Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases, so it is important that the information on packages be accurate. Suppose that a random sample of n = 12 frozen dinners of a certain type was selected and the calorie content of each one was determined. Below are the resulting observations, along with a boxplot and normal probability plot. 255 244 239 242 265 245 259 248 225 226 251 233 A normal probability plot has 12 points plotted on it. The horizontal axis ranges from −1.5 to 1.5 and is labeled "Normal score." The vertical axis ranges from 225 to 265 and is labeled "Calories." The first point is plotted in the bottom left. The second through twelfth points are plotted from the bottom left towards the top right in roughly the shape of a slanted line. The approximate locations of the points from left to right are as follows: (−1.6, 225), (−1.1, 226), (−0.8, 233), (−0.5, 239), (−0.3, 242), (−0.1, 244), (0.1, 245), (0.4, 248), (0.6, 251), (0.8, 255), (1.1, 259), (1.7, 265). (a) Is it reasonable to test hypotheses about true average calorie content μ by using a one-sample t test? Yes, it is reasonable.No, a t test is not applicable here. It depends on the results of a t test. (b) The manufacturer claims that the mean calorie content for this particular type of frozen dinner is 239 calories. Does the boxplot suggest that actual mean content differs from the stated value? Yes, it is clear that actual mean content differs from the stated value.No, it is possible that actual mean content is 239. There's not enough evidence to decide. (c) Carry out a formal test of the hypotheses suggested in part (b). Use α = 0.05. State the appropriate null and alternative hypotheses.

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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Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases, so it is important that the information on packages be accurate. Suppose that a random sample of n = 12 frozen dinners of a certain type was selected and the calorie content of each one was determined. Below are the resulting observations, along with a boxplot and normal probability plot.

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

A normal probability plot has 12 points plotted on it. The horizontal axis ranges from −1.5 to 1.5 and is labeled "Normal score." The vertical axis ranges from 225 to 265 and is labeled "Calories." The first point is plotted in the bottom left. The second through twelfth points are plotted from the bottom left towards the top right in roughly the shape of a slanted line. The approximate locations of the points from left to right are as follows:

(−1.6, 225),
(−1.1, 226),
(−0.8, 233),
(−0.5, 239),
(−0.3, 242),
(−0.1, 244),
(0.1, 245),
(0.4, 248),
(0.6, 251),
(0.8, 255),
(1.1, 259),
(1.7, 265).

(a)

Is it reasonable to test hypotheses about true average calorie content μ by using a one-sample t test?

Yes, it is reasonable.No, a t test is not applicable here. It depends on the results of a t test.

(b)

The manufacturer claims that the mean calorie content for this particular type of frozen dinner is 239 calories. Does the boxplot suggest that actual mean content differs from the stated value?

Yes, it is clear that actual mean content differs from the stated value.No, it is possible that actual mean content is 239. There's not enough evidence to decide.

(c)

Carry out a formal test of the hypotheses suggested in part (b). Use α = 0.05.

State the appropriate null and alternative hypotheses.

H₀: μ > 239

H_a: μ < 239

H₀: μ = 239

H_a: μ > 239

H₀: μ < 239

H_a: μ > 239

H₀: μ = 239

H_a: μ < 239

H₀: μ = 239

H_a: μ ≠ 239

Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.)

t= P-value =

State the conclusion in the problem context.

We fail to reject H₀. We do not have convincing evidence that the mean calorie content for this particular type of frozen dinner differs from 239 calories.We fail to reject H₀. We have convincing evidence that the mean calorie content for this particular type of frozen dinner differs from 239 calories. We reject H₀. We do not have convincing evidence that the mean calorie content for this particular type of frozen dinner differs from 239 calories.We reject H₀. We have convincing evidence that the mean calorie content for this particular type of frozen dinner differs from 239 calories.

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