A researcher conducted a two-tailed paired sample t-test with an alpha level of .05 to compare pre and post scores. The t-test resulted in a t value of -2.042 with 10 degrees of freedom and a standard deviation of 8.85 based on a sample of 11 participants. The p value obtained was .068. This p value is not considered statistically significant based on the .05 alpha level criteria for the study.

1. Is a p value of .068 significant based on a .05 alpha level for a pre and post 2 tailed paired
sample t-test?
df 10
t=-2.042
SD 8.85
N=11
Thanks
Solution
Most t-test statistics have the form , where Z and s are functions of the data.
Typically, Z is designed to be sensitive to the alternative hypothesis (i.e. its magnitude tends to
be larger when the alternative hypothesis is true), whereas s is a scaling parameter that allows the
distribution of T to be determined. As an example, in the one-sample t-test , where is the sample
mean of the data, n is the sample size, and s is the population standard deviation of the data; s in
the one-sample t-test is , where is the sample standard deviation. The assumptions underlying a t-
test are that Z follows a standard normal distribution under the null hypothesis ps2 follows a ?2
distribution with p degrees of freedom under the null hypothesis, where p is a positive constant Z
and s are independent.