testing a hypothesis in statistics with p-value, two tails. HELP please & Thank you!?

Question

I always help you guys with math, now I need a little love!  I only know basic statistics and need help with a more qualitative analysis.  Here's the data and questions.

Sample mean of student GPAs = 2.73
Sample std dev = .495
Sample n = 25

Test the hypothesis Ho: Mu = 2.5 versus Ha: Mu ≠ 2.5.  Calculate the P-value.  (Include a sketch with the axis labeled and showing the sample mean).  Use a significance level, alpha=0.05, and state your conclusion carefully in terms of GPAs.  

Please help with some steps.  I will understand it if you help me through the various steps of the analysis.  Thanks so much!

M · Accepted Answer

ANSWER:  Conclusion: H1: μ ≠ μ0 is true with 97.1% confidence										


SINGLE SAMPLE TEST, TWO-TAILED, 6 - Step Procedure for t Distributions, "two-tailed test"										


Step 1: State the hypothesis to be tested.										
H0: μ = μ0										 
H1: μ ≠ μ0										
										
										
Step 2: Determine a planning value for α [level of significance]							0.05			
										
Step 3: From the sample data determine x-bar, s  and n; then compute										
Standardized Test Statistic: t = ( x-bar - μ0 )/( s/ SQRT(n) ) 										
										
x-bar = estimate of the Population Mean (statistical mean of the sample)							2.73			
n = number of individuals in the sample							25			
s = sample standard deviation 							0.495			
μ0 = Population Mean							2.5			
significant digits							3			
										
Standardized Test Statistic t = ( 2.73 - 2.5 )/( 0.495 / SQRT( 25 )) = 							2.323			


Step 4: Using Students t distribution, "lookup" the area to the left of t							=TDIST( 2.323 , 24 , 2 )			
(if lower-tail test) or to the right of t (if upper-tail test) using Excel										
TDIST(x, n-1 degrees_freedom, 2 tails)										

Step 5: Area  in Step 4 is equal to P value							0.029			
 based on n -1 = 24  df (degrees of freedom).										

Table look-up value shows area under the 24 df curve outside of t = +/- 2.323 is (approx.) 									 	
probability = 0.029									 	

Step 6: For P ≥ α, fail to reject H0; and for P < α, reject H0 with										
0.95% confidence in		H1								
									 	 
Conclusion: H1: μ ≠ μ0 is true with 97.1% confidence									 	 

Note: level of significance [α] is the maximum level of risk an experimenter is willing										
to take in making a "reject H0" or "conclude H1" conclusion (i.e. it is the maximum										
risk in making a Type I error).

testing a hypothesis in statistics with p-value, two tails. HELP please & Thank you!?

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