During the last year, 83% of the orders for food delivery from restaurants have been done using an online platform, was found in a research on the tendency in the online shopping with food products. What is the standard error on a random sample of 30 orders? Please, show your full solution!
To find the standard error, we need to know the sample size (n), the population proportion (p), and the standard deviation (σ).
In this case, the sample size (n) is 30 orders, and the population proportion (p) is given as 83% or 0.83. However, we don't know the standard deviation (σ) from the information provided.
To estimate the standard deviation, we can use the formula for the standard error of the proportion:
SE = sqrt((p * (1 - p)) / n)
Now, let's calculate the standard error:
SE = sqrt((0.83 * (1 - 0.83)) / 30)
First, we calculate (p * (1 - p)):
0.83 * (1 - 0.83) = 0.83 * 0.17 = 0.1409
Then, we divide this value by the sample size (n):
0.1409 / 30 = 0.0046966667 (rounded to 10 decimal places)
Finally, we take the square root of this result to get the standard error:
SE = sqrt(0.0046966667) = 0.0685 (rounded to 4 decimal places)
Therefore, the standard error on a random sample of 30 orders is approximately 0.0685.