Note:
- In part (e) of each question below you MUST not say μ – rather you should say what μ represents (e.g., “true population mean body temperature of all men and women” in the first question).
Body Temperatures
- C=0.95
- Confidence Interval
- Z^{*}=\(\pm\)-1.960.
- 36.8\(\pm\)-1.960\(\frac{0.45}{\sqrt{130}}\) = 36.73-36.89.
- I am 95% confident that the true population mean body temperature of all men and women is between 36.73 and 36.89^{o}C.
R Appendix.
( zstar <- distrib(0.025,type="q",lower.tail=FALSE) )
Beetle Usage
- C=0.95
- Lower Confidence Bound
- Z^{*}=-1.645
- 194.17-1.645\(\frac{15}{\sqrt{18}}\) = 188.4
- I am 95% confident that the true population mean thorax length of the Halticus oleracea beetle is greater than 188.4 mm (i.e., a lower bound).
R Appendix.
( zstar <- distrib(0.95,type="q",lower.tail=FALSE) )
Internet Usage
Note:
- These questions are “sample size” and not “confidence region” calculations.
- Note that all sample size calculations should be rounded UP to a whole number. For example, in the second question below, note how 154.25 was rounded up to 155.
- One should take a sample size of 219 household to achieve the desired level of confidence and margin-of-error.
- One should take a sample size of 155 household to achieve the desired level of confidence and margin-of-error.
- One should take a sample size of 876 household to achieve the desired level of confidence and margin-of-error.
R Appendix.
sigma <- 7.55
me <- 1
(zstar <- distrib(0.025,type="q",lower.tail=FALSE))
(round(zstar,3)*sigma/me)^2
(zstar <- distrib(0.05,type="q",lower.tail=FALSE))
(round(zstar,3)*sigma/me)^2
me <- 0.5
(zstar <- distrib(0.025,type="q",lower.tail=FALSE))
(round(zstar,3)*sigma/me)^2