Complete the following:

1. Given that = 36, use the t-score Table (Table IV, you can find a copy online or in the Blackboard course) to find

a)P(t 2.030) = _____________, that is the area under the density curve to the right of 2.030.

b)P(t 2.030) = _____________, that is the area under the density curve to the left of -2.030.

c)P(t 2.6) = _____________, that is the area under the density curve to the right of 2.6.

2. The following statement appeared on a box of Tide laundry detergent: "Individual packages of Tide may weigh slightly more or less than the marked weight due to normal variations incurred with high speed packaging machines, but each day's production of Tide will average slightly above the marked weight."

a) Explain in statistical terms what the statement means.

b) Suppose that the marked weight is 1 liter. State in words the null and alternative hypotheses for the hypothesis test.

c) State the Type I and Type II errors in the context of this application.

d) Propose procedures to collect data to test the statement.

3. For a fixed sample size, what happens to the probability of a Type II error if the significance level is decreased from 0.05 to 0.01?

4. For a one-sample test with = 40, find the P-values of the following hypothesis tests.

a) 0 : = 4 years versus : 4 years, with the observed test statistic = 1.5.

b) 0 : 4 years versus :

c)0 : 4 years versus : > 4 years, with the observed test statistic = 3.5.

5) The following table gives the age (in years) of 36 randomly selected U.S. millionaires. The sample mean = 58.53 years. Assume that the standard deviation of ages of all U.S. millionaires is 13.0 years. (See data on file: M08_Age_Millionaire_Q4.xlsx)

\f