A test has a mean of 104 and a standard deviation of 16. We want to be 98% certain that we are within 4 points of the true mean. Determine the sample size.
Use a formula to find sample size.
Here is one:
n = [(z-value * sd)/E]^2
...where n = sample size, z-value will be found using a z-table to represent the 98% confidence interval, sd = 16, E = 4, ^2 means squared, and * means to multiply.
Plug the values into the formula and finish the calculation. Round your answer to the next highest whole number.
Hope this helps.
87
To determine the sample size, we can use the formula:
n = (Z * σ / E)^2
Where:
n is the sample size,
Z is the Z-score corresponding to the desired level of confidence (98% confidence level corresponds to a Z-score of approximately 2.33),
σ is the standard deviation, and
E is the margin of error (which is the desired distance from the mean).
In this case, the mean is given as 104, the standard deviation is 16, and we want to be within 4 points of the true mean. So, the margin of error (E) is 4.
Plugging the values into the formula, we can calculate the sample size:
n = (2.33 * 16 / 4)^2
n = (37.28 / 4)^2
n = 9.32^2
n ≈ 86.592
Since we cannot have a fractional sample size, we round up to the nearest whole number. So, the sample size (n) should be 87 in order to be 98% confident that we are within 4 points of the true mean.