Can you provide solutions for the below plz? Recently, the number of airline com

Question

Can you provide solutions for the below plz?

Recently, the number of airline companies that o er in-ight Wi-Fi service to

passengers has increased. However, it is estimated that only 10% of the passengers who have
Wi-Fi available to them are willing to pay for it. Suppose Gogo, the largest provider of airline
Wi-Fi service, would like to test this hypothesis by randomly sampling 125 passengers and
asking them if they would be willing to pay $4.95 for 90 minutes of onboard Internet access.
Suppose that 20 passengers indicated they would use this service. What is the signi cance
probability? Based on this sample, can we conclude that the proportion of airline passengers
willing to pay for onboard Wi-Fi service is di erent than 10%? Use = 5%. (Use Binomial
probability)

Explanation / Answer

Given that,
possibile chances (x)=20
sample size(n)=125
success rate ( p )= x/n = 0.16
success probability,( po )=0.1
failure probability,( qo) = 0.9
null, Ho:p=0.1  
alternate, H1: p!=0.1
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.16-0.1/(sqrt(0.09)/125)
zo =2.2361
| zo | =2.2361
critical value
the value of |z | at los 0.05% is 1.96
we got |zo| =2.236 & | z | =1.96
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 2.23607 ) = 0.02535
hence value of p0.05 > 0.0253,here we reject Ho
ANSWERS
---------------
test statistic: 2.2361
p-value: 0.02535

we have evidencce to conclude that the proportion of airline passengers willing to pay for onboard Wi-Fi service is dfferent than 10%

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