Respuesta :
Answer:
[tex]t=\frac{3.55-3.5}{\frac{0.2}{\sqrt{52}}}=1.80[/tex]
The degrees of freedom are given by:
[tex]df=n-1=52-1=51[/tex]
The p value for this case can be calculated on this way:
[tex]p_v =P(t_{(51)}>1.80)=0.036[/tex]
And the most appropiate value for this case would be :
e) p= 0.0357
Step-by-step explanation:
Information given
[tex]\bar X=3.55[/tex] represent the sample mean for the GPA
[tex]s=0.2[/tex] represent the sample standard deviation
[tex]n=52[/tex] sample size
[tex]\mu_o =3.5[/tex] represent the value that we want to test
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We need want to verify if students in an honors seminar course are greater than 3.5, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 3.5[/tex]
Alternative hypothesis:[tex]\mu > 3.5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{3.55-3.5}{\frac{0.2}{\sqrt{52}}}=1.80[/tex]
The degrees of freedom are given by:
[tex]df=n-1=52-1=51[/tex]
The p value for this case can be calculated on this way:
[tex]p_v =P(t_{(51)}>1.80)=0.036[/tex]
And the most appropiate value for this case would be :
e) p= 0.0357
