Researchers investigated whether the proportion of American teenagers with some level of hearing loss was diff erent in 2005–2006 than in 1988–1994. They collected data on random samples of American teenagers in those two time periods. Let the symbol π05-06 denote the population proportion of American teenagers with some level of hearing loss in 2005–2006 and similarly for π88-94. A 95% confidence interval for the parameter π05-06 − π88-94 turns out to be (0.0015, 0.0467). Required:
What is an appropriate conclusion to draw?

Complete Question

Researchers investigated whether the proportion of American teenagers with some level of hearing loss was different in 2005–2006 than in 1988–1994. They collected data on random samples of American teenagers in those two time periods. Let the symbol denote the population proportion of American teenagers with some level of hearing loss in 2005–2006 and similarly for . A 95% confidence interval for the parameter turns out to be (0.0015, 0.0467).

Required:

What is an appropriate conclusion to draw?

The appropriate conclusion is  

The sample data provide little evidence to doubt that the proportion of American teenagers with hearing loss was the same in 1988-1994 as in 2005-2006

Step-by-step explanation:

Generally the appropriate conclusion is

The sample data provide little evidence to doubt that the proportion of American teenagers with hearing loss was the same in 1988-1994 as in 2005-2006.

This because the confidence intervals are very close to zero , i.e both the upper limit and the lower limit are close to zero  and if we are take 0.05 as our level of significance we see that the both values of the confidence level are small to be significant

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.