### Dr. Wilson

1. A group of teachers has developed a new reading program designed to help second graders learn to read. In order to test the effectiveness of their program, they check the scores on their students achievement tests and compare them to the nationwide average. The 20 students in their class had a mean score of 179. The achievement test has been used for quite a long time, and it has been established that the population mean for the test is 145 with a population standard deviation of 50.

• a) State the null hypothesis and the alternative hypothesis.
• b) Find the z-score
• c) Find the p-value
• d) Do the scores for the sample of 20 students provide enough evidence to conclude that the test is effective at a .01 level of significance?
• e) Professional educators consider that if a reading program would produce a difference of 30 points in mean scores for this test, it would represent a significant improvement in teaching reading. What is the power of this test to detect such an improvement at a .01 level of significance?

2. At a fast food restaurant where customers who dine inside have unlimited access to refilling their drinks, the management wants to determine how many times such a customer who buys a small drink will fill it up. They perform a survey by observing their customers for a day and find that 87 customers who bought small drinks poured themselves 143 drinks. They also determined that the standard deviation for this sample was .37 drinks. Find a 95% confidence interval for the mean number of drinks that a customer who orders a small drink will pour. Can you think of anything which could introduce bias into this test?

3. Two teachers are up for a promotion, but their district will only give it to one of them if there is a significant difference in their teaching effectiveness. They decide to determine if one of them is a better teacher by having them give their students a common final. The results are summarized in the following table.

 number of students mean score standard deviation Teacher A 27 79 5.2 Teacher B 35 84 6.3

Is their a significant difference between the two teachers?

• a) State the null hypothesis and the alternative hypothesis
• b) Is there a significant difference at the .05 level of significance?

4. A candidate is running for election. Her supporters conduct a poll, which they hope incorporate the same biases as will be found in the sample of voters who actually vote on election day, to determine if she is likely to win. Out of 200 voters contacted, 105 indicate that they will vote for her, and the other 95 indicate that they will vote for her opponent.

• a) Find a 95% confidence interval for the proportion of the population who intend to vote for her.
• b) What is the probability that she will win, based on this sample?
• c)How many voters should be included in the sample so that the margin of error is within 3%?

5. In problem 4, the candidate wants to get a better estimate of her chances, so she commissions another poll, and this time she asks 1000 potential voters, and 510 indicate that they will vote for her. Does this represent a significant drop in support from the previous poll?