1. Chapter 12. Population mean (20 points) The article "americans' big Debt burden growing, not evenly Distributed" (www.gallup.com, retrieved December 14, 2016) reported that for a representative sample of Americans born between 1965 and 1971 (known as Generation X), the sample mean number of credit cards owned was 4.5. Suppose that the sample standard deviation (which was not reported) was 1.0 and that the sample size was \( n=300 \). Construct a \( 95 \% \) confidence interval.
a. Define \( \mathscr{M} \)
b. Check
c. Calculate
Answer
\(\mathscr{M} = (4.5 - z \frac{1.0}{\sqrt{300}}, 4.5 + z \frac{1.0}{\sqrt{300}})\)
Step 1 ：\(\mathscr{M} = (\overline{X} - E, \overline{X} + E)\)
Step 2 ：\(E = z \frac{\sigma}{\sqrt{n}}\)
Step 3 ：\(\mathscr{M} = (4.5 - z \frac{1.0}{\sqrt{300}}, 4.5 + z \frac{1.0}{\sqrt{300}})\)
