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.

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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