the true mean differs from 190 hours. Do not actually carry out the complete test, but do state the
null and alternative hypotheses.
A young researcher thinks there is a difference between the mean ages at which males and females
win Oscars for best actor or actress. The student found the mean age for all best actor winners and all
best actress winners and constructed a 95% confidence interval for the mean difference between their
ages. Is this an appropriate use of a confidence interval? Why or why not?
Cumulative Review Problems
Use a normal approximation to the binomial to determine the probability of getting between 470 and
530 heads in 1000 flips of a fair coin.
- A survey of the number of televisions per household found the following probability distribution:
What is the mean number of television sets per household?
A bag of marbles contains four red marbles and five blue marbles. A marble is drawn, its color is
observed, and it is returned to the bag.
(a) What is the probability that the first red marble is drawn on trial 3?
(b) What is the average wait until a red marble is drawn?
- A study is conducted to determine which of two competing weight-loss programs is the most
effective. Random samples of 50 people from each program are evaluated for losing and maintaining
weight loss over a 1-year period. The average number of pounds lost per person over the year is used
as a basis for comparison.
(a) Why is this an observational study and not an experiment?
(b) Describe an experiment that could be used to compare the two programs. Assume that you have
available 100 overweight volunteers who are not presently in any program. - The correlation between the first and second statistics tests in a class is 0.78.
(a) Interpret this value.
(b) What proportion of the variation in the scores on the second test can be explained by the scores
on the first test?