Final answer:
To estimate the average time that subjects can spend in the sensory isolation chamber before experiencing discomfort, we can calculate the sample size needed. Using the formula for sample size, assuming a standard deviation of 5 minutes (conservative estimate), a desired confidence level of 95%, and a margin of error of 5 minutes, we find that at least 386 subjects should be removed before discomfort is experienced on average.
Step-by-step explanation:
To estimate the average time that subjects can spend in the sensory isolation chamber before experiencing discomfort, we need to calculate the sample size required. The formula to calculate the sample size for estimating a population mean with a desired confidence level and margin of error is:
n = (z * σ / E)^2
Where:
- n is the sample size
- z is the z-score corresponding to the desired confidence level (for 95%, the z-score is approximately 1.96)
- σ is the standard deviation of the population (unknown in this case but can be estimated from a pilot study or previous data)
- E is the margin of error (in this case, 5 minutes)
Since the standard deviation is unknown, we can use a conservative estimate of 50% of the range of possible values. Let's assume the range is 10 minutes (from 0 to 10 minutes of discomfort). So, σ = range / 2 = 10 / 2 = 5 minutes.
Plugging the values into the formula, we get:
n = (1.96 * 5 / 5)^2 = 19.6^2 ≈ 385.2
Since we cannot have a fractional number of subjects, we round up to the nearest whole number. Therefore, we should remove at least 386 subjects before discomfort is experienced on average.