Discuss the following:
1. A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. Assuming a standard deviation of 6 hours, what is the required sample size if the error is to be less than ½ hour with a 95% level of confidence?
2. A survey of an urban university (population of 25,450) showed that 750 of 1100 students sampled attended a home football game during the season. What inferences can be made about student attendance at football games? Using the 99% level of confidence, what is the confidence interval?
3. There are 15 rolls of film in a box and 3 are defective. Two rolls are to be selected, one after the other. What is the probability of selecting a defective roll followed by another defective roll?
4. A tire manufacturer advertises that "the average life of our new all-season radial tire is 50,000 miles. An immediate adjustment will be made on any tire that does not last 50,000 miles." You purchased four of these tires. What is the probability that all four tires will last more than 50,000 miles?
5. Dr. Barton has been teaching basic statistics for many years. He knows that 80 percent of the students will complete the assigned problems. He has also determined that among those who do complete the assignments, 90 percent will pass the course. Among those students who do not complete their assignments, 50 percent will pass. Mike Fishman took statistics last semester from Dr. Barton and received a passing grade. What is the probability he completed the assignments?
6. A particular hair treatment program has caused hair growth in 70% of its users. A random sample of 20 users is obtained. Using the Binomial Probability Distribution, determine the following probabilities:
a) That exactly 15 experienced hair growth. .179
b) That less than 9 experienced hair growth. .005
c) That more than 12 experience hair growth. .77
d) That 15 or more experience hair growth. .42