Researchers measured food intake of 100 students. The following table summarizes the protein intake measurements. Boys Girls MeanS.d.n1MeanS.d.n2Protein intake (g)24.54.14520.58.355Construct a two-sided 99% confidence interval for the difference in mean protein intake measurements between the boys and girls.Does the above give evidence to suggest the boys intake more protein than the girls in average? Test at the 5% significance level.

There are two independent samples which are boys and girls. We have to construct 99% confidence…

Answered: Researchers measured food intake of 100…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Researchers measured food intake of 100 students. The following table summarizes the protein intake measurements.

		Boys			Girls
	Mean	S.d.	n₁	Mean	S.d.	n₂
Protein intake (g)	24.5	4.1	45	20.5	8.3	55

Construct a two-sided 99% confidence interval for the difference in mean protein intake measurements between the boys and girls.
Does the above give evidence to suggest the boys intake more protein than the girls in average? Test at the 5% significance level.

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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