Part 2 - The president of the company is uncomfortable with the precision of the estimates derived for the sample mean. They are not willing to tolerate a very large error. e = .04, how large would the sample size have to be if they specify a 98% confidence level?
Formula:
n = [(z-value * sd)/E]^2
Note: n = sample size, z-value will be 2.33 using a z-table to represent the 98% confidence interval, sd = standard deviation, E = 0.04, ^2 means squared, and * means to multiply.
Plug known values into the formula and finish the calculation. Round your answer to the next highest whole number.
I hope this will help.
To calculate the required sample size with a specified confidence level and desired margin of error, we can use the formula:
n = [(z-value * sd)/E]^2
where
n is the sample size,
z-value is the critical value from the z-table corresponding to the desired confidence level,
sd is the standard deviation, and
E is the desired margin of error.
In this case, the specified confidence level is 98%, which means we need to find the critical value corresponding to this confidence level. Using a z-table or a calculator, the z-value for a 98% confidence level is approximately 2.33.
We are also given the desired margin of error, E, which is 0.04.
Now, we can substitute the known values into the formula and solve for n:
n = [(2.33 * sd)/0.04]^2
To complete the calculation, we need the value of the standard deviation (sd) of the population. If you have this information, you can substitute it into the formula. If not, you may need to estimate the standard deviation based on any available data or consult with a statistician.
Once you have all the necessary values, solve the equation. Finally, round the result to the next highest whole number since the sample size must be a whole number.
I hope this explanation helps you understand the process of calculating the required sample size in this scenario.