True or False
1. Chi square tests of independence and homogeneity are both usually right-tailed tests.
2. A chi square goodness-of-fit test is appropriate for determining whether a random number generator is truly random.
1. False. The chi-square tests of independence and homogeneity are both usually considered to be two-tailed tests, not right-tailed tests. In hypothesis testing, a right-tailed test is used when the alternative hypothesis suggests a greater-than relationship. However, for chi-square tests, the alternative hypothesis typically suggests a two-sided relationship, without specifying whether it is greater or smaller.
To conduct a chi-square test of independence, you would first gather categorical data from two groups and organize it into a contingency table. Then, you would calculate the expected frequencies under the assumption of independence between the two variables. Finally, you would use the chi-square test statistic to assess whether the observed frequencies significantly differ from the expected frequencies.
2. False. A chi-square goodness-of-fit test is not appropriate for determining whether a random number generator is truly random. The chi-square goodness-of-fit test is used to check if the observed data significantly deviates from a hypothesized probability distribution. It compares the observed frequencies with the expected frequencies from a specific distribution.
To assess whether a random number generator is truly random, you would need to employ different statistical methods specifically designed for that purpose, such as randomness tests or statistical batteries that examine particular properties of randomness, like runs tests or correlation tests. These tests consider various aspects of randomness and analyze the generated sequence to detect any patterns or predictability.