Answered: (c) Carry out a formal test of 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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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.

Yes, it is reasonable. The pattern in the normal probability plot is roughly linear, and since the sample was a random sample from the population, the t test is appropriate.No, the t test is not applicable here. The pattern in the normal probability plot is roughly linear. Therefore, the t test is not appropriate. Yes, it is reasonable. The pattern in the normal probability plot is not linear, and since the sample was a random sample from the population, the t test is appropriate.No, the t test is not applicable here. The sample was not a random sample from the population so the t test is not appropriate.It depends on the results of t test.

(b)

The stated calorie content is 241. Does the boxplot suggest that true average content differs from the stated value? Explain your reasoning.

Yes, the center of the boxplot is different from the stated value indicating the true average content must differ from the stated value.Not necessarily, it is possible that true average content is 241 and observed differences could be due to sampling variability. No, the true average content must be 241 since 241 is inside the box of the boxplot.Yes, the true average content must be different from 241 since 241 is inside the box of the boxplot.

(c)

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

Find the test statistic and P-value. (Use

? = 0.05.

Round your test statistic to two decimal places and your P-value to four decimal places.)

t=P-value=

State the conclusion in the context of the problem.

Reject H₀. We do not have convincing evidence that the stated calorie content is not 241.Fail to reject H₀. We have convincing evidence that the stated calorie content is not 241. Fail to reject H₀. We do not have convincing evidence that the stated calorie content is not 241.Reject H₀. We have convincing evidence that the stated calorie content is not 241.

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