(Use R)_Independent random samples of professional football and basketball players gave thefollowing information.3.Heights (in ft) of pro football players: x1; n1 = 456.31 6.52 6.50 6.25 6.50 6.33 6.25 6.17 6.42 6.336.42 6.58 6.08 6.58 6.50 6.42 6.25 6.67 5.91 6.005.83 6.00 5.83 5.08 6.75 5.83 6.17 5.75 6.00 5.756.50 5.83 5.91 5.67 6.00 6.08 6.17 6.58 6.50 6.256.33 5.25 6.65 6.50 5.85Heights (in ft) of pro basketball players: x2; n2 = 406.07 6.58 6.25 6.58 6.25 5.92 7.00 6.41 6.75 6.256.00 6.92 6.84 6.58 6.41 6.67 6.67 5.75 6.25 6.256.50 6.00 6.92 6.25 6.42 6.58 6.58 6.08 6.75 6.506.83 6.08 6.92 6.00 6.33 6.50 6.58 6.82 6.50 6.58(b) Let µ1 be the population mean for x1 and let µ2 be the population mean for x2. Find a 90%confidence interval for u1 - µ2. Round your answers to 3 decimal places.(a)LowerUpperPaste R Output:(b) Examine the confidence interval and explain what it means in the context of this problem. Does theinterval consist of numbers that are all positive? all negative? of different signs? At the 90% level ofconfidence, do professional football players tend to have a higher population mean height thanprofessional basketball players?

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3. (Use R)_Independent random samples of professional football and basketball players gave the following information.

MATLAB: An Introduction with Applications

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Author:Amos Gilat

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Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

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Question

(Use R)_Independent random samples of professional football and basketball players gave the
following information.
3.
Heights (in ft) of pro football players: x1; n1 = 45
6.31 6.52 6.50 6.25 6.50 6.33 6.25 6.17 6.42 6.33
6.42 6.58 6.08 6.58 6.50 6.42 6.25 6.67 5.91 6.00
5.83 6.00 5.83 5.08 6.75 5.83 6.17 5.75 6.00 5.75
6.50 5.83 5.91 5.67 6.00 6.08 6.17 6.58 6.50 6.25
6.33 5.25 6.65 6.50 5.85
Heights (in ft) of pro basketball players: x2; n2 = 40
6.07 6.58 6.25 6.58 6.25 5.92 7.00 6.41 6.75 6.25
6.00 6.92 6.84 6.58 6.41 6.67 6.67 5.75 6.25 6.25
6.50 6.00 6.92 6.25 6.42 6.58 6.58 6.08 6.75 6.50
6.83 6.08 6.92 6.00 6.33 6.50 6.58 6.82 6.50 6.58
(b) Let µ1 be the population mean for x1 and let µ2 be the population mean for x2. Find a 90%
confidence interval for u1 - µ2. Round your answers to 3 decimal places.
(a)
Lower
Upper
Paste R Output:
(b) Examine the confidence interval and explain what it means in the context of this problem. Does the
interval consist of numbers that are all positive? all negative? of different signs? At the 90% level of
confidence, do professional football players tend to have a higher population mean height than
professional basketball players?

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