Problem Set 9 | Assignments | Introduction to Probability and Statistics | Mathematics

Problem Set 9 Answer Checker

Work on the assigned problems in the associated Problem Set PDF file, then use the problem set checker to find out if the answer was correct or incorrect. To check your answers put them in the appropriate box and click the 'Check' button. Every checker box can do arithmetic and calculate standard functions (see calculator help). If you give decimal answers, give them to at least 3 decimal places.

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Problem 1.

(a) No online check

(b.i) Give the lower limit of the 80% confidence interval.

(b.ii) Give the upper limit of the 80% confidence interval.

(b.iii) Give the lower limit of the 95% confidence interval.

(b.iv) Give the upper limit of the 95% confidence interval.

(c.i) Give the lower limit of the 80% posterior probability interval.

(c.ii) Give the upper limit of the 80% posterior probability interval.

Problem 2.

(a.i) Give the lower limit of the 90%

t

-confidence interval.

(a.ii) Give the upper limit of the 90% $t-$ confidence interval.

(b.i) Give the lower limit of the 90% $z$ -confidence interval.

(b.ii) Give the upper limit of the 90% $z$ -confidence interval.

(d) Give the number of people needed to make the width of the interval 1 inch.

Problem 3.

(a.i) Give the lower limit of the precise (i.e. let R compute

z_{α∕2}

) 95%

z

-confidence interval.

(a.ii) Give the upper limit of the 95% precise $z$ -confidence interval.

(b.i) Give the lower limit of the 98% $z$ -confidence interval.

(b.ii) Give the upper limit of the 98% $z$ -confidence interval.

(c.i) Give the lower limit of the 95% $t$ -confidence interval.

(c.ii) Give the upper limit of the 95% $t$ -confidence interval.

(c.iii) Give the lower limit of the 98% $t$ -confidence interval.

(c.iv) Give the upper limit of the 98% $t$ -confidence interval.

Problem 4.

(a.i) Give the lower limit of the 95% confidence interval for

σ^2

(a.ii) Give the upper limit of the 95% confidence interval for $σ^2$ .

(b) No online check

Problem 5.

(a.i) Give the lower limit of the 95% confidence interval for

σ

(a.ii) Give the upper limit of the 95% confidence interval for $σ$ .

(b) No online check

Problem 6.

No online check