How many computers? In a simple random sample of 175 households, the sample mean number of personal computers was 1.18. Assume the population standard deviation is σ=0.23.
(a) Construct a 99.9% confidence interval for the mean number of personal computers. Round the answer to at least two decimal places. A 99.9% confidence interval for the mean number of personal computers is 1.12 < μ < 1.24.
(b) If the sample size were 220 rather than 175, would the margin of error be larger or smaller than the result in part (a)? Explain. The margin of error would be smaller, since an increase in the sample size will decrease the standard error.
(c) If the confidence levels were 99.5% rather than 99.9%, would the margin of error be larger or smaller than the result in part (a)? Explain. The margin of error would be smaller, since a decrease in the confidence level will decrease the critical value zα/2.
(d) Based on the confidence interval constructed in part (a), is it likely that the mean number of personal computers is less than 1.36? It is likely that the mean number of personal computers is less than 1.36.