Problem Set 7 | Assignments | Introduction to Probability and Statistics | Mathematics

Problem Set 7 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.

As you work you should have pencil and paper handy for calculations and thinking!

Note: some questions ask for a formula. For the checker we ask you to plug a value into the formula. For your pset you still need to give the whole formula.

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Problem 1.

(a.i)} Give the exact (binomial) one-sided

p

-value for the data.

(a.ii) Give the exact (binomial) two-sided $p$ -value for the data.

(b) No online check

For parts c-e use a two-sided rejection region.

(c.i) Less than or equal to:

(c.ii) More than or equal to:

(d.i) What's the power when $α = 0.05$ for $θ = 0.55$ ?

(d.ii) What's the power when $α = 0.05$ for $θ = 0.6$ ?

(e) How many spins with $α = 0.05$ to have power $0.9$ when $θ = 0.55$ ?

(f) What's the posterior probability of $θ = 0.55$ ?

(g) No online check

Problem 2.

(a.i) Estimate the probability of type I error.

(a.ii) Estimate the probability of type II error.

(b) No online check

Problem 3.

(a) Give the

p

-value of the test for this data.

(b) Give the $p$ -value of the test for this data.

Problem 4.

(a) No online check

(b.i) Give the threshhold for $\ov{x}$ for which they should use issue a ticket.

(b.ii) No online check

(c.i) What is the power of this test?

(c.ii) How many cameras are needed to insure a power of 0.9?

Problem 5.

(a) What is the probability of a type I error?

(b) What is the probability of a type II error?

Problem 6.

No online check