Question

Suppose you are trying to assess whether or not the GPAs of 52 students in an honors seminar course are greater than 3.5. The 52 seminar students have a mean GPA of 3.55, with a standard deviation of 0.2. Which of the following corresponds to the p-value for this test?

a) p 0.0211
b) p 0.0053
c) p 0.9947
d) p 0.964
e) p 0.0357
f) p 0.053
g) p 1.803

Answer 1

`t=(3.55-3.5)/((0.2)/(√(52)))=1.80`

The degrees of freedom are given by:

`df=n-1=52-1=51`

The p value for this case can be calculated on this way:

`p_v =P(t_((51))>1.80)=0.036`

And the most appropiate value for this case would be :

e) p= 0.0357

Explanation:

Information given

`\bar X=3.55` represent the sample mean for the GPA

`s=0.2` represent the sample standard deviation

`n=52` sample size

`\mu_o =3.5` represent the value that we want to test

t would represent the statistic

`p_v` 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:
`\mu \leq 3.5`

Alternative hypothesis:
`\mu > 3.5`

The statistic is given by:

`t=(\bar X-\mu_o)/((s)/(√(n)))` (1)

Replacing the info given we got:

`t=(3.55-3.5)/((0.2)/(√(52)))=1.80`

The degrees of freedom are given by:

`df=n-1=52-1=51`

The p value for this case can be calculated on this way:

`p_v =P(t_((51))>1.80)=0.036`

And the most appropiate value for this case would be :

e) p= 0.0357