Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases. It is therefore important that the information on packages be accurate. A random sample of n = 12 frozen dinners of a certain type was selected from production during a particular period, and the calorie content of each one was determined. (This determination entails destroying the product, so a census would certainly not be desirable!) Here are the resulting observations, along with a boxplot and normal probability plot. (Use this dataset for your analysis software.) 255 244 239 242 265 245 259 248 225 226 251 233 The box-and-whisker plot has a vertical axis numbered from 220 to 270. The box-and-whisker is also vertical. The bottom whisker is approximately 225, the bottom edge of the box is approximately 236, the line inside the box is approximately 244.5, the top edge of the box is approximately 253, and the top whisker is approximately 265. A scatterplot has 12 points. The plot's horizontal axis is labeled "Normal score" and ranges from −1.7 to 1.7. Its vertical axis is labeled "Calories" and ranges from 223 to 267. There is one point plotted near (−1.7, 225) and a second near (−1.1, 227). After the second point, the 10 remaining points are plotted from left to right in upward, mostly diagonal direction. The pattern begins near the bottom left of the diagram and ends at approximately (1.7, 265). The distance between each point varies slightly. All points are between the approximate horizontal axis values of −1.7 and 1.7 and between the approximate vertical axis values of 223 and 267. (a) Is it reasonable to test hypotheses about mean calorie content ? by using a t test? Explain why or why not. (b) The stated calorie content is 238. Does the boxplot suggest that true average content differs from the stated value? Explain your reasoning. (c) Carry out a formal test of the hypotheses suggested in part (b).

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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Question

Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases. It is therefore important that the information on packages be accurate. A random sample of

n = 12

frozen dinners of a certain type was selected from production during a particular period, and the calorie content of each one was determined. (This determination entails destroying the product, so a census would certainly not be desirable!) Here are the resulting observations, along with a boxplot and normal probability plot. (Use this dataset for your analysis software.)

255	244	239	242	265	245	259	248
225	226	251	233

The box-and-whisker plot has a vertical axis numbered from 220 to 270. The box-and-whisker is also vertical. The bottom whisker is approximately 225, the bottom edge of the box is approximately 236, the line inside the box is approximately 244.5, the top edge of the box is approximately 253, and the top whisker is approximately 265.

A scatterplot has 12 points. The plot's horizontal axis is labeled "Normal score" and ranges from −1.7 to 1.7. Its vertical axis is labeled "Calories" and ranges from 223 to 267. There is one point plotted near (−1.7, 225) and a second near (−1.1, 227). After the second point, the 10 remaining points are plotted from left to right in upward, mostly diagonal direction. The pattern begins near the bottom left of the diagram and ends at approximately (1.7, 265). The distance between each point varies slightly. All points are between the approximate horizontal axis values of −1.7 and 1.7 and between the approximate vertical axis values of 223 and 267.

(a)

Is it reasonable to test hypotheses about mean calorie content ? by using a t test? Explain why or why not.

(b)

The stated calorie content is 238. Does the boxplot suggest that true average content differs from the stated value? Explain your reasoning.

(c)

Carry out a formal test of the hypotheses suggested in part (b).

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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