Respuesta :
Answer:
a) Null hypothesis:[tex]\mu \leq 50[/tex]
Alternative hypothesis:[tex]\mu > 50[/tex]
b) [tex]z=\frac{52-50}{\frac{15}{\sqrt{60}}}=1.033[/tex]
[tex]p_v =P(z>1.033)=0.1508[/tex]
Step-by-step explanation:
Information suministred
[tex]\bar X=52[/tex] represent the sample mean score for the econd graders
[tex]\sigma=15[/tex] represent the population standard deviation
[tex]n=60[/tex] sample size
[tex]\mu_o =50[/tex] represent the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value for the test (variable of interest)
Part a: System of hypothesis
We want to check if the second graders in her school district have greater math skills than the nationwide average, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 50[/tex]
Alternative hypothesis:[tex]\mu > 50[/tex]
Part b
The statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing into the formula we got:
[tex]z=\frac{52-50}{\frac{15}{\sqrt{60}}}=1.033[/tex]
We have a right tailed test then the p value would be:
[tex]p_v =P(z>1.033)=0.1508[/tex]
