Respuesta :
Answer:
[tex]z=\frac{0.939 -0.87}{\sqrt{\frac{0.87(1-0.87)}{115}}}=2.20[/tex]
Now we can claculate the p value since is a right tailed test would be:
[tex]p_v =P(z>2.20)=0.0139[/tex]
For this case since the p value is lower than the significance level provided [tex]\alpha=0.05[/tex] we have enough evidence to reject the null hypothesis and we can conclude that hotel chains customers are more satisfied with their service
Step-by-step explanation:
Information given
n=115 represent the random sample selected
X=108 represent the number of people who were satisfied with their service
[tex]\hat p=\frac{108}{115}=0.939[/tex] estimated proportion of people who were satisfied with their service
[tex]p_o=0.87[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to verify if hotel chains customers are more satisfied with their service.:
Null hypothesis:[tex]p\leq 0.87[/tex]
Alternative hypothesis:[tex]p> 0.87[/tex]
The statistic for this case is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.939 -0.87}{\sqrt{\frac{0.87(1-0.87)}{115}}}=2.20[/tex]
Now we can claculate the p value since is a right tailed test would be:
[tex]p_v =P(z>2.20)=0.0139[/tex]
For this case since the p value is lower than the significance level provided [tex]\alpha=0.05[/tex] we have enough evidence to reject the null hypothesis and we can conclude that hotel chains customers are more satisfied with their service
