Question

A phone company is testing a device that would allow visitors to museums, movie goers and other attractions to get information at the touch of a digital code. For example, moviegoers can listen to an announcement recorded on a microchip that provides them a preview of the movies they want to watch. It is anticipated that the device would rent for $3.00 each. The installation cost for the complete system is expected to be approximately $400,000, but movie theater owners are unsure as to whether or not to take the risk. A financial analysis of the issue indicates that if more than 10% of the movie patrons use the device the movie theater will make a profit. To help make the decision, a random sample of 400 moviegoers is given details of the system’s capabilities and cost. If 48 people say they would rent the device, can the management of the movie theater conclude at the 5% significance level that the investment would result in a profit? (The responses to the survey are: Yes, I would rent the device; and No, I would not rent the device)

The research question is: Is the product profitable? The parameter is p (the proportion of movie goers who would rent the device). Conduct a One Sample Test for Independent Proportions and accept or reject the hypothesis (show your work). Write the steps for hypotheses testing:

1. Hypotheses
2. Test statistic
3. Set up the decision rule/rejection region (i.e. reject Ho if z…..) (Draw the curve)
4. Compute test statistic.
5. Write the conclusion
6. P Value ( Show Work )

Answer 1

Given that,
possible chances (x)=48
sample size(n)=400
success rate ( p )= x/n = 0.12
success probability,( po )=0.1
failure probability,( qo) = 0.9
null, Ho:p=0.1
alternate, H1: p>0.1
level of significance, α = 0.05
from standard normal table,right tailed z α/2 =1.64
since our test is right-tailed
reject Ho, if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.12-0.1/(sqrt(0.09)/400)
zo =1.333
| zo | =1.333
critical value
the value of |z α| at los 0.05% is 1.64
we got |zo| =1.333 & | z α | =1.64
make decision
hence value of |zo | < | z α | and here we do not reject Ho
p-value: right tail - Ha : ( p > 1.33333 ) = 0.09121
hence value of p0.05 < 0.09121,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.1
alternate, H1: p>0.1
test statistic: 1.333
critical value: 1.64
decision: do not reject Ho
p-value: 0.09121
we have enough evidence to support the claim that more than 10% of the movie patrons use the device the movie theater will make a profit