Assignment 11

Due in class on Monday, April 10.

This assignment is review of the material in Chapter 6.

Graded Problems

1.

Problem 6.55

2.

Problem 6.54

3.

Consider the same situation as in problem 6.55 and answer the following questions.

(a)

Consider the test that addresses whether or not coaching increases mean tests scores to more than 475. Consider a situation where n=100 people are coached and their mean score recorded. Calculate the values of the z-score test statistic such that the test concludes that coaching does increase the mean score of the population for a test of level 5%.

(b)

Re-express the region above in terms of $\bar{x}$. That is, for what values of $\bar{x}$ does the test conclude that the mean score of the population is increased?

(c)

Suppose the mean of the population is $\mu=480$, that is coaching increases the scores, on average, by 5 points. What is the probability of rejecting the null hypotheses for a test of level 5%?

(d)

Suppose the mean of the population is $\mu=490$, and coaching increases the scores, on average, by 15 points. What is the probability of rejecting the null hypotheses for a test of level 5%?

(e)

Suppose the mean of the population is $\mu=500$, and coaching increases the scores, on average, by 25 points. What is the probability of rejecting the null hypotheses for a test of level 5%?

(f)

Draw a rough sketch of the probability of rejecting the null hypothesis against the value of the population mean $\mu$, for $\mu$ between 475 and 500. Note that for $\mu=475$ the probability of rejecting the null hypothesis is 0.05 for a test of level 5%.

4.

Repeat the problem above for a sample of size n=1000. Note that you have drawn what is often called a ``power curve'', which is useful in choosing a sample size when you design a survey or experiment.

5.

Consider the same situation of problem 6.55. Suppose coaching actually increases the mean test score by 20 points, from 475 to 495. If you take a random sample of n=25 people who have received coaching what is the probability of concluding that coaching does increase test scores using a test of level 5%?

Additional Ungraded Problems

1.

Problem 6.56

2.

Problem 6.59

3.

Problem 6.79