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11.5 The chi-square distribution: practice 2

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This module provides a practice on Chi-Square Distribution as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean.

Student learning outcomes

  • The student will conduct a test for independence using contingency tables.

Conduct a hypothesis test to determine if smoking level and ethnicity are independent.

Collect the data

Copy the data provided in Probability Topics Practice 1: Contingency Tables into the table below.

Smoking levels by ethnicity (observed)
Smoking Level Per Day African American Native Hawaiian Latino Japanese Americans White TOTALS
1-10
11-20
21-30
31+
TOTALS

Hypothesis

State the hypotheses.

  • H o : size 12{H rSub { size 8{O} } :} {}
  • H a : size 12{H rSub { size 8{a} } :} {}

Expected values

Enter expected values in the above below. Round to two decimal places.

Analyze the data

Calculate the following values:

Degrees of freedom =

12

Chi 2 size 12{ ital "Chi" rSup { size 8{2} } } {} test statistic =

10301.8

p-value =

0

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

right

Graph the data

Graph the situation. Label and scale the horizontal axis. Mark the mean and test statistic. Shade in the region corresponding to the p-value.

Blank graph with vertical and horizontal axes.

Conclusions

State the decision and conclusion (in a complete sentence) for the following preconceived levels of α size 12{α} {} .

α = 0 . 05 size 12{α=0 "." "05"} {}

  • Decision:
  • Reason for the decision:
  • Conclusion (write out in a complete sentence):

  • Reject the null hypothesis

α = 0.01

  • Decision:
  • Reason for the decision:
  • Conclusion (write out in a complete sentence):

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Source:  OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
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