3. The TV shows \"Pretty Little Liars\" and \"Breaking Bad\" are listed among th

Question

3. The TV shows "Pretty Little Liars" and "Breaking Bad" are listed among the top 20 TV series during the years 2012-2013. A recent survey claimed that 45% of college students named "Pretty Little Liars" as their favorite of the two shows. Fans of "Breaking Bad" believed that percentage was inflated (that is, these fans believe that the proportion of college students who would say "Pretty Little Liars" was their favorite show is actually less that 45%). They decided to take a survey of 100 college students. Each student was asked the question: "Did you prefer Pretty Little Liars' over "Breaking Bad" during the years 2012-2013?" Each person could answer either Yes or No. The data is found in TV1.MTW a. State the appropriate null and alternative hypotheses. Perform the test of hypothesis. What is the test statistic? At = .05, what is your decision? Why? b. Write a short statement summarizing your results.

Explanation / Answer

3.

Given that,
possibile chances (x)=50
sample size(n)=100
success rate ( p )= x/n = 0.5
success probability,( po )=0.45
failure probability,( qo) = 0.55
null, Ho:p=0.45  
alternate, H1: p<0.45
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.64
since our test is left-tailed
reject Ho, if zo < -1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.5-0.45/(sqrt(0.2475)/100)
zo =1.005
| zo | =1.005
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =1.005 & | z | =1.64
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: left tail - Ha : ( p < 1.00504 ) = 0.84256
hence value of p0.05 < 0.84256,here we do not reject Ho
ANSWERS
---------------
a.
null, Ho:p=0.45
alternate, H1: p<0.45
b.
test statistic: 1.005
critical value: -1.64
decision: do not reject Ho
p-value: 0.84256
we do not have enough evidence to support the claim that would prefer pretty little liars over breaking bad

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