Question

A particular cookie company has a double-feature box of cookies. These boxes come with two types of cookies; oatmeal raisin and chocolate-chip. However, the proportion of cookies of each type varies. A data analyst working for the company wonders if there is a tendency for the boxes to have more of one type of cookie than the other. In order to investigate, he selects 54 boxes of the double-feature oatmeal raisin/choc-chip cookies and counts the number of each type of cookie. He finds out that, in his sample of 54 boxes, the proportion of chocolate chip cookies is 0.65. What is the standard deviation of the sampling proportion for the proportion of chocolate chip cookies?

Answer 1

The standard deviation of the sampling proportion for the proportion of chocolate chip cookies can be calculated using the formula sqrt((p(1-p))/n), where p is the proportion of chocolate chip cookies and n is the sample size. In this case, the proportion of chocolate chip cookies is 0.65 and the sample size is 54. Plugging these values into the formula, we get a standard deviation of 0.0809.

Step-by-step explanation:

The standard deviation of the sampling proportion for the proportion of chocolate chip cookies can be calculated using the formula:

Standard Deviation = sqrt((p(1-p))/n)

Where:

• p is the proportion of chocolate chip cookies
• n is the sample size

In this case, the proportion of chocolate chip cookies is 0.65 and the sample size is 54. Plugging these values into the formula:

Standard Deviation = sqrt((0.65(1-0.65))/54)

Calculating the expression inside the square root gives:

Standard Deviation = sqrt(0.2275/54)

And taking the square root gives the final answer:

Standard Deviation = 0.0809