1. A survey from The Child Research Foundation found that 65% of all children under the age 10 have chronic sinus infections. If 7 Children under the age of 10 are selected at random, find the probability that:

exactly 3 will have chronic sinus infections.

at least 3 of them will have chronic sinus infections.

no more than 3 will have chronic sinus infections.

2. Using the same "p" from number one. Assume you have 500 children and you want to determine the following:

a. First, can you use a normal approximation to abinomial distribution for this problem now that the n=500? (answer yes or no) ____________ b. How can you tell? (show the computations you used to determine the answer to part a here)

If you can use the normal approximation to abinomial distribution you must do so for parts c and d.

c. Find the probability that at most 295 will have chronic sinus infections. d. Find the probability that at least 305 will have chronic sinus infections.

3. Explain in writing how you correct for continuity when you have the following wording and explain why:

a. At least 10 b. greater than 10

4. Construct the confidence interval for the following data making sure to list your calculator steps so I can tell which interval you used:

a. The sample mean is 32 and the population standard deviation is 2 with a sample size of 36.

b. The sample mean is 40 and the sample standard deviation is 1.5 with a sample size of 14. Assume the population is normally distributed.

5. Find the minimum sample size for the following: A soccer ball manufacturer wants to estimate the mean circumference of soccer balls to within 0.02 of an inch. Determine the minimum sample size required to have the 95% confident interval for the population parameter

. Assume the population standard deviation is 0.3 inches. 6. You are running a political campaign and wish to estimate, with 90% confidence the population proportion of voters who will vote for your candidate. Your estimate must be within 10% of the population proportion. Find the minimum sample size if:

a. no preliminary estimate for p is given. b. A preliminary estimate for p-hat is 72%. 7. Construct the 90% confidence interval for the following proportion: In a survey of 709 Michigan ducks, 286 have been tagged. 8. What is the default level for confidence intervals if none is given?

0.95

Reminder: Perform all the steps of hypothesis testing that were presented in the demonstration videos.

Note: You are to do 2 of the three problems but no more. As a result you can do 9 and 10

9. An Oceanographer claims that the mean dive depth for the North Atlantic Cod is 205 meters. A random sample of 32 dive depths has a mean of 198.7 meters with a standard deviation of 35.6 meters. Is there enough evidence to support the claim? (note: noalpha was given so you need to use the default level of significance)

10. A medical researcher is conducting a study to test the effect of an anti-depression drug. The researcher claims that the percent of people who feel no difference is 32%. The researcher found that of the 5400 randomly selected subjects who 12. Suppose the mean of a data set is 50 and the population standard deviation is 6. You do arandom selection of 49 from this population. What is the probability that you would have a mean sample that is between 49.5 and 53?

Do either 13 or 14 but not both.

13. (comparing two means)

There are two math teachers at College who are at odds about pedagogy. One teacher (teacher A) claims that the traditional way of teaching math is better. Teacher A's students had a mean score of 85 with a standard deviation of 8. This teacher had 20 students take the placement test. Teacher B's students had a mean score of 83 with a standard deviation of 3. This teacher had 10 students take the test. Can you conclude that the traditional way is better? Assume that the populations are normal and that the variances are equal.

14. (comparing two proportions)

A medical researcher is conducting a study to test the effect of an anti-depression drug. At the end of the study, the researcher found that of the 400 randomly selected subjects who took the drug 201 had no improvement at all. Of the 700 randomly selected subjects who took the placebo 307 had no improvement at all. At the level of significance of .05, can you support the claim that the proportion of subjects that have no improvement is the same for both groups?