In: Statistics and Probability
Suppose you have a sample of 36 observations with the sample mean = 2 and the sample standard deviation = 7. Compute the t-statistic corresponding to these values for the null hypothesis that mean = 0. Test two-sided alternative hypothesis that mean 6= 0. Do you reject the null hypothesis at p = 0:05? At p = 0:01? If the sample size is reduced to 25, do you get the same conclusions?
i)
Since P-value = 0.0953 > 0.01, so we fail to reject H0 at 1% level of significance.
ii)
Since P-value = 0.1660 > 0.01, so we fail to reject H0 at 1% level of significance.