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 Ho  Against  H1. Do you reject Ho at the 5% level? at 1% please help me!!

Mar 8th, 2015

Hi iceman,

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)

-2.1098


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:

= 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).


Mar 8th, 2015

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