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

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).