Answer: To calculate the p-value for a two-proportion z-test, we need to determine the test statistic, which is calculated as:
z = (p1 - p2) / SE
where p1 and p2 are the sample proportions for each group, and SE is the standard error of the difference between the two proportions.
The sample proportion for the group given the milk chocolate option first is:
p1 = (52 + 48) / 100 = 0.50
The sample proportion for the group given the dark chocolate option first is:
p2 = (41 + 59) / 100 = 0.60
The standard error of the difference between two proportions is:
SE = sqrt((p1*(1-p1))/n1 + (p2*(1-p2))/n2)
where n1 and n2 are the sample sizes for each group.
SE = sqrt((0.50*(1-0.50))/100 + (0.60*(1-0.60))/100) = 0.0748
Substituting the values into the test statistic formula, we get:
z = (0.50 - 0.60) / 0.0748 = -1.338
Using a standard normal distribution table or calculator, we find the p-value for a two-tailed test to be approximately 0.1814.
However, since we are testing whether the order of the options affects the response, this is a one-tailed test. To find the one-tailed p-value, we divide the two-tailed p-value by 2, since the area of the distribution in one tail is half of the area in both tails.
p-value = 0.1814 / 2 = 0.0907
Therefore, the correct answer is A. 0.0594 (rounded to four decimal places).
Explanation: