Suppose a researcher is trying to understand whether people who purchase fast-food hamburgers would be willing to pay more if the hamburger comes with a free whistle. Prior research suggests the mean amount customers say they are willing to pay for a hamburger is μ = 3.68 and σ = 0.70. The researcher plans to conduct a study very similar to the prior research by selecting a sample of customers and asking them how much they are willing to pay for the hamburger. Before asking, however, he will tell the customer about the free whistle that will come with the hamburger. The researcher’s null hypothesis is that the mean amount the customers are willing to pay when they are told about the free whistle is no different than the amount customers are willing to pay when they are not told they will receive a free whistle. The researcher’s sample of 49 customers has a sample mean of M = 4.04. The test statistic for this sample mean is 3.60. Using a significance level of α = .05, which of the following is the most appropriate statement of the result? (Hint: For a two-tailed test with α = .05 and σ known, the boundaries of the critical region are always ±1.96.) Telling customers they will receive a free whistle with their hamburger did not have a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05. Telling customers they will receive a free whistle with their hamburger did not have a significant effect on the amount they say they are willing to pay for a hamburger, z = 4.04, p > .05. Telling customers they will receive a free whistle with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05. Telling customers they will receive a free whistle with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.68, p < .05. Compute the estimated Cohen’s d to measure the size of the treatment effect. Note: Cohen’s d is always reported as a positive value and reflects the proportion of the standard deviation that is affected by the treatment. Estimated Cohen’s d = Using Cohen’s criteria, the estimated Cohen’s d indicates that telling customers they will receive a free whistle is associated with a in the amount they are willing to pay for the hamburger.

Suppose a researcher is trying to understand whether people who purchase fast-food hamburgers would be willing to pay more if the hamburger comes with a free whistle. Prior research suggests the mean amount customers say they are willing to pay for a hamburger is μ = 3.68 and σ = 0.70. The researcher plans to conduct a study very similar to the prior research by selecting a sample of customers and asking them how much they are willing to pay for the hamburger. Before asking, however, he will tell the customer about the free whistle that will come with the hamburger. The researcher’s null hypothesis is that the mean amount the customers are willing to pay when they are told about the free whistle is no different than the amount customers are willing to pay when they are not told they will receive a free whistle. The researcher’s sample of 49 customers has a sample mean of M = 4.04. The test statistic for this sample mean is 3.60. Using a significance level of α = .05, which of the following is the most appropriate statement of the result? (Hint: For a two-tailed test with α = .05 and σ known, the boundaries of the critical region are always ±1.96.) Telling customers they will receive a free whistle with their hamburger did not have a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05. Telling customers they will receive a free whistle with their hamburger did not have a significant effect on the amount they say they are willing to pay for a hamburger, z = 4.04, p > .05. Telling customers they will receive a free whistle with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05. Telling customers they will receive a free whistle with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.68, p < .05. Compute the estimated Cohen’s d to measure the size of the treatment effect. Note: Cohen’s d is always reported as a positive value and reflects the proportion of the standard deviation that is affected by the treatment. Estimated Cohen’s d = Using Cohen’s criteria, the estimated Cohen’s d indicates that telling customers they will receive a free whistle is associated with a in the amount they are willing to pay for the hamburger.

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Description: Suppose a researcher is trying to understand whether people who purchase fast-food hamburgers would be willing to pay more if the hamburger comes with a free whistle. Prior research suggests the mean amount customers say they are willing to pay for a

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 researcher plans to conduct a study very similar to the prior research by selecting a sample of customers and asking them how much they are willing to pay for the hamburger. Before asking, however, he will tell the customer about the free whistle that will come with the hamburger.

The researcher’s null hypothesis is that the mean amount the customers are willing to pay when they are told about the free whistle is no different than the amount customers are willing to pay when they are not told they will receive a free whistle.

The researcher’s sample of 49 customers has a sample mean of M = 4.04. The test statistic for this sample mean is 3.60. Using a significance level of α = .05, which of the following is the most appropriate statement of the result?

(Hint: For a two-tailed test with α = .05 and σ known, the boundaries of the critical region are always ±1.96.)

Telling customers they will receive a free whistle with their hamburger did not have a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05.

Telling customers they will receive a free whistle with their hamburger did not have a significant effect on the amount they say they are willing to pay for a hamburger, z = 4.04, p > .05.

Telling customers they will receive a free whistle with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05.

Telling customers they will receive a free whistle with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.68, p < .05.

Compute the estimated Cohen’s d to measure the size of the treatment effect.

Note: Cohen’s d is always reported as a positive value and reflects the proportion of the standard deviation that is affected by the treatment.

Estimated Cohen’s d =

Using Cohen’s criteria, the estimated Cohen’s d indicates that telling customers they will receive a free whistle is associated with a in the amount they are willing to pay for the hamburger.

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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