Question

A simple random sample of kitchen toasters is to be taken to determine the mean operational lifetime in hours. Assume that the lifetimes are normally distributed with population standard deviation σ =30 hours.

Find the sample size needed so that a 98% confidence interval for the mean lifetime will have a margin of error of 8.

Answer 1

To calculate the sample size needed for a 98% confidence interval with a margin of error of 8, we can use the formula: n = (Z * σ / E)^2, where n is the required sample size, Z is the Z-value corresponding to the desired confidence level, σ is the population standard deviation, and E is the desired margin of error.

Step-by-step explanation:

To calculate the sample size needed for a 98% confidence interval with a margin of error of 8, we can use the formula:

n = (Z * σ / E)^2

Where:

• n is the required sample size
• Z is the Z-value corresponding to the desired confidence level (98% = 2.33)
• σ is the population standard deviation (30 hours)
• E is the desired margin of error (8 hours)

Plugging in the values:

n = (2.33 * 30 / 8)^2 = 201.42

Rounding up to the nearest whole number, the sample size needed is 202.