Question 980611
alpha = 0.05
xbar = 42.5
s = 5.9
n = 15
df = n-1 = 15 - 1 = 14
We will use the T distribution because n > 30 is not true and we don't know sigma.


Hypothesis:
H0: mu = 32.6
H1: mu =/= 32.6


Claim is in the null hypothesis H0. This is a two tailed test. The null will be rejected if the test statistic is not between the critical values.


Test Statistic:
t = (xbar - mu)/(s/sqrt(n))
t = (42.5 - 32.6)/(5.9/sqrt(15))
t = 6.49873476736499
t = 6.4987


Critical Values (alpha = 0.05, df = 14)

Use a table like <a href="http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf">this one</a> to find the critical values to be -2.145 and 2.145


The test statistic 6.4987 is NOT between the critical values -2.145 and 2.145. So we reject the null hypothesis. There is enough statistically significant evidence to reject the null.


This means that the population mean mu is NOT 32.6. The initial claim is false.