A random sample of \(n\) measurements was selected from a population with standard deviation \(\sigma = 10.2\) and unknown mean \(\mu\text{.}\) Calculate a \(90\) % confidence interval for \(\mu\) for each of the following situations:
(a) \(n = 55, \ \overline{x} = 83.3\)
\(\leq \mu \leq\)
(b) \(n = 70, \ \overline{x} = 83.3\)
\(\leq \mu \leq\)
(c) \(n = 85, \ \overline{x} = 83.3\)
\(\leq \mu \leq\)
(d) In general, we can say that for the same confidence level, increasing the sample size the margin of error (width) of the confidence interval. (Enter: ’’DECREASES’’, ’’DOES NOT CHANGE’’ or ’’INCREASES’’, without the quotes.)
Answer 1.Answer 2.Answer 3.Answer 4.Answer 5.Answer 6.Answer 7.