Below are 3 confidence intervals,\

(6,14)

\

(5,15)

\

(8,12)

\ a. ( 2 points) Identify the sample mean in each case.\ b. (3 points) Which is most precise? Why?\ (5 points) Below are three

95%Cls

(where

\\\\sigma

was known and

\\\\bar{x}

happened to be the same); one with sample size 30 , one with sample size 40 , and one with sample size 50 . Which is which?\

(66.2,76.2)

\

(61.2,81.2)

\

(56.2,86.2)

\ Has atmospheric methane

(CH4)

concentration increased significantly in the past 30 years? To answer this question, you take a sample of

100CH4

concentration measurements from 1988 - the sample mean is 1693 parts per billion (ppb). You also take a sample of

144CH4

concentration measurements from 2018 - the sample mean is 1857 ppb. Assume that the population standard deviation of

CH4

concentrations has remained constant at approximately

240ppb

.\ a. (10 points) Construct a

95%

confidence interval estimate of the mean

CH4

concentration in 1988.\ b. (10 points) Construct a

95%

confidence interval estimate of the mean

CH4

concentration in 2018 .\ c. (10 points) Graph the confidence intervals on a single number line and use them to deduce whether there is statistically significant evidence to reject the claim that

CH4

concentration has not changed. Explain your answer!

8. Below are 3 confidence intervals, - (6,14) - (5,15) - (8,12) a. ( 2 points) Identify the sample mean in each case. b. ( 3 points) Which is most precise? Why? 9. ( 5 points) Below are three 95% Cls (where was known and x happened to be the same); one with sample size 30 , one with sample size 40 , and one with sample size 50 . Which is which? - (66.2,76.2) - (61.2,81.2) - (56.2,86.2) 10. Has atmospheric methane (CH4) concentration increased significantly in the past 30 years? To answer this question, you take a sample of 100CH4 concentration measurements from 1988 - the sample mean is 1693 parts per billion (ppb). You also take a sample of 144CH4 concentration measurements from 2018 - the sample mean is 1857ppb. Assume that the population standard deviation of CH4 concentrations has remained constant at approximately 240ppb. a. (10 points) Construct a 95% confidence interval estimate of the mean CH4 concentration in 1988. b. (10 points) Construct a 95% confidence interval estimate of the mean CH4 concentration in 2018. b. (10 points) Construct a 95% confidence interval estimate of the mean CH4 concentration in 2018