Probability challenge help

[yeungmei]

Hi, I have no idea of this ±.03

A population proportion is .40. A simple random sample of size 200 will be taken and the sample proportion 'p' will be used to estimate the population proportion.

a. what is the probability that the sample proportion will be within ±.03 of the population proportion?

 

[e(ho0n3]

Are you confused as to what ±.03 means?

 

[Architeuthis Dux]

Hello,

I understand your confusion with the ±.03 notation. In statistics, it is common to use the notation ± to represent a range of values. So in this case, ±.03 means a range of values that are within 0.03 above and below the given number.

To answer the question, we need to use the formula for calculating the standard error of the sample proportion:

SE = √(p*(1-p)/n)

Where p is the population proportion and n is the sample size.

In this case, p = 0.40 and n = 200. Plugging these values into the formula, we get:

SE = √(0.40*(1-0.40)/200) = √(0.24/200) = 0.03099

This means that the standard error of the sample proportion is 0.03099. Now, to find the probability that the sample proportion will be within ±.03 of the population proportion, we need to calculate the probability that the sample proportion falls within the range of 0.37 (0.40 - 0.03) and 0.43 (0.40 + 0.03).

To do this, we can use the z-score formula:

z = (x - μ)/SE

Where x is the sample proportion, μ is the population proportion (0.40 in this case), and SE is the standard error calculated earlier.

Plugging in the values, we get:

z = (0.37 - 0.40)/0.03099 = -0.966

z = (0.43 - 0.40)/0.03099 = 0.966

Using a z-score table, we can find that the probability of z being between -0.966 and 0.966 is approximately 0.808. This means that there is an 80.8% chance that the sample proportion will fall within ±.03 of the population proportion.

I hope this helps clarify the concept and how to calculate the probability. Let me know if you have any further questions.