6.
Which distribution has the larger mean?
i) t distribution, (df = 30)
ii) standard normal distribution
A)
i)
B)
ii)
C)
They are the same.
To determine which distribution has the larger mean, we need to compare the means of the t distribution and the standard normal distribution.
The mean of a standard normal distribution is always 0.
To find the mean of a t distribution with a specified degrees of freedom (df), we can use the following formula:
Mean = 0 (always for the standard normal) + (df / (df - 2)) if df > 2
In this case, we are given that the degrees of freedom for the t distribution is df = 30. Therefore, the mean of the t distribution is:
Mean = 0 + (30 / (30 - 2)) = 0 + (30 / 28) ≈ 1.071
Comparing the mean of the t distribution (approximately 1.071) with the mean of the standard normal distribution (0), we can conclude that:
The t distribution with df = 30 has a larger mean than the standard normal distribution.
Therefore, the correct answer is A) i)