The test statistic is t = –2.74 and the P-value is between 0.005 and 0.01. What conclusion should be made at the significance level, ? Reject H0. There is convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds. Reject H0. There is not convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds. Fail to reject H0. There is convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds. Fail to reject H0. There is not convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.

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 pool supply company sells 50-pound buckets of chlorine tablets. A customer believes that the company may be underfilling the buckets. To investigate, an inspector is hired. The inspector randomly selects 30 of these buckets of chlorine tablets and weighs the contents of each bucket. The sample mean is 49.4 pounds with a standard deviation of 1.2 pounds. The inspector would like to know if this provides convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds, so he plans to test the hypotheses H₀: μ = 50 versus H_a: μ < 50, where μ = the true mean weight of all 50-pound buckets of chlorine tablets. The conditions for inference are met. The test statistic is t = –2.74 and the P-value is between 0.005 and 0.01. What conclusion should be made at the significance level, ?

Reject H₀. There is convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.

Reject H₀. There is not convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.

Fail to reject H₀. There is convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.

Fail to reject H₀. There is not convincing evidence that the true mean weight of the chlorine tablets in the 50-pound buckets is less than 50 pounds.

An engineer would like to design a parking garage in the most cost-effective manner. He reads that the average
height of pickup trucks, which is the largest type of vehicle that should be expected to fit into the parking garage,
is 76.4 inches. To double-check this figure, the engineer employs a statistician. The statistician selects a random
sample of 100 trucks and finds the mean height of the sample to be 77.1 inches with a standard deviation of 5.2
inches. The statistician will determine if these data provide convincing evidence that the true mean height of all
trucks is greater than 76.4 inches. The statistician plans to test the hypotheses, Ho: µ = 76.4 versus H₂: µ > 76.4,
where μ = the true mean height of all trucks. The conditions for inference are met. The test statistic is t = 1.35 and
the P-value is between 0.05 and 0.10. What conclusion should be made at the significance level, x = 0.05?
Reject Ho. There is convincing evidence that the true mean height of all trucks is greater than 76.4 inches.
Reject Ho. There is not convincing evidence that the true mean height of all trucks is greater than 76.4 inches.
Fail to reject Ho. There is convincing evidence that the true mean height of all trucks is greater than 76.4 inches.
O Fail to reject Ho. There is not convincing evidence that the true mean height of all trucks is greater than 76.4
inches.
Ο Ο Ο

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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