Question

Choice blindness is the term that psychologists use to describe a situation in which a person expresses a preference and then doesn't notice when they receive something different than what they asked for. The authors of the paper "Can Chocolate Cure Blindness? Investigating the Effect of Preference Strength and Incentives on the Incidence of Choice Blindness"† wondered if choice blindness would occur more often if people made their initial selection by looking at pictures of different kinds of chocolate compared with if they made their initial selection by looking at the actual different chocolate candies.

Suppose that 200 people were randomly assigned to one of two groups. The 100 people in the first group are shown a picture of eight different kinds of chocolate candy and asked which one they would like to have. After they selected, the picture is removed and they are given a chocolate candy, but not the one they actually selected. The 100 people in the second group are shown a tray with the eight different kinds of candy and asked which one they would like to receive. Then the tray is removed and they are given a chocolate candy, but not the one they selected.

If 20 of the people in the picture group and 13 of the people in the actual candy group failed to detect the switch, would you conclude that there is convincing evidence that the proportion who experience choice blindness is different for the two treatments (choice based on a picture and choice based on seeing the actual candy)? Test the relevant hypotheses using a 0.01 significance level. (Let p1 be the proportion who experience choice blindness based on a picture treatment, and p2 be the proportion who experience choice blindness based on seeing the actual candy treatment.)

State the appropriate null and alternative hypotheses.

H0: p1 − p2 > 0 Ha: p1 − p2 < 0

H0: p1 − p2 = 0 Ha: p1 − p2 ≠ 0

H0: p1 − p2 = 0 Ha: p1 − p2 < 0

H0: p1 − p2 < 0 Ha: p1 − p2 > 0

H0: p1 − p2 = 0 Ha: p1 − p2 > 0

Find the test statistic and P-value. (Use a table or technology. Round your test statistic to two decimal places and your P-value to four decimal places.)

z =

P-value =

State your conclusion.

We fail to reject H0. We do not have convincing evidence that the proportion who experience choice blindness is different for the two treatments.

We reject H0. We do not have convincing evidence that the proportion who experience choice blindness is different for the two treatments.

We reject H0. We have convincing evidence that the proportion who experience choice blindness is different for the two treatments.

We fail to reject H0. We have convincing evidence that the proportion who experience choice blindness is different for the two treatments.

Answer 1

Given that,

For picture group : n1 = 100 and x1 = 20

For actual candy group : n2 = 100 and x2 = 13

The null and the alternative hypotheses are,

H0: p1 − p2 = 0 Versus Ha: p1 − p2 ≠ 0

Using TI-84 calculator we get,

Test statistic is, Z = 1.33

p-value = 2 * P(Z > 1.33) = 2 * 0.0918 = 0.1836

=> p-value = 0.1836

Since, p-value = 0.1836 > 0.01

We fail to reject H0. We do not have convincing evidence that the proportion who experience choice blindness is different for the two treatments.