The club will be preparing his male team players for the next basketball competition and the club randomly selects 30 of his male players and check their weights. The following table shows summary statistics for those players weights. Variable n Mean Standard deviation, s Weight 30 102 14 Calculate a 95% confidence interval (C.I.) for the population mean weight of all basketball male players in the club. What assumption would you need to make for the CI to be valid. Choose one from below. - Since nπnπ and n(1−π)n(1−π) are both ≥5, the Central Limit Theorem applies and we can assume that p arises from a normal distribution - The shape of the histogram indicates that the scores may be from a normal distribution and/or the sample size is reasonably large so the sample mean will be from a normal population - Since the population is normal, therefore sample means follow a normal distribution - The points are randomly scattered around a straight line, so the assumptions of linearity and constant spread are satisfied. The shape of the histogram indicates that the residuals come from a normal distribution - The boxplots indicate that the samples are fairly symmetric and the spreads are similar, so we can assume both sets of data come from normal distributions with the same spread - None of these Q2) What is the critical value for the 95% confidence interval

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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The club will be preparing his male team players for the next basketball competition and the club randomly selects 30 of his male players and check their weights. The following table shows summary statistics for those players weights.

Variable	n	Mean	Standard deviation, s
Weight	30	102	14

Calculate a 95% confidence interval (C.I.) for the population mean weight of all basketball male players in the club.

What assumption would you need to make for the CI to be valid. Choose one from below.

- Since nπnπ and n(1−π)n(1−π) are both ≥5, the Central Limit Theorem applies and we can assume that p arises from a normal distribution

- The shape of the histogram indicates that the scores may be from a normal distribution and/or the sample size is reasonably large so the sample mean will be from a normal population

- Since the population is normal, therefore sample means follow a normal distribution

- The points are randomly scattered around a straight line, so the assumptions of linearity and constant spread are satisfied. The shape of the histogram indicates that the residuals come from a normal distribution

- The boxplots indicate that the samples are fairly symmetric and the spreads are similar, so we can assume both sets of data come from normal distributions with the same spread

- None of these

Q2) What is the critical value for the 95% confidence interval

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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