Exam 15: Chi-Squared Tests Optional

A calculus professor posted the following grade distribution guidelines for her elementary calculus class: 8% A, 35% B, 40% C, 12% D, and 5% F. A sample of 100 elementary statistics grades at the end of last semester showed 12 As, 30 Bs, 35 Cs, 15 Ds, and 8 Fs. Test at the 5% significance level to determine whether the actual grades deviate significantly from the posted grade distribution guidelines.

Consider a multinomial experiment involving 160 trials 4 categories (cells). The observed frequencies resulting from the experiment are shown in the accompanying table. Categary 1 2 3 4 Frequency 53 35 30 42 Use the 10% significance level to test the hypotheses: H₀: p₁ = p₂ = p₃ = p₄ = 0.25 vs. H₁: At least two proportions differ from their specified values.

If we square the value of z (the test statistic in the test of a proportion) we produce the ____________________ statistic.

Suppose that a random sample of 60 observations was drawn from a population. After calculating the mean and standard deviation, each observation was standardized and the number of observations in each of the intervals below was counted. Can we infer at the 10% significance level that the data were drawn from a normal population? Intervals Frequency Z\leq-1 -11 5

A chi-squared test is used to describe a population of nominal data.

In a goodness-of-fit test, the null hypothesis states that the data came from a normally distributed population. The researcher estimated the population mean and population standard deviation from a sample of 200 observations. In addition, the researcher used 5 standardized intervals to test for normality. Using a 10% level of significance, the critical value for this test is 4.60517.

The alternative hypothesis in a chi-squared test of a contingency table is that the two nominal variables are ____________________.

The rule of five requires that the:

A(n) ____________________ experiment is like a binomial experiment except it contains two or more categories.

Before a chi-squared test of a contingency table can be carried out, the expected values of all cells should be greater than or equal to ____________________.

Which of the following is not a characteristic of a multinomial experiment?

In a goodness-of-fit test, the null hypothesis states that the data came from a normally distributed population. The researcher estimated the population mean and population standard deviation from a sample of 300 observations. In addition, the researcher used 6 standardized intervals to test for normality. Using a 2.5% level of significance, the critical value for this test is 14.4494.

The alternative hypothesis in a goodness-of-fit test is that none of the p_i values are equal to their values specified in H₀.

The sampling distribution of the test statistic for a goodness-of-fit test with k categories is a:

A multinomial experiment with two categories is identical to a binomial experiment.

When we test for differences between two populations of nominal data with two categories, we can use only one technique, namely, the chi-squared test of a contingency table.

If you want to compare two populations that each have more than two categories, you can use a chi-squared test of a(n) ____________________.

A chi-squared test of a contingency table with 6 degrees of freedom results in a test statistic of 13.25. Using the chi-squared table, the most accurate statement that can be made about the p-value for this test is that p-value is greater than 0.025 but smaller than 0.05.

Which of the following tests is used to analyze nominal data?

If the expected frequencies and the observed frequencies are quite different, you are likely to ____________________ the null hypothesis.