Question: 25 students were chosen randomly from a statistics class to solve some problems on confidence intervals. The time required to complete all problems was recorded for every student. The sample mean time was 11 minutes with a sample standard deviation of 5 minutes.



1. Construct a 95% confidence interval for mu, the mean time for the population of students in that statistics class, to solve those problems.




2. Interpret your answer to question 1, i.e., state your conclusion.




3. Describe how the sample size n affects the width of the confidence interval on mu.




4. Describe how the variability of the data affects the width of the confidence interval on mu.




5. Describe how the confidence level affects the width of the confidence interval on mu.  Edit

Answer: Here n=25, x bar= 11 , sigma=5
margin of error,e= σ/sqrt(n)* z_c [z_c= critical z at c% confidence interval.]
={5/sqrt(25)}*1.96=1.96 [z_c=1.96 at 95% confidence.]
1. Confidence interval==(x bar -e, x bar +e)=(11-1.96, 11+1.96)=(9.04, 12.96)(Ans.)

2. Middle 95% of values lie in between 9.04 to 12.96.

3. width of confidence=2e=2*σ/sqrt(n)* z_c

if n increase e is decreased so, width is decreased.

4. if data are more variable that affects sigma , if sigma increase , width of confidence is also increased.

5. confidence level affects the value of z_c , if z_c increased e also increased so width also increased and if z-c decreased width is also decreased.  Edit