Two independent simple random samples of professional NBA and NFL players heights are given below. NBA Data: NBA Heights (ft) 6.47 6.47 6.44 6.56 6.49 6.68 6.59 6.73 6.36 6.75 6.49 6.69 6.45 6.53 6.73 6.37 6.54 6.42 6.46 6.92 6.42 6.69 6.5 6.37 6.95 6.24 6.6 6.45 6.64 6.56 6.68 6.56 6.6 6.66 6.58 6.47 6.59 6.29 6.49 6.35 6.36 6.41 6.43 6.86 NFL Data: NFL Heights (ft) 5.856.666.695.976.816.296.45.985.746.586.136.666.086.056.796.666.587.036.485.826.026.426.646.326.36.176.756.176.366.156.826.726.786.285.755.975.996.265.796.386.52 Let μ1μ1 by the population mean height for NBA players and μ2μ2 be the population mean for NFL players. Find a 92% confidence interval μ1−μ2μ1-μ2. (Round answers to two decimal places.) margin of error: lower limit: upper limit: Examine the confidence interval and explain what it means in the context of this problem. At the 92% level of confidence, do NBA players tend to have a higher population mean height than NFL players? It's not clear, since the interval contains both negative and positive numbers, we can't say that NBA players have a higher population mean height than NFL players. No, since the interval contains only negative numbers, we can say that NBA players have a lower population mean height than NFL players. Yes, since the interval contains only positive numbers, we can say that NBA players have a higher population mean height than NFL players.

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

Two independent simple random samples of professional NBA and NFL players heights are given below.

NBA Data:

NBA Heights (ft)
6.47
6.47
6.44
6.56
6.49
6.68
6.59
6.73
6.36
6.75
6.49
6.69
6.45
6.53
6.73
6.37
6.54
6.42
6.46
6.92
6.42
6.69
6.5
6.37
6.95
6.24
6.6
6.45
6.64
6.56
6.68
6.56
6.6
6.66
6.58
6.47
6.59
6.29
6.49
6.35
6.36
6.41
6.43
6.86

NFL Data: NFL Heights (ft) 5.856.666.695.976.816.296.45.985.746.586.136.666.086.056.796.666.587.036.485.826.026.426.646.326.36.176.756.176.366.156.826.726.786.285.755.975.996.265.796.386.52

Let μ1μ1 by the population mean height for NBA players and μ2μ2 be the population mean for NFL players. Find a 92% confidence interval μ1−μ2μ1-μ2. (Round answers to two decimal places.)

margin of error:
lower limit:
upper limit:

Examine the confidence interval and explain what it means in the context of this problem. At the 92% level of confidence, do NBA players tend to have a higher population mean height than NFL players?

It's not clear, since the interval contains both negative and positive numbers, we can't say that NBA players have a higher population mean height than NFL players.
No, since the interval contains only negative numbers, we can say that NBA players have a lower population mean height than NFL players.
Yes, since the interval contains only positive numbers, we can say that NBA players have a higher population mean height than NFL players.

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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