A sample of n = 25 scores has a mean of M = 40 and a variance of s2 = 100. If this sample is being used to test a null hypothesis stating that m = 43, then what is the t statistic for the sample
To find the t-statistic for the sample, you need to use the formula:
t = (M - m) / (s / √n),
where M is the sample mean, m is the value you are testing against (in this case, 43), s is the sample standard deviation (which is the square root of the variance), and n is the number of scores in the sample.
Given the information provided, we have:
M = 40 (sample mean)
s^2 = 100 (sample variance)
n = 25 (number of scores)
First, calculate the sample standard deviation (s) by taking the square root of the variance:
s = √s^2 = √100 = 10.
Now, substitute the given values into the t-statistic formula:
t = (40 - 43) / (10 / √25)
= -3 / (10 / 5)
= -3 / 2
= -1.5.
Therefore, the t-statistic for the sample is -1.5.