Answered: The authors of the paper "Changes in…

Name: The authors of the paper "Changes in Quantity, Spending, and Nutrition
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Description: The authors of the paper "Changes in Quantity, Spending, and Nutritional Characteristics of Adult, Adolescent and Child Urban Corner Store Purchases After an Environmental Intervention"†wondered if increasing the availability of healthy food options

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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The authors of the paper "Changes in Quantity, Spending, and Nutritional Characteristics of Adult, Adolescent and Child Urban Corner Store Purchases After an Environmental Intervention"†wondered if increasing the availability of healthy food options would also increase the amount people spend at the corner store. They collected data from a representative sample of 5,949 purchases at corner stores in Philadelphia after the stores increased their healthy food options. The sample mean amount spent for this sample of purchases was $2.86 and the sample standard deviation was $5.40.

(a)

Notice that for this sample, the sample standard deviation is greater than the sample mean. What does this tell you about the distribution of purchase amounts?

The fact that the sample standard deviation is greater than the sample mean indicates that there is ---Select--- quite a bit of very little variability in the distribution of purchase amounts. In addition, since purchase amounts cannot be negative, the larger standard deviation indicates that the distribution is ---Select--- positively skewed approximately normal negatively skewed .

(b)

Before the stores increased the availability of healthy foods, the population mean total amount spent per purchase was thought to be about $2.81. Do the data from this study provide convincing evidence that the population mean amount spent per purchase is greater after the change to increased healthy food options? Carry out a hypothesis test with a significance level of 0.05.

State the appropriate null and alternative hypotheses.

H₀: μ = 2.81

H_a: μ ≠ 2.81

H₀: μ < 2.81

H_a: μ > 2.81

H₀: μ > 2.81

H_a: μ < 2.81

H₀: μ = 2.81

H_a: μ > 2.81

H₀: μ = 2.81

H_a: μ < 2.81

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 reject H₀. We have convincing evidence that the population mean amount spent per purchase is greater after the change to increased healthy food options.We fail to reject H₀. We do not have convincing evidence that the population mean amount spent per purchase is greater after the change to increased healthy food options. We reject H₀. We do not have convincing evidence that the population mean amount spent per purchase is greater after the change to increased healthy food options.We fail to reject H₀. We have convincing evidence that the population mean amount spent per purchase is greater after the change to increased healthy food options.

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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