# 800:072 Take-home Quizzes

### R. B. Campbell

Quiz 1

Consider the data set: {5, 12, 8, 19, 13, 7, 4, 6, 14, 16, 11}

1) What is the mean?
2) What is the median?
3) What is the midrange?
4) What is the range?
5) What is the interquartile range?
6) What is the variance (s²)?
7) What is the standard deviation (s)?

Quiz 2

For the data represented in the following histogram:

```                                _______
|       |
|       |_______
_______|       |       |
|       |   7   |       |
|   4   |       |   5   |_______
_______|       |       |       |   2   |
__________|___1___|_______|_______|_______|_______|_________
|       |       |       |       |
100     125     150     175     200 ```

1) What is the greatest possible value of the mean?
2) What is the least possible value of the mean?
3) What is the "best" estimate for the mean?
4) What is the greatest possible value of the median?
5) What is the least possible value of the median?
6) What is the "best" estimate for the median?

Quiz 3

Consider an unfair die with the associated probabilities:

```             x    1    2   3   4   5   6

P(x)  .1  .2  .2  .1  .1  .3   ```

Let A = {1, 3, 5} and B = (2, 3, 5}

Show appropriate work.

1) P(A) =
2) P(A') =
3) P(A U B) =
4) P(AB) =
5) Are A and B independent? (why?)
6) Are A and B mutually exclusive (disjoint)? (why?)
7) Are A and B complementary? (why?)

Quiz 4

Consider the binomial experiment of flipping an unfair (p = 0.4) coin 7 times.
Show appropriate work.

1) What is the probability of no successes?
2) What is the probability of at least one success?
3) What is the probability of exactly three successes?
4) What is the expected number of successes (E[X])?
5) What is the variance of the number of successes V[X])?
6) What is the standard deviation of the number of successes?

Quiz 5

1) If one-third of the balls in a large (infinite) urn weigh one pound, one-third of the balls weigh three pounds, and one-third of the balls weigh five pounds; what is the probability that the total weight of 300 balls randomly drawn from the urn will be greater than 1200 pounds?
2) If one-third of the balls in a large (infinite) urn weigh one pound, one-third of the balls weigh three pounds, and one-third of the balls weigh five pounds; what is the probability that the total weight of 3 balls randomly drawn from the urn will be greater than 12 pounds?

Quiz 6

1) If x-bar = 150, *sigma* = 25, and n = 72, what is the 95% confidence interval for the mean?
2) If x-bar = 150, *sigma* = 25, and n = 144, what is the 95% confidence interval for the mean?
3) If *sigma* = 25, how large must n be to get a 95% confidence interval with radius (margin of error) less than or equal to 2?

Quiz 7

1) If x-bar = 14 based on a sample of size 25, at what significance level (10%?, 5%?, 1%?) would you reject the null hypothesis that µ=16 and *sigma*^2=36? (versus the alternative hypothesis µ *not equal* 16)
2) If x-bar = 14 based on a sample of size 25, at what significance level (10%?, 5%?, 1%?) would you reject the null hypothesis that µ *greater than or equal to* 16 and *sigma*^2=36? (versus the alternative hypothesis µ < 16)
3) If x-bar = 14 based on a sample of size 25, at what significance level (10%?, 5%?, 1%?) would you reject the null hypothesis that µ *less than or equal to* 16 and *sigma*^2=36? (versus the alternative hypothesis µ > 16)

Quiz 8

The weight of genuine coins is normally distributed with µ = 1 and *sigma* = 0.02, and the weight of counterfeit coins is normally distributed with µ = 0.90 and *sigma* = 0.05. Ninety percent of coins are genuine, and the other 10% are counterfeit.

1) What is the probability that a randomly chosen counterfeit coin weighs more than 0.95?
2) What is the probability that a randomly chosen genuine coin weighs more than 0.95?
3) What is the probability that a randomly chosen coin weighs more than 0.95 and is counterfeit?
4) What is the probability that a randomly chosen coin which weighs more than 0.95 is genuine?

Quiz 9

If you roll a die 50 times with the following results, at what significance level do you question that it is fair?
Results: 4 1's, 11 2's, 8 3's, 7 4's, 15 5's, 5 6's
In particular,

a) What is X²?
b) How many degrees of freedom are there?
c) At what level is this significant (10%?, 5%?, 1%?)

Quiz 10

Consider the data set {(1,6), (4,3), (4,4), (6,2), (3,5)}.

a) What is the mean of the x values?
b) What is the standard deviation of the x values?
c) What is the least squares regression line for y as a function of x?
d) What is the coefficient of determination?