Quiz #4

Q: Suppose the z-score of xbar is 1.34. Calculate the p-value associated with this z-score.

A: The p-value is the area under the curve of the normal distribution above the given value. From the standard normal distribution table we find that from the mean to 1.34, the area is 0.4099. Since we know that the area under the curve above the mean is 0.5,
p-value of 1.34 = 0.5-0.4099 = 0.0901

Quiz #3

Question:
Calculate the margin of error for a 95% confidence interval where:
the sample size is 64
the sample mean is 350
the population standard deviation is 64

Answer:
The formula for margin of error = x-bar +/- (z-alpha/2)(stddev/sqrt(n))

We find z-alpha/2 for a 95% confidence interval = 1.96 from our class notes. Manually, you work it out as:
alpha = 1-0.95 = 0.05
alpha/2 = 0.05/2 = 0.025
Since the z-scored table gives us the area from 0 to z, we need to use the "complement" of 0.025 which is 0.5-0.025 = 0.475
Do a reverse lookup in a z-score table for 0.475 and we find that it corresponds to a z-score of 1.96.

So,
margin of error = 350 +/- 1.96(64/(sqrt(64)) = 350 +/- (1.96)(8)
= 350 +/- 15.68*

* technically, our textbook refers to this as a "95% confidence interval for the mean". Although our text doesn't use the term "margin of error" explicitly, it seems to me that the margin of error is just the 15.68 term. I've looked at some web sites that define the terms, but there's still some ambiguity - is the margin the range of values or just the half-width of the range? Perhaps that's why our text avoids the issue by not using the term.

Lecture 2 - Pop quiz #2

Prove: If A is independent of B, then B is independent of A. I.e. P(A|B) = P(A) implies P(B|A) = P(B).

Answer:

That's how I did it. If you have a different proof, I'd be interested in hearing it.

Lecture 1 - Quiz

Given:
Variance = 25
Coefficient of Variation = 10%

Compute the mean.

Answer:

We know the relationship between the coefficient of variation, standard deviation and the mean:
CV=(stddev/mean) * 100

We also know that the standard deviation is simply the square root of the variance:
Stddev = sqroot(variance)

Therefore, combining these two formulas and plugging in our givens, we get:
10 = (sqroot(25) / mean) * 100

10 = (5/mean) * 100

10 = 500 / mean

10 * mean = 500

mean = 50

The only thing tricky about this question is that you have to remember that the CV is stddev/mean, not variance/mean. If you remember that, along with the relationship between the stddev and variance, it's simple.