Some balls are placed in a large box; the balls include one ball marked "10", two balls marked "9", and so forth up to ten balls marked "1". A ball is drawn at random.

is an integer between 1 and 10 inclusive. True or false: the probability that the ball will have the number marked on it is greater than .

Statement 1: is a perfect square integer.

Statement 2:

Bronson has a box of 16 markers. The markers are green, red and yellow.

I) The number of green markers is twice the number of red markers

II) There are 4 yellow markers

What are the odds of pulling a yellow marker followed by a green marker followed by a red marker? (Assume no replacement.)

A certain major league baseball player gets on base 25% of the time (once every 4 times at bat).

For any game where he comes to bat 5 times, what is the probability that he will get on base either 3 or 4 times? - Hint – add the probability of 3 to the probability of 4.

A bag contains red, yellow and green marbles. There are marbles total.

I) There are green marbles.

II) The number of yellow marbles is half of one less than the number of green marbles.

What are the odds of picking a red followed by a green followed by a yellow? Assume no replacement.

In a standard deck of cards (4 suits, 13 cards of each suit) 3 cards have been removed. What are the odds of choosing one red card followed by 2 black cards? Assume replacement.

I) Two of the cards that were removed were black.

II) One of the removed cards was red.

Two dice are thrown; one is fair, one is loaded, but each has the usual numbers 1-6 on its faces. What is the probability of the outcome being a sum of 12?

Statement 1: The loaded die will come up 6 with probability .

Statement 2: The loaded die will come up 5 with probability .

Four cards are removed from a standard deck of fifty-two cards. Did the probability that a randomly drawn card will be a heart increase, decrease, or stay the same?

Statement 1: At least three of the cards are spades.

Statement 2: At least one of the cards is a club.

Assume that we are the immortal gods of statistics and we know the following population statistics:

1. average driving speed for women=50 mph with a standard deviation of 12

2. average driving speed for men=45 mph with a standard deviation of 11

We look down from our statistical Mount Olympus and notice that the Earth mortals have randomly sampled 60 women and 65 men in an attempt to detect a significant difference in the average driving speed.

What is the probability that the Earth mortals will properly reject the assumption (i.e. the null hypothesis) that there is no significant difference between the average driving speeds. The Earth mortals have decided to use a 2-tailed 95% confidence test.

Jerry is a Cardinal fan and he and his family live on a street with 9 other families that are all Cardinal fans. One block to the north, there are 11 families and they are all Cub fans. These 21 households all buy their lawn fertilizer from Ben's Lawn and Garden Shop. Jerry suspects that Ben (who is originally from Chicago) is a Cub fan and that he provides better fertilizer to the Cub fans than to the Cardinal fans, while charging the same price for all.

Last Saturday everyone in town mowed their lawn. At 2:00 AM Sunday morning, Jerry snuck around town and weighed all of the grass clippings for the 21 households in question.

The weights (in lbs) of the grass clippings for the 10 Cardinal homes were:

82, 85, 90, 74, 80, 89, 75, 81, 93, 75

The weights (in lbs) of the grass clippings for the 11 Cub homes were:

90, 87, 93, 75, 88, 96, 90, 82, 95, 97, 78

The Cardinal average was 82.4; the Cub average was 88.27.

At what level is the 5.87 lb difference significant? - Asked another way - what is the p value for the 5.87 lb difference.

A certain tutor boasts that his 2 week training program will increase a student's score on a 2400 point exam by at least 100 points (4.167%). A 10 student 'before-and-after' study was conducted to validate the claim. The following results were obtained - the 3 columns represent the before, afer and increase numbers for each of the 10 students:

1300 1340 40
1670 1790 120
1500 1710 210
1360 1660 300
1580 1730 150
1160 1320 160
1910 2100 190
1410 1490 80
1710 1880 170
1990 2060 70

Assume the null Hypothesis:

'The average increase is less than 100 points'

What is the highest level of significance (p-value) at which the null hypothesis will be rejected?