Question

College needs to estimate the mean number of students in the MATH classes. How many classes must be surveyed if we need to be 86% confident that the sample mean size is within one student of the population mean? Take the standard deviation equal to 4 students. Round your answer up to the whole number, i.e., 6.01 classes will be rounded to 7 classes,

Answer 1

To estimate the mean number of students in the MATH classes with 86% confidence and a margin of error of 1 student, we need to survey at least 15 classes.

Step-by-step explanation:

To estimate the mean number of students in the MATH classes with a certain level of confidence, we can use the formula:

n = (Z * σ / E)^2

Where:

• n is the number of classes to be surveyed
• Z is the z-score corresponding to the desired confidence level
• σ is the standard deviation of the population
• E is the desired margin of error

In this case, the desired confidence level is 86%, which corresponds to a z-score of approximately 1.08 (using a standard normal distribution table). The standard deviation is given as 4 students, and the desired margin of error is 1 student. Plugging in these values into the formula:

n = (1.08 * 4 / 1)^2 = 14.56

Rounding up to the nearest whole number, we need to survey at least 15 classes to be 86% confident that the sample mean size is within one student of the population mean.

Answer 2

There is a need to survey at least 33% of MATH classes to be 86% confident that the sample mean size is within one student of the population mean.

Calculating the Z-score of a sample mean size.

To determine the number of classes that must be surveyed, we need to follow these steps.

First, we need to determine the required sample size (n) and this can be estimated by using the formula:

`n=(Z^2* \sigma^2)/(E^2)`

here;

• population standard deviation
  `\sigma =4`
• desired margin of error (E) = 1
• confidence level = 86%
• Z-score for 86% C.L = 1.44

`n=((1.44)^2* 4^2)/(1^2)`

`n =(2.0736* 16)/(1)`

n = 33.1776

n ≅ 34

Therefore, we can conclude that there is a need to survey at least 34% of MATH classes to be 86% confident that the sample mean size is within one student of the population mean.