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.

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