Answer to Question #97576 in Statistics and Probability for Juliet Beglaryan

Question

5. If the manager of a paint supply store wants to estimate, with 95% confidence, the mean amount of paint in a 1-gallon can to within ± 0.004 gallon and also assumes that the standard deviation is 0.02 gallon, what sample size is needed?
6. You want to rent an unfurnished one-bedroom apartment for next semester. The mean monthly rent for a random sample of 10 apartments advertised in the local newspaper is $540. Assume that the 휎=$80.a) Find a 95% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community.b) If we increase the sample size to 100 apartments, the sdandard error becomes ________, then with a fixed confidence level, the margin of error E becomes _______________ and finally the interval is ________________.

Answer 1

5 . Sample = $n =(\frac {\sigma*z} {me})^2 = \frac{(0.02*1.96)^2}{0.004^2} = 96.04, \therefore n =97$

6 . (a) 95% confidence interval =$540± 1.96 \times \frac{80}{\sqrt{10}} = 540 ±49.58 = (490.42, 589.58)$

(b) standard error = $\frac{80} {\sqrt{100}}=8$

margin of error =$E=1.96\times\frac{80} {\sqrt{100}}=1.96\times8=15.68$

95% confidence interval =$540 ± 15.68 = (524.32, 555.68)$