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An Introduction to Statistics

Homework for Statistics Lesson 9

Answer Completely.
 
Some calculations are required.
Due Thu., October 11, 2005, 8:00:00.000, EDT.
 
Due on the teacher's desk in SH100.
  1. Identify the four steps of hypothesis testing.

    1. State H0 and Ha
    2. Set alpha and beta
    3. Compute test statistic/confidence interval
    4. Form conclusion (state P-value)

  2. Describe Type I and Type II errors, giving alternate nameS as well.

     

     

     

  3. Give alternate names for one- and two-tailed tests.

    A one-sided hypothesis/test is directional.
    A two-sided hypothesis/test is non-directional.

  4. How are the level of significance and confidence interval related?

     

     

     

  5. How are the critical value(s) and the region of rejection related?

    The reg. of rej. is bounded by the critical values.

  6. Under what circumstances must you use the Student t distribution instead of the normal distribution?

     

     

     

  7. Describe several characteristics of the Student t distribution.

    1. Varies with sample size.
    2. Generally bell-shaped but thick tails at small n.
    3. Symmetric with mean of zero.
    4. Variance > 1, but approaches 1 as n increases.

  8. What are degrees of freedom?

     

     

     

  9. Find the 90th, 95th, and 99th percentile for the Student t distribution with 10 degrees of freedom.

    t(P90) = 1.372 for df=10.
    t(P95) = 1.812 for df=10.
    t(P99) = 2.764 for df=10.

  10. Suppose a large college dean wishes to check for a dramatic nondirectional change in GPA in recent years. The mean for the last five years has been established as 2.95 and the mean for a random sample of 225 recent graduates is 2.85 with a standard deviation of 0.55. Test H0: GPA=2.95 at the alpha=0.01 level. Be sure to show your steps and state your conclusions in a professional manner. How would this change if the sample size was only 25?

     

     

     

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