Answered: Suppose a paper reported that the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose a paper reported that the freshman year weight gain for the students in a representative sample of 103 freshmen at a midwestern university was 5.8 pounds and that the standard deviation of the weight gain was 6.8 pounds. The authors also reported that 75.7% of these students gained more than 1 pounds, 17.4% maintained their weight within 1 pounds, and 6.8% lost more than 1 pounds.

(a)

Based on the given information, explain why it is not reasonable to think that the distribution of weight gains for the population of freshmen students at this university is approximately normal.

If the distribution of weight gains is approximately normal, for the sample standard deviation of

s = 6.8 pounds

and the sample mean of

x = 5.8 pounds,

we should see approximately ? 3 5 16 32 % of the weight gain observations be less than one standard deviation below the mean and we should see approximately ? 3 5 16 32 % of the weight gain observations be greater than one standard deviation above the mean. This ---Select--- is is not true, therefore it is not reasonable to think that the distribution of weight gains is approximately normal.

(b)

Explain why it is reasonable to use a one-sample t confidence interval to estimate the population mean even though the population distribution is not approximately normal. (Select all that apply.)

It is reasonable to use a one-sample t confidence interval to estimate the population mean since the sample size is at least 30.It is reasonable to use a one-sample t confidence interval to estimate the population mean since the sample size is at most 30.It is reasonable to use a one-sample t confidence interval to estimate the population mean since the statistics came from a paper.It is reasonable to use a one-sample t confidence interval to estimate the population mean since all freshman at a midwestern university where surveyed. It is reasonable to use a one-sample t confidence interval to estimate the population mean since the sample is representative of the population.

(c)

Calculate a 95% confidence interval (in pounds) for the population mean weight gain of freshmen students at this university. (Use technology. Round your answers to three decimal places.)

lbs

Interpret the interval.

We are 95% confident that the weight gain of freshmen students at this university falls within this interval.There is a 95% chance that the true mean number weight gain of freshmen students at this university falls directly in the middle of this interval. There is a 95% chance that the weight gain of freshmen students at this university falls within this interval.We are 95% confident that the true mean weight gain of freshmen students at this university falls within this interval.There is a 95% chance that the weight gain of freshmen students at this university falls directly in the middle of this 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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