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Various concepts related to hypothesis testing, including the p-value, type i and type ii errors, null and alternative hypotheses, test statistics, and the use of t-distributions. It also discusses the differences between independent and matched sample designs, and how to make inferences about the difference between two population means. A comprehensive overview of the key principles and applications of hypothesis testing, which is a fundamental statistical technique used in a wide range of fields, including business, economics, social sciences, and scientific research. By studying this document, students can gain a deeper understanding of the underlying logic and practical considerations involved in hypothesis testing, enabling them to effectively apply these concepts in their academic and professional endeavors.
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As the test statistic becomes larger, the p-value: - becomes smaller. The probability of making a Type I error when the null hypothesis is true as an equality is called the: - level of significance. In hypothesis testing, the tentative assumption about the population parameter is called: - the null hypothesis. The p-value: - must be a number between 0 and 1. For a two-tailed test, the p-value is the probability of obtaining a value for the test statistic as: - unlikely as that provided by the sample. What is the probability of making a Type I error? - 𝛼 Applications of hypothesis testing that only control for the Type I error are called: - significance tests. Which of the following does not need to be known in order to compute the p-value? - The level of significance. The p-value is a probability that measures the support (or lack of support) for the: - null hypothesis. Whenever the probability of making a Type II error has not been determined and controlled, only two conclusions are possible. We either reject H0 or: - do not reject H0. For a lower tail test, the p-value is the probability of obtaining a value for the test statistic: - at least as small as that provided by the sample.
For the case where σ is unknown, the test statistic has a t distribution. How many degrees of freedom does it have? - n - 1 Which of the following describes a Type I Error? - Reject H0 when H0 is true. For the case where σ is unknown, which statistic is used to estimate σ? - s Which of the following describes a Type II Error? - Accept H0 when H0 is false. In most applications of the interval estimation and hypothesis testing procedures, random samples with n1 ≥ 30 and n2 ≥ 30 are adequate. In cases where either or both sample sizes are less than 30: - the distribution of the populations becomes an important consideration. If two large independent random samples are taken from two populations, the sampling distribution of the difference between the two sample means: - can be approximated by a normal distribution. When completing a two-tailed hypothesis test about the difference between two population means, the