Problem 1. Suppose you have a coin that is known to be one of two types: either the probability of heads is p = 1/5 (call that H0) or the probability of heads is p = 3/10 (call that HA). Consider
testing H0 versus HA by flipping the coin independently a certain number n of times.
a) Write down the usual sample space for n = 5, the probabilities P0 and PA, and the random
variable X =number of heads. In a table, give the Type I error rate α and the power β for
each decision rule of the form reject H0 if X > c. (How many values of c do you need to
consider?)
b) If you flip n = 10 times, is there a decision rule with α ≤ 0.1 and β ≥ 0.7? (You'd want that
decision rule to be of the form "reject H0 if #heads > c" why is that again?). If so, what
is it and what are α and β? If not, why not?
c) If you flip n = 100 times, is there a decision rule with α ≤ 0.05 and β ≥ 0.8? Explain.
d) How large should the number n of trials be so that there is decision rule with α ≤ 0.05 while
β ≥ 0.95? Give the decision rule and its α and β.

fabric (square meters)                   cloaks

7                                                           21

4/3                                                         4

step-by-step explanation:

we are told that harry needs 2 square meters of fabric for every 6 wizard cloaks he makes.

1. first of all we will find how many cloaks can be made from 1 square meter of fabric by dividing 6 by 2.

we can see that 3 cloaks can be made from 1 square meter of fabric. now we will multiply 3 by 7 to find number of cloaks made from 7 square meters of fabric.

therefore, harry will make 21 cloaks from 7 square meters of fabric.

2. let us find how many square meters of fabric will be needed to make 4 cloaks.

first of all we will find fabric needed for 1 cloak by dividing 2 by 6.

we can see that fabric needed for 1 cloak is   square meter. now we will multiply   by 4 to find fabric needed for 4 cloaks.

answer: 104.283185

step-by-step explanation:

3.14159265359 + 3.14159265359= 6.28318530718

since you're subtracting 3 twice, i'm just gonna say -6

6.28318530718 - 6 = 0.28318530718

0.28318530718 + 5 = 5.28318530718

5.28318530718 + 99 = 104.283185307