Steps for hypothesis test

For the first part we want to prove the claim that mean life of time of battery exceeds 400 hours, so Ho would be that the mean is 400 and Ha is that the mean is greater than 400
step 1: Ho: Mu = 400
Ha: Mu > 400
for the second step, recall that since sample size is small and standard deviation is not known, have to use the t-distribution, so test statistic is t
t = (sample mean - population mean)/(sample standard deviation/square root (n))
x-bar = 473.46
s = 210.77 as done on the calculator
n = 13
t = (473.46 - 400)/(210.77/square root(13))
t = 1.26
For the next step,we know using the p-value approach that we reject if p-value is less than alpha level of the test. So we reject Ho if p-value < .025
For the next step, I obtained the p-value from this site..
http://www.socscistatistics.com/pvalues/tdistribution.aspx
Putting in the values for t-statistic and one-tailed test, p-value is .11581
Last step, since .115811 > .025, we do not reject Ho since there is not significant evidence to conclude mean battery life is more than 400 hours.