Question

Scientists want to estimate the mean weight of mice after they have been fed a special diet. from previous studies, it is known that the weight is normally distributed with a standard deviation of 4 grams. what is the minimum required sample size if the scientists wish to estimate the true mean to within 0.5 grams with 80% confidence?

Answer 1

To estimate the mean weight of mice to within 0.5 grams with 80% confidence, we use the sample size formula involving a z-value, the standard deviation, and margin of error. The minimum required sample size calculation yields 106 mice.

Step-by-step explanation:

To estimate the mean weight of mice after being fed a special diet to within 0.5 grams with 80% confidence, the minimum required sample size is needed. This can be calculated using the formula for sample size in hypothesis testing or confidence interval calculations:

n = (Z * σ / E)^2

Where:

• n is the sample size
• Z is the z-value corresponding to the desired confidence level
• σ (sigma) is the population standard deviation
• E is the margin of error

For an 80% confidence interval, the z-value (Z) is approximately 1.282. The known standard deviation (σ) is 4 grams, and the desired margin of error (E) is 0.5 grams.

Let's plug the values into the formula:

n = (1.282 * 4 / 0.5)^2

n = (5.128 / 0.5)^2

n = (10.256)^2

n = 105.12

Since we cannot have a fraction of a mouse, we'll round up to the nearest whole number. Therefore, the minimum required sample size is 106 mice.