Suppose that your sample size is n=900 and you obtain the estimates x̄ = 32.8..
Statistics

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and S= 466.4 calculate the t statistic for testing H_{o Against }H_{1. Do you reject }H_{o at the 5% level? at 1% please help me!!}
Hi iceman,
To calculate the tstatistic 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 tstatistic is: t = [ x ] / [ S / sqrt( n ) ]
t = [32.8] / [466.4 / sqrt(900)]
= 32.8 / (466.4 / 30)
= 2.1098
You then compare this to the critical tstats 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 = n1 (899 in your example). For example, in excel we would use:
= T.INV(alpha/2,df)
= T.INV(0.025,899)
= 1.96
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%
= T.INV(alpha/2,df)
= T.INV(0.005,899)
= 2.58
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).
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