Effect size and Cohen\'s d Suppose a researcher is trying to understand whether

Question

Effect size and Cohen's d Suppose a researcher is trying to understand whether people who purchase fast-food hamburgers would be willing to are willing to pay for a hamburger is mu = 2.88 and sigma = 1.12. 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, she about the free whistle that will come with the hamburger. The researchers 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 researchers sample of 144 customers has a sample mean of M = 2.68. The test statistic for this sample mean is -2.14. using a significance level of sigma = 05, which of the following is the most appropriate statement of the result? Using Cohen's criteria, the estimated Cohen's indicates that telling customers they will receive a free whistle is associated with a _____ in the amount they say they are willing to pay for a hamburger.

Explanation / Answer

Alternative hypothesis : Mean amount the customers provided with free whistle with hamburger are willing to pay > 2.88.
For known standard deviation of the population, test statistic T=n(Xbar–)/ , follows N(0,1) under null hypothesis.
Here, critical value = Z = 1.644854, where Z = Upper 100% point of N(0,1) distribution.
Since here observed |T| = 2.14 >1.644854, thus we reject our null hypothesis.
Here, p-value = 2*P[ |T| >| t0|], where t0 = -2.14
                          = 0.03235477 < 0.05.
Hence, 3rd option is correct : 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.
Cohen’s d = |( Xbar – ) / | = 0.17857
Therefore, associated with small effect.

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