Exam 17: Additional Tests for Nominal Data: Chi-Squared Tests

A chi-squared test for independence with 6 degrees of freedom results in a test statistic $\chi ^ { 2 } = 13.58$ . Using the $\chi ^ { 2 }$ tables, the most accurate statement that can be made about the p-value for this test is that: A. $p$ -value $>0.10$ . B. $p$ -value $>0.05$ . C. $0.05 < p \text {-value }<0.10$ D. $0.025 < p \text {-value }<0.05$

When doing a Chi-squared goodness of fit test, we use Ho: The data are not normally distributed.

A test for independence is applied to a contingency table with 4 rows and 4 columns for two nominal variables. The number of degrees of freedom for this test will be 9.

Which of the following tests do not use the Chi-squared distribution? A. Test of a contingency table. B. Goodness-of-fit test. C. Test for the difference between two population means. D. All of these choices are correct.

To determine the critical values in the chi-squared distribution table, the process requires which of the following information? A. Degrees of freedom. B. Probability of Type I error. C. Frobability of Type II error. D. Degrees of freedom and Frobability of Type I error.

A test for independence is applied to a contingency table with 5 rows and 2 columns for two nominal variables. The number of degrees of freedom for this chi-squared test must be 4.

The rule of five is used to ensure that the discrete distribution of the test statistic can be approximated by the continuous Chi-squared distribution.

The chi-squared test of independence is a Chi-squared test of a contingency table.

Consider a multinomial experiment involving 160 trials and 4 categories (cells). The observed frequencies resulting from the experiment are shown in the following table. Category 1 2 3 4 Frequency 53 35 30 42 Use the 10% significance level to test the hypotheses. $H _ { 0 } : p _ { 1 } = p _ { 2 } = p _ { 3 } = p _ { 4 }$ . $H _ { 1 } :$ At least two proportions differ from their specified values.

In 2003, computers of Brand A controlled 25% of the market, Brand B 20%, Brand C 10% and Brand D 45%. In 2004, sample data were collected from many randomly selected stores throughout the country. Of the 1200 computers sold, 280 were Brand A, 270 were Brand B, 90 were Brand C and 560 were Brand D. Has the market changed since 2003? Test at the 1% significance level.

A biology professor claimed that the proportions of grades in his classes are the same. A sample of 100 students showed the following frequencies. Grade A B C D F Frequency 14 23 27 26 10 Do the data provide enough evidence to support the professor's claim?

Which of the following uses a contingency table? A. Chi-squared test of independence of two numerical variables in a population. B. Chi-squared test of independence of two nominal variables in a sample. C. Chi-squared test of independence of two numerical variables in a sample. D. Chi-squared test of independence of two nominal variables in a population.

Which statistical technique is appropriate when we describe a single population of nominal data with exactly two categories? A Zz-test of a population proportion. B Chi-squared test of a multinomial experiment. C Chi-squared test of a contingency table. D Z-test of a population proportion and Chi-squared test of a multinomial experiment. E Chi-squared test of a multinomial experiment and Chi-squared test of a contingency table.

A left-tailed area in the chi-squared distribution equals 0.10. For 5 degrees of freedom, the table value equals 9.23635.

A telephone company prepared four versions of a set of instructions for placing collect calls. The company asked a sample of 1600 people which one of the four forms was easiest to understand. In the sample, 425 people preferred Form A, 385 preferred Form B, 375 preferred Form C, and 415 preferred Form D. At the 5% level of significance, can one conclude that in the population there is a preferred form?

The degrees of freedom in a chi-squared test for normality, where the number of standardised intervals is 13 and there are 2 population parameters to be estimated from the data, is equal to: A. 13. B. 10 C. 11 D. 2.

A left-tailed area in the chi-squared distribution equals 0.975. For df = 11, the table value equals: A. 20.4831. B. 19.6751. C. 3.81575. D. 21.9200.

At present in Australia, voting in a Federal election is compulsory for all citizens 18 years or over. There has been some discussion to have this changed from being compulsory to voluntary. A study was done to investigate whether there was a relationship between gender and attitude towards changing voting in Australia from compulsory to voluntary. Participants were asked "Do you agree to change voting in Australian Federal Elections from compulsory to voluntary? A table of results from the sample is given below. At the 1% level of significance, is there a relationship between gender and attitude towards voluntary voting? Agreed Disagreed Undecided Female 15 25 30 Male 25 20 25

Suppose that a random sample of 150 observations was drawn from a population. After calculating the mean and standard deviation, each observation was standardised and the number of observations in each of the intervals below was counted. Can we infer at the 5% significance level that the data were drawn from a normal population? Intervals Frequency Z\leq-1.5 15 -1.51.5 13

For a chi-squared distributed random variable with 12 degrees of freedom and a level of significance of 0.05, the chi-squared value from the table is 21.0261. The computed value of the test statistics is 25.1687. This will lead us to reject the null hypothesis.