<< Chapter < Page Chapter >> Page >

Suppose that 600 thirty–year–olds were surveyed to determine whether or not there is a relationship between the level of education an individual has and salary. Conduct a test for independence.

Annual Salary Not a high school graduate High school graduate College graduate Masters or doctorate
<$30,000 15 25 10 5
$30,000 - $40,000 20 40 70 30
$40,000 - $50,000 10 20 40 55
$50,000 - $60,000 5 10 20 60
$60,000 + 0 5 10 150

A Psychologist is interested in testing whether there is a relationship between personality types and majors majors. The results of the study are shown below. Conduct a Test of Independnce. Test at a 5% level of significance.

Open Conscientious Extrovert Agreeable Neurotic
Business 41 52 46 61 58
Social Science 72 75 63 80 65

  • 4
  • Chi-Square with df = 4
  • 3.01
  • p-value = 0.5568

  • ii. Do not reject the null hypothesis.
    iv. There is insufficient evidence to conclude that the personality types are dependent majors.

Do men and women select different breakfasts? The breakfast ordered by randomly selected men and women at a popular breakfast place is shown below. Conduct a test of independance. Test at a 5% level of significance

French Toast Pancakes Waffles Omelettes
Men 47 35 28 53
Women 65 59 55 60

  • 3
  • 4.01
  • p-value = 0.2601

  • ii. Do not reject the null hypothesis.
    iv. There is insufficient evidence to conclude that the distribution of breakfast ordered is dependent on gender.

Is there a relationship between the distribution of community college statistics students and the distribution of university statistics students in what technology they use on their homework? Of the randomly selected community college students 43 used a computer, 102 used a calculator with built in statistics functions, and 65 used a table from the textbook. Of the randomly selected university students 28 used a computer, 33 used a calculator with built in statistics functions, and 40 used a table from the textbook. Conduct an appropriate hypothesis test using a 0.05 level of significance.

  • 2
  • 7.05
  • p-value = 0.0294

  • ii. Reject the null hypothesis.
    iv. There is sufficient evidence to conclude that the distribution of technology use for statistics homework is not independent for statistics students at community colleges and at universities.

A fisherman is interested in whether the distribution of fish caught is independent of the fishing lake. Of the 191 randomly selected fish caught in Green Valley Lake, 105 were rainbow trout, 27 were other trout, 35 were bass, and 24 were catfish. Of the 293 randomly selected fish caught in Echo Lake, 115 were rainbow trout, 58 were other trout, 67 were bass, and 53 were catfish. Perform the hypothesis test at a 5% level of significance.

  • 3
  • Chi-Square with df = 3
  • 11.75
  • p-value = 0.0083

  • ii. Reject the null hypothesis.
    iv. There is sufficient evidence to conclude that the distribution of fish is dependent on the fishing lake. Green Valley Lake does not have the same distribution of fish as Echo Lake.

Try these true/false questions.

As the degrees of freedom increase, the graph of the chi-square distribution looks more and more symmetrical.

True

The standard deviation of the chi-square distribution is twice the mean.

False

The mean and the median of the chi-square distribution are the same if df = 24 size 12{ ital "df"="24"} {} .

False

In general, if the observed values and expected values of a Test for Independance are not close together, then the test statistic can get very large and on a graph will be way out in the right tail.

True

The degrees of freedom for a Test for Independence are equal to the sample size minus 1.

False

The Test for Independence uses tables of observed and expected data values.

True

The test to use when determining if the college or university a student chooses to attend is related to his/her socioeconomic status is a Test for Independence.

True

In a Test of Independence, the expected number is equal to the row total multiplied by the column total divided by the total surveyed.

True

In a Test for Independance, if the p-value is 0.0113, in general, do not reject the null hypothesis.

False

For a Chi-Square distribution with degrees of freedom of 17, the probability that a value is greater than 20 is 0.7258.

False

If df = 2 size 12{ ital "df"=2} {} , the chi-square distribution has a shape that reminds us of the exponential.

True

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Collaborative statistics using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Collaborative statistics using spreadsheets' conversation and receive update notifications?

Ask