Answer:
The value of the test statistic and the number of degrees of freedom is 2.148 and 11 respectively.
Step-by-step explanation:
The mean annual tuition and fees for a sample of 12 private colleges was $36,800 with a standard deviation of $5000
[tex]x= 36800\\s = 5000[/tex]
n = 12
Claim: You wish to test whether the mean tuition and fees for private colleges is different from $33,700
[tex]H_0:\mu = 33700\\H_a:\mu \neq 33700[/tex]
Since n < 30 and sample standard deviation is given so, we will use t test
Formula : [tex]t = \frac{x-\mu}{\frac{s}{\sqrt{n}}}[/tex]
Substitute the values in the formula :
[tex]t = \frac{36800-33700}{\frac{5000}{\sqrt{12}}}[/tex]
[tex]t = 2.148[/tex]
Degree of freedom = n-1 = 12-1 =11
So,. Option D is true
Hence the value of the test statistic and the number of degrees of freedom is 2.148 and 11 respectively.
