1. The U.S. Department of Agriculture reports that the mean cost of raising a child from birth to age 2 in a rural area is $8390. You believe this value is incorrect, so you select a random sample of 900 children (age 2) and find that the mean cost is $8275. Assume the standard deviation for the cost of raising a child from birth to age 2 is $1540. Test your claim at the .05 level of significance.

2. Three experiments investigating the relation between need for cognitive closure and persuasion were reported in "Motivated Resistance and Openness to Persuasion in the Presence or Absence of Prior Information". Part of the study involved administering a "need for closure scale" to a group of students enrolled in an introductory psychology course. The "need for closure scale" has scores ranging from 101 to 201. For the 73 students in the highest quartile of the distribution, the mean score was 178.70. Assume the population standard deviation is 7.81. These students were all classified as high on their need for closure. Assume that the 73 students represent a random sample of all students who are classified as high on their need for closure. Find a 95% confidence interval for the mean score on the "need for closure scale" for all students with a high need for closure.

How large of a sample is needed if we wish to be 99% confident that the sample mean score is within 2 points of the population mean score for students who are high on the need for closure?

3. Jeffrey, as an eight-year old, established a mean time of 16.43 seconds for swimming the 25-yard freestyle, with a standard deviation of 0.8 seconds. His dad, Frank, thought that Jeffrey could swim the 25-yard freestyle faster using goggles. Frank bought Jeffrey a new pair of expensive goggles and timed Jeffrey for 15 25-yard freestyle swims. For the 15 swims, Jeffrey's mean time was 16 seconds. Frank thought that the goggles helped Jeffrey to swim faster than the 16.43 seconds. Conduct a hypothesis test using a preset = 0.05. Assume that the swim times for the 25-yard freestyle are normal.

4. A company that makes cola drinks states that the mean caffeine content per one 12-ounce bottle of cola is 40 milligrams. Suppose you work as a quality control manager and are asked to verify this claim. During your tests, you find that a random sample of thirty 12-ouce bottles of cola has a mean caffeine content of 39.2 milligrams and a standard deviation of 1.59. Assume caffeine content is normally distributed. Can you reject the claim at the .01 level of significance?

5. Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car.When designing a study to determine this population proportion, what is the minimum number you would need to survey to be 95% confident that the population proportion is estimated to within 0.03?

If it were later determined that it was important to be more than 95% confident and a new survey was commissioned, how would that affect the minimum number you would need to survey? Why?

6. Allie does a study of hypnotherapy to determine how effective it is in increasing the number of hours of sleep subjects get each night. You measure hours of sleep for 12 subjects with the following results. Construct a 95% confidence interval for the mean number of hours slept for the population (assumed normal) from which you took the data.

8.2; 9.1; 7.7; 8.6; 6.9; 11.2; 10.1; 9.9; 8.9; 9.2; 7.5; 10.5