Chapter 26 Exercises

1. A gambler goes to the local casino and observes the action at the craps table for 100 throws of the dice. He notices that 21 of the throws come up 7. State the null and alternative hypotheses, and find the P-value of his observations. Is this a statistically significant result?

2. A gambler goes to the local casino and observes the action at the craps table for 400 throws of the dice. He finds that 80 of the throws come up 7. State the null and alternative hypotheses, and find the P-value of his observations. Is this a statistically significant result?

3. Suppose you want to determine if a coin is biased to land tails more often than heads. You flip the coin 25 times and find that you got 10 heads. State the null and alternative hypotheses, and find the P-value of your observations. Is this a statistically significant result? 4. Suppose you want to determine if a coin is biased to land tails more often than heads. You flip the coin 125 times and find that you got 53 heads. State the null and alternative hypotheses, and find the P-value of your observations. Is this a statistically significant result?

5. A teacher is trying to calibrate his 50g mass by placing it on a balance. However, before starting his measurements, he accidentally knocks the mass off the table. Concerned that he has chipped it, he measures the mass 25 times, finding an average of 10mg below 50g and an SD of 23mg. Find the P-value for the observation. Assuming that the original weight was exactly 50g, can the teacher conclude that he did in fact chip the mass and reduce its weight? 6. In many cities, chlorine is added to drinking water to remove microbes. A typical recommended concentration is 3ppm (parts per million). A reservoir technician wants to determine if the chlorine concentration is low enough to warrant adding more to the water. She takes 50 samples from the reservoir outlet and measures the concentration. She finds that the average concentration is 2.6ppm with an SD of 0.9ppm. State the null hypothesis and the alternate hypothesis, and find the P-value for the observation. Should the technician restock the reservoir?

7. In the early 1930’s, a psychologist named Karl Zener developed a method of testing for ESP. He took a deck of 25 cards containing 5 symbols (○, +, ≈, □,) and five cards each with a given symbol. He then drew the cards one at a time and asked the tester what was on the cards. He then recorded whether the tester was right or wrong for each card. a) How many cards could a tester expect to get right if they were randomly guessing? How far off are they likely to be?

b) Suppose that a tester gets 9 cards right. Find the P-value for this result. Is it significant?

c) Does a significant result show that the tester has ESP or simply that chance variation was an unlikely factor? 8. A card player wants to determine if she is shuffling her cards sufficiently well. She tests this by dealing the top card off the deck 100 times and counting the number of spades, shuffling the card back in after each deal. She gets a total of 19 spades. Find the P-value for this observation. Is the card player shuffling adequately? (Note: she could get significantly more or fewer spades than she should.)