The standard deviation of the lifetime of certain TV picture tubes is estimated as 150 hours. How much large a sample must be taken in order to be 99% confident that the error in the estimated means lifetime will not exceed 25 hours
Large sample= 67.8
To determine the sample size needed, we can use the formula for the sample size required for estimating the population mean with a specified margin of error at a given confidence level:
n = (Z * σ / E)²
where:
- n is the required sample size
- Z is the Z-score corresponding to the desired confidence level (in this case, 99%, or 2.58)
- σ is the standard deviation of the population (150 hours)
- E is the desired margin of error (25 hours)
Plugging in the values:
n = (2.58 * 150 / 25)²
n = (387 / 25)²
n ≈ 15.48²
n ≈ 239.2
Since the sample size must be a whole number, we will need to round up to the nearest whole number. Therefore, the required sample size is 240.