STA 6166 UNIT 2 Section 3 Exercises
Welcome < Begin <

Section 3

 < Unit 2 Section 3 Exercises > Unit 2 Test

Unit 2 Section 3 Exercises

You can choose to work some or all of the problems listed below. We recommend that you at least work the problems listed in your major area of interest. Answers to these questions are posted here (ANSWERS).

General Questions.
  1. What is the unbiased estimator for the population variance, s2?
  2. The Chi square distribution is the sampling distribution for the statistic . What can you say about the Chi Square distribution (what shape?, what parameters define its center/shape?)
  3. Suppose that Y has a Chi Square distribution with 27 df, using Table 7 (page 1100) find the following probabilities.
    1. Find P(Y>46.96)
    2. Find P(Y>18.81)
    3. Find P(Y<12.88)
    4. Find P(12.88<Y<46.96)
  4. A random sample of sample size n=21 was collected an the sample variance computed to be 3.29. Compute the 95% confidence interval for s2. [Hint use the equation on page 346 but make sure you get the upper and lower Chi Square values correct].
  5. When random samples of sizes n1 and n2 have been drawn independently from two normally distributed populations, the ratio has an F distribution. What can you say about the F distribution (what shape?, what parameters define its center/shape?)
  6. Using Table 8 (page 1102) find the value of F that has 0.05 (5%) area in the upper tail for the following degrees of freedom.
    1. df1=7, df2=12
    2. df1=3, df2=10
    3. df1=10, df2=20
    4. df1=8, df2=15
  7. Random samples of n1=6 and n2=11 observations were selected from populations 1 and 2 respectively. The corresponding sample variances were s12=7.5 and s22=13.2. Compute the 95% confidence interval for the ratio s22/s12? [Hint use the equation on page 359 but make sure you get the degrees of freedom right.]
For students in agriculture and environmental fields.

Do problem 7.41, page 377. Concentrate on doing the F-test for the difference in population variances. Given the results of this test, perform the associated two independent sample t-test for means? What do you conclude about the distributions of the two groups from these two tests?

Think of a situation in your studies or research where testing the equality of variances would provide useful information?
For students in engineering fields.

Do problem 7.30, page 375. Concentrate on doing the F-test for the difference in population variances. Given the results of this test, perform the associated two independent sample t-test for means? What do you conclude about the distributions of the two groups from these two tests?

Think of a situation in your studies or research where testing the equality of variances would provide useful information?
For students in toxicology and health science fields.

Carbon monoxide (CO) concentrations (in ppm) were measured at two locations in San Jose, CA over a two-month period. Summary data are presented below. Perform an F-test for the difference in population variances. Given the results of this test, perform the associated two independent sample t-test for means? What do you conclude about the distributions of the two groups from these two tests?

         Class    n     Sample_Mean   Sample_Std_Dev
           I       24             19.6                   8.1
           II      18             29.8                   6.6

Think of a situation in your studies or research where testing the equality of variances would provide useful information?

For students in community development, education and social services fields.

A study was designed to evaluate whether socioeconomic factors have an effect on verbalization skills of young children. Assume two socioeconomic classes have been defined and random samples of similar-aged children from each class have been tested. Summary statistics for a verbal skills test are presented below. Perform an F-test for the difference in population variances. Given the results of this test, perform the associated two independent sample t-test for means? What do you conclude about the distributions of the two groups from these two tests?

         Site    n     Sample_Mean   Sample_Std_Dev
         R1    54             3.4                   3.8
         R6    48             2.1                   2.1

Think of a situation in your studies or research where testing the equality of variances would provide useful information?