Question

if a sample of 36 measurements has a variance of 25, what is the standard error?
6
5
25/36
5/6
question 5
if you run a t - test and you get p < 0.04, what does the value mean?
we can be completely confident the means are different
the two populations have different means
the probability that the two populations have the same mean is less than 4%
none of the above are true

Explanation:

Step1: Recall standard - error formula

$SE=\frac{\sigma}{\sqrt{n}}$, $\sigma^{2} = 25$ so $\sigma = 5$, $n = 36$.

Step2: Calculate standard error

$SE=\frac{5}{\sqrt{36}}=\frac{5}{6}$.

Step3: Interpret p - value

A p - value of less than 0.04 means probability of same means < 4%.

Answer:

1. D. 5/6
2. C. The probability that the two populations have the same mean is less than 4%