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SHOW ALL WORK STEP BY STEP FOR EACH SECTION. SHOW CALCULATOR FUNCTION USED ON YOUR T-83 OR T-84 CALCULATOR AS WELL.

Suppose that a health expert has claimed that 18 % of college students smoke cigarettes. To investigate this claim, researchers survey a random sample of college students. Using this sample, a 99 % confidence interval for the percentage of college students who smoke is found to be 12.66 % to 17.34 %. Based this interval, can we conclude that the claim that 18 % of all college students smoke is reasonable?

Select ONLY ONE ANSWER FROM A, B or C

a) the claim 18% is NOT reasonable, because the value 18% is not in the confidence interval.
b) the claim 18% is reasonable, because the value 18% is not in the confidence interval.
c) the claim 18% is NOT reasonable because the value 18% s in the confidence interval.

For each of the following changes choose whether the effect on the width of the confidence interval would be an increase, a decrease, remain the same, or indeterminable. Assume all other variables remain constant.

A) IS ALREADY SOLVED- Increase the sample size and simultaneously decrease the confidence level: DECREASE

B) Decrease the sample size and increase the confidence level :Increase, decrease, remain the same or indeterminable?

C) Increase the population size from 3 million to 25 million :Increase, decrease, remain the same or indeterminable?

D) Increase the sample size and, simultaneously, increase the confidence level :Increase, decrease, remain the same or indeterminable?

Solution

Q 1 : Here we have 99% confidence interval ( 12.66% , 17.34 % )

Answer : a) the claim 18% is NOT reasonable, because the value 18% is not in the confidence interval.

Q 2 :

B) Decrease the sample size and increase the confidence level : Increase

C ) Increase the population size from 3 million to 25 million : remain the same or indeterminable

D) Increase the sample size and, simultaneously, increase the confidence level : decrease