Worksheet for Recitation 13 STT 200, Lecture 5, Sec 23 and 24, 2013-4-9

Worksheet for recitation 13 STT 200, Lecture 5, Sec 23 and 24, 2013-4-9

Question #1:

Suppose we want to test whether a coin is fair. We toss it many times, count the proportion of heads, and find a P-value of 0.32. Which conclusion is appropriate?

a)There’s a 32% chance that the coin is fair.

b)There’s a 32% chance that the coin is not fair.

c)There’s a 32% chance that natural sampling variation could produce coin-tossing results like these if the coin is really fair.

d)There’s a 32% chance that natural sampling variation could produce coin-tossing results like these if the coin is not fair.

Question #2:

Many people have trouble setting up all the features of their cell phones, so a company has developed what it hopes will be easier instructions. The goal is to have at least 96% of customers succeed. The company test it on 200 people, and 188 were successful. Is this a strong evidence that their system fails to meet the goal? A student’s test of this hypothesis is shown. How many mistakes can you find?

To test: versus .

The sample is SRS, with 0.96(200)>10.

. , and the z-score with P-value .

There is strong evidence that the new instructions do not work.

Question #3:

Many people have trouble setting up all the features of their cell phones, so a company has developed what it hopes will be easier instructions. The goal is to have at least 86% of customers succeed. The company test it on 100 people, and 93 were successful. Is this a strong evidence that their system fails to meet the goal? Our second student’s test of this hypothesis is shown. How many mistakes can you find?

To test: versus .

The sample is SRS, with 0.86(100)>10 and 0.14(100)>10 .

. , and the z-score with P-value .

Since this is significant under ?=0.05, we reject and conclude there is strong evidence that the new instructions do not work.

Question #4:

A basketball player with a poor foul-shot record practices intensively during the off-season. He tells the coach that he has raised his proficiency from 60% to 80%. Dubious, the coach asks him to take 10 shots, and surprised when the player hits 9 out 10 shots. Did the player prove that he has improved?

a)Suppose the player really is no better than before, still 60% shooter. What’s the probability he can hit at least 9 of 10 shots anyway?

b)If that is what happened, now the coach thinks the player has improved when he has not. Which type of error is that?

c)If the player really can hit 80% now, and it takes at least 9 out of 10 successful shots to convince the coach, what’s the power of the test?

d)List two ways the coach and player could increase the power to detect any improvement.