Question

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 cookie. 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, she will tell the customer about the free cookie 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 cookie is no different than the amount customers are willing to pay when they are not told they will receive a free cookie.

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 cookie 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 cookie 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 cookie 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 cookie 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 cookie is associated with a _______ in the amount they are willing to pay for the hamburger.

Answer 1

P-value = 2 * P(Z > 3.60)

= 2 * (1 - P(Z < 3.60))

= 2 * (1 - 0.9998)

= 2 * 0.0002 = 0.0004

Telling customer they will receive a free cookie with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, P < 0.05

Cohen's d = (M - )/

= (4.04 - 3.68)/0.7 = 0.51

Using Cohen's criteria the estimated Cohen's d indicates that telling customers they will receive a free cookie is associated with a 0.51 in the amount they are willing to pay for the hamburger.