To calculate the t-statistic you'd need to define what H0 and H1 actually are (and check what s is). I'm going to assume that:
H0 is the null hypothesis, that the true mean of x is zero
H1 is the opposite, the hypothesis that the true mean for x is different to zero.
S = 466.4 is your standard deviation.
OK, then your t-statistic is: t = [ x ] / [ S / sqrt( n ) ]
t = [-32.8] / [466.4 / sqrt(900)]
= -32.8 / (466.4 / 30)
You then compare this to the critical t-stats for alpha = 0.05 and alpha = 0.01. You do this by finding the value of t for which the cumulative probability is alpha/2, using df = n-1 (899 in your example). For example, in excel we would use:
Since our calculated value of -2.11 exceed this magnitude, we would reject the null hypothesis at the alpha = 0.05 level (the sample mean -32.8 is further from the mean than we would expect through chance under the null hypothesis H0; chance alone would give <5% chance of seeing such a small sample mean).
And for alpha = 1%
At this more stringent level, our calculated value of -2.11 does not exceed the magnitude of the critical t. So we would NOT reject the null hypothesis at the alpha = 0.01 level (the sample mean -32.8 is not further from the mean than we would expect through chance under the null hypothesis H0; chance alone would give >1% chance of seeing such a small sample mean).
Mar 8th, 2015
Did you know? You can earn $20 for every friend you invite to Studypool!