Question

Jimin wants to know whether if there is a difference in proportion of people who like mint chocolate chip-flavored ice cream between Americans and Koreans. She takes a random sample of 46 Americans and find that 30 of them like the flavor, and then she takes a random sample of 53 Koreans and find that 24 of them like the flavor. For a 95% confidence interval of the true difference in proportion of people who like this ice cream flavor, what is the margin of error (MOE)

Answer 1

To calculate the margin of error for a 95% confidence interval of the true difference in proportion of people who like mint chocolate chip-flavored ice cream between Americans and Koreans, you can use the formula: MOE = Z * sqrt((p1 * (1 - p1))/n1 + (p2 * (1 - p2))/n2). Plugging in the values, we get the margin of error for the 95% confidence interval.

Step-by-step explanation:

To calculate the margin of error for a 95% confidence interval of the true difference in proportion of people who like mint chocolate chip-flavored ice cream between Americans and Koreans, you can use the formula:

MOE = Z * sqrt((p1 * (1 - p1))/n1 + (p2 * (1 - p2))/n2)

where:

• Z is the z-value corresponding to the desired confidence level (in this case, 95% corresponds to a z-value of approximately 1.96)
• p1 is the proportion of Americans who like the flavor (30/46)
• n1 is the sample size of Americans (46)
• p2 is the proportion of Koreans who like the flavor (24/53)
• n2 is the sample size of Koreans (53)

Plugging in the values, we get:

MOE = 1.96 * sqrt(((30/46) * (1 - 30/46))/46 + ((24/53) * (1 - 24/53))/53)

Calculating this will give you the margin of error for the 95% confidence interval.