Strength of concrete: The compressive strength, in kilopascals, was measured for concrete blocks from five different batches of concrete, both three and six days after pouring. The data are as follows. Can you conclude that the mean strength after three days differs from the mean strength after six days? Let μ1 represent the mean strength after three days and =μd−μ1μ2. Use the =α0.10 level and the P-value method with the table. Block 12345After 3 days13561337134413101348After 6 days13521355135513241380 State the appropriate null and alternate hypotheses.test statistic:Estimate the P-value. Identify the form of the interval based on the Critical Values for the Student's t Distribution Table.Determine whether to reject H0State the conclusion: There enough evidence to conclude that the mean strength after three days differs from the mean strength after six days.

The objective of this question is to determine whether there is a significant difference in the mean…

Answered: Strength of concrete: The compressive…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter11: Data Analysis And Displays

Section: Chapter Questions

Problem 10CR

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Question

Strength of concrete: The compressive strength, in kilopascals, was measured for concrete blocks from five different batches of concrete, both three and six days after pouring. The data are as follows. Can you conclude that the mean strength after three days differs from the mean strength after six days? Let

μ1

represent the mean strength after three days and

=μd−μ1μ2

. Use the

=α0.10

level and the

-value method with the table.

	Block
	1	2	3	4	5
After 3 days	1356	1337	1344	1310	1348
After 6 days	1352	1355	1355	1324	1380

State the appropriate null and alternate hypotheses.

test statistic:

Estimate the P-value. Identify the form of the interval based on the Critical Values for the Student's t Distribution Table.

Determine whether to reject H0

State the conclusion:

There enough evidence to conclude that the mean strength after three days differs from the mean strength after six days.

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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