Independence Statistics

Which test would you use to see if gender is a factor choosing a person’s favorite fruit?  900 college students were surveyed and their favorite fruit recorded.

• Chi-square Goodness of Fit Test

• Chi-Square Test for Homogeneity

• Chi-Square Test for Independence/Association

• Not a Chi-square test

What is the expected count of a female who likes Pepsi?

• 10.5

• 11

• 14.5

• 6.3

Does the data give evidence of an association between gender and soft drink choice?

• Yes, we reject the null hypothesis.

• No, we fail to reject the null hypothesis

• No, we reject the null hypothesis.

• Yes, we fail to reject the null hypothesis.

• Cannot be determined because the large counts condition is not met.

The degrees of freedom for the chi-square test for this two-way table are

• 4

• 8

• 10

• 20

• 4876

The appropriate null hypothesis for performing a chi-square test is that

• equal proportions of female and male teenagers are almost certain they will be married in 10 years.

• there is no difference between the distributions of female and male teenagers' opinions about marriage in this sample.

• there is no difference between the distributions of female and male teenagers' opinions about marriage in the population.

• there is no association between gender and opinion about marriage in the sample.

• there is no association between gender and opinion about marriage in the population.

Recent revenue shortfalls in a midwestern state led to a reduction in the state budget for higher education.  To offset the reduction, the largest state university proposed a 25% tuition increase.  It was determined that such an increase was needed simply to compensate for the lost support from the state.  Separate random samples of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels.  The results are in the table provided.  Why hypotheses would be appropriate for performing a chi-square test?

• The null hypothesis is that the closer students get to graduation, the less likely they are to be opposed to tuition increases.  The alternative is that how close students are to graduation makes no difference in their opinion.

• The null hypothesis is that the mean number of students who are strongly are opposed is the same for each of the 4 years.  The alternative is that the mean is different for at least 2 of the 4 years.

• The null hypothesis is that the distribution of student opinion about the proposed tuition increase is the same for each of the 4 years at the university.  The alternative is that the distribution is different for at least 2 of the 4 years.

• The null hypothesis is that year in school and student opinion about the tuition increase in the sample are independent.  The alternative is that these variables are dependent.

A random sample of traffic tickets given to motorists in a large city is examined.  The tickets are classified according to the race of the driver.  The results are summarized in the table provided.  Assuming H₀ is true, the expected number of Hispanic drivers who would receive a ticket is

• 10.36

• 11

• 11.84

• 12

A random sample of traffic tickets given to motorists in a large city is examined.  The tickets are classified according to the race of the driver.  The results are summarized in the table provided.  We compute the value of the χ² statistic to be 6.58.  Assuming that the conditions for inference are met, the P-value of our test is

• Between 0.10 and 0.20.

• Between 0.05 and 0.10.

• Between 0.01 and 0.05.

• Less than 0.01.

A random sample of traffic tickets given to motorists in a large city is examined.  The tickets are classified according to the race of the driver.  The results are summarized in the table provided.  The category that contributes the largest component to the χ² statistic is

• White.

• Black.

• Hispanic.

• Other.