Answer to Question #257757 in Statistics and Probability for Sunil

Question

Let p be the probability that a coin will fall head in a single toss in order to test Ho : p = 1/2 against H_1:p=3/4. The coin is tossed 5 time and Ho is rejected if more than 3 heads obtained. Find the level of significance

Select one:  a. 3/16  b. 3/64  c. 3/32  d. 1/2 

Answer 1

$H_0: p=0.5 \\ H_1: p = 0.75$

Critical region: W = {X>3}

where X is the number of heads in 5 tosses

X ~ Bin(n=5,p)

α =P[Reject H₀ | H₀ is true]

= P[X $\in$ W | p=0.5]

= P[X>3| p =0.5]

= P[X=4|p=0.5] +P[X=5| p=0.5]

$= \binom{5}{4}(0.5)^5 + \binom{5}{5}(0.5)^5 = 0.1875 = 3/16$

Answer: a. 3/16