STAtistics / Mr. Hansen

Name: _______________________________

2/18/2014

Mr. Hansen’s use only: ______

 

Test on Confidence Intervals, Type I/Type II Error, Etc.

 

1.

The heights of cornstalks in Farmer Jane’s field are known to be normally distributed. An SRS produces the following data (in cm):

235, 218, 217, 212, 215, 231, 221, 216, 225, 231, 230, 228

(a) Compute and interpret an 85% confidence interval for the mean height of Farmer Jane’s cornstalks. Show your work.

























(b) What concerns would you have in publishing your C.I. from part (a) as a fact in the local agricultural newsletter? In other words, how robust are your findings?

 

2.

Frod Motor Company manufactures a car called the Celeste. It is a piece of junk, with a claimed top speed of only 77 mph. However, manufacturing processes vary, and not all Celestes will be able to attain 77 mph, and some may have a higher top speed. Consumer Retorts, an independent testing magazine, will test 5 Celestes, randomly chosen from the assembly line, to see whether there is evidence that Frod is overstating the claimed top speed for the Celeste automobiles. If evidence is found that the true mean top speed is lower than 77 mph, Consumer Retorts will publish a scathing exposé claiming that the Frod Motor Company is guilty of (ahem) fraud.

(a) State H0 and Ha for suitable hypotheses regarding the true mean top speed of Celestes.




(b) What, exactly, constitutes a Type I error in the context of this problem?




(c) What, exactly, constitutes a Type II error in the context of this problem?




(d) What are the real-world consequences of each type of error?









(e) Which type of error should Consumer Retorts fear worse in this context: Type I or Type II? Explain.

 

3.

Given: A pilot survey reveals that somewhere between 40% and 55% (rough estimate) of the residents of the District of Columbia are addicted to time-wasting.

(a) How many residents must be polled in order to estimate the incidence of time-wasting addiction within plus or minus 3.5 percentage points with 90% confidence? Show your work.


















(b) What assumptions need to be made in order for the procedure you performed in part (a) to be valid? Are these assumptions met? Show all supporting evidence. Use reverse side.

(c) Suppose that an SRS of 700 DC residents includes 335 who admit to being addicted to time-wasting. Use this fact to compute and interpret a 95% confidence interval for the incidence of time-wasting addiction in DC.




















(d) Explain briefly why your answer to part (c) is almost certainly wrong.