Skip to main content
Statistics LibreTexts

11.11: Chapter Practice

  1. Last updated
  2. Save as PDF
  • Page ID
    6136

    • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    11.1 Facts About the Chi-Square Distribution

    1.

    This is a nonsymmetrical chi-square curve which slopes downward continually.
    Figure \(\PageIndex{10}\)

    11.2 Test of a Single Variance

    Use the following information to answer the next three exercises: An archer’s standard deviation for his hits is six (data is measured in distance from the center of the target). An observer claims the standard deviation is less.

    6.

    What type of test should be used?

    7.

    State the null and alternative hypotheses.

    8.

    Is this a right-tailed, left-tailed, or two-tailed test?

    Figure \(\PageIndex{11}\)

    Let \(\alpha = 0.05\)

    Decision: ________________

    Reason for the Decision: ________________

    Conclusion (write out in complete sentences): ________________

    29.

    Does it appear that the pattern of AIDS cases in Santa Clara County corresponds to the distribution of ethnic groups in this county? Why or why not?

    11.4 Test of Independence

    Determine the appropriate test to be used in the next three exercises.

    30.

    A pharmaceutical company is interested in the relationship between age and presentation of symptoms for a common viral infection. A random sample is taken of 500 people with the infection across different age groups.

    31.

    The owner of a baseball team is interested in the relationship between player salaries and team winning percentage. He takes a random sample of 100 players from different organizations.

    32.

    A marathon runner is interested in the relationship between the brand of shoes runners wear and their run times. She takes a random sample of 50 runners and records their run times as well as the brand of shoes they were wearing.

    Use the following information to answer the next seven exercises: Transit Railroads is interested in the relationship between travel distance and the ticket class purchased. A random sample of 200 passengers is taken. Table \(\PageIndex{25}\) shows the results. The railroad wants to know if a passenger’s choice in ticket class is independent of the distance they must travel.

    Traveling distance Third class Second class First class Total
    1–100 miles 21 14 6 41
    101–200 miles 18 16 8 42
    201–300 miles 16 17 15 48
    301–400 miles 12 14 21 47
    401–500 miles 6 6 10 22
    Total 73 67 60 200
    Table \(\PageIndex{25}\)

    33.

    State the hypotheses.
    \(H_0\): _______
    \(H_a\): _______

    34.

    \(df\) = _______

    35.

    How many passengers are expected to travel between 201 and 300 miles and purchase second-class tickets?

    36.

    How many passengers are expected to travel between 401 and 500 miles and purchase first-class tickets?

    37.

    What is the test statistic?

    38.

    What can you conclude at the 5% level of significance?

    Use the following information to answer the next eight exercises: An article in the New England Journal of Medicine, discussed a study on smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans and 7,650 whites. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 whites. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 whites. Of the people smoking at least 31 cigarettes per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 whites.

    39.

    Complete the table.

    Smoking level per day African American Native Hawaiian Latino Japanese Americans White Totals
    1-10            
    11-20            
    21-30            
    31+            
    Totals            
    Table \(\PageIndex{26}\) Smoking Levels by Ethnicity (Observed)

    40.

    State the hypotheses.
    \(H_0\): _______
    \(H_a\): _______

    41.

    Enter expected values in Table \(\PageIndex{26}\). Round to two decimal places.

    Calculate the following values:

    42.

    \(df\) = _______

    43.

    \(\chi^2\) test statistic = ______

    44.

    Is this a right-tailed, left-tailed, or two-tailed test? Explain why.

    45.

    Graph the situation. Label and scale the horizontal axis. Mark the mean and test statistic. Shade in the region corresponding to the confidence level.

    Blank graph with vertical and horizontal axes.
    Figure \(\PageIndex{12}\)

    State the decision and conclusion (in a complete sentence) for the following preconceived levels of \alpha.

    46.

    \(\alpha = 0.05\)

    1. Decision: ___________________
    2. Reason for the decision: ___________________
    3. Conclusion (write out in a complete sentence): ___________________

    47.

    \(\alpha = 0.01\)

    1. Decision: ___________________
    2. Reason for the decision: ___________________
    3. Conclusion (write out in a complete sentence): ___________________

    11.5 Test for Homogeneity

    48.

    A math teacher wants to see if two of her classes have the same distribution of test scores. What test should she use?

    49.

    What are the null and alternative hypotheses for Table \(\PageIndex{27}\).

    20–30 30–40 40–50 50–60
    Private practice 16 40 38 6
    Hospital 8 44 59 39
    Table \(\PageIndex{27}\)

    53.

    State the null and alternative hypotheses.

    54.

    \(df\) = _______

    55.

    What is the test statistic?

    56.

    What can you conclude at the 5% significance level?

    11.6 Comparison of the Chi-Square Tests

    57.

    Which test do you use to decide whether an observed distribution is the same as an expected distribution?

    58.

    What is the null hypothesis for the type of test from Exercise \(\PageIndex{57}\)?

    59.

    Which test would you use to decide whether two factors have a relationship?

    60.

    Which test would you use to decide if two populations have the same distribution?

    61.

    How are tests of independence similar to tests for homogeneity?

    62.

    How are tests of independence different from tests for homogeneity?

    This page titled 11.11: Chapter Practice is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.