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Quiz 13 : Chi-Square Tests

A multinomial probability distribution describes data that are classified into two or more categories when a multinomial experiment is carried out.
Free
True False

True
Explanation: They are similar to the one that defines a binomial experiment (where K = 2).

A fastener manufacturing company uses a chi-square goodness-of-fit test to determine if a population of all lengths of ¼-inch bolts it manufactures is distributed according to a normal distribution. If we reject the null hypothesis, it is reasonable to assume that the population distribution is approximately normally distributed.
Free
True False

False
Explanation: If the null hypothesis is rejected, then the population does not have a normal distribution.

The chi-square goodness-of-fit test can only be used to test whether a population has specified multinomial probabilities or to test if a sample has been selected from a normally distributed population. It cannot be used if sample data come from other distribution forms, such as the Poisson.
Free
True False

False
Explanation: The chi-square goodness-of-fit test can be used to test sample data from other distribution forms.

When we carry out a chi-square test of independence, the expected frequencies are based on the null hypothesis.
True False
The χ2 goodness-of-fit test requires the nominative level of data.
True False
One use of the chi-square goodness-of-fit test is to determine if specified multinomial probabilities in the null hypothesis are favored over the alternative hypothesis.
True False
In a contingency table, if all of the expected frequencies equal the observed frequencies, then we can conclude that there is a perfect association between rows and columns.
True False
The actual counts in the cells of a contingency table are referred to as the expected cell frequencies.
True False
When we carry out a chi-square test of independence, in the alternative hypothesis we state that the two classifications are statistically independent.
True False
When using a chi-square goodness-of-fit test with multinomial probabilities, the rejection of the null hypothesis indicates that at least one of the multinomial probabilities is not equal to the value stated in the null hypothesis.
True False
In a contingency table, when all the expected frequencies equal the observed frequencies, the calculated χ2 statistic equals zero.
True False
A contingency table summarizes data that has been classified into two dimensions or scales.
True False
The trials of a multinomial probability are assumed to be dependent.
True False
In performing a chi-square test of independence, as the difference between the respective observed and expected frequencies calculated by assuming independence decreases, the probability of concluding that the row variable is independent of the column variable decreases.
True False
In performing a chi-square goodness-of-fit test with multinomial probabilities, the smaller the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are favored over the alternative hypothesis.
True False
When using the chi-square goodness-of-fit test, if the value of the chi-square statistic is large enough, we reject the null hypothesis.
True False