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- https://stats.libretexts.org/Courses/American_River_College/STAT_300%3A_My_Introductory_Statistics_Textbook_(Mirzaagha)/09%3A_Hypothesis_Testing_about_Population_Mean_and_Proportion/9.02%3A_Inference_for_Categorical_Data/9.2.03%3A_Testing_for_Goodness_of_Fit_using_Chi-Square_(Special_Topic)The chi-square distribution is sometimes used to characterize data sets and statistics that are always positive and typically right skewed. Recall the normal distribution had two parameters - mean and...The chi-square distribution is sometimes used to characterize data sets and statistics that are always positive and typically right skewed. Recall the normal distribution had two parameters - mean and standard deviation - that could be used to describe its exact characteristics. The chi-square distribution has just one parameter called degrees of freedom (df), which inuences the shape, center, and spread of the distribution.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Business_Statistics_(OpenStax)/09%3A_Hypothesis_Testing_with_One_Sample/9.03%3A_One-Sample_TestThis page covers hypothesis testing for population means and proportions, detailing the use of normal and Student's \(t\)-distributions, calculation of test statistics (Z-values), and decision-making ...This page covers hypothesis testing for population means and proportions, detailing the use of normal and Student's \(t\)-distributions, calculation of test statistics (Z-values), and decision-making based on critical values and p-values. It emphasizes the bias towards the null hypothesis, discusses one-tailed and two-tailed tests, and outlines a systematic approach for hypothesis testing, including the importance of sample size and the appropriate distribution based on known standard deviation.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/An_Introduction_to_Psychological_Statistics_(Foster_et_al.)/07%3A__Introduction_to_Hypothesis_Testing/7.05%3A_Critical_values_p-values_and_significance_levelIf we go to the normal table, we will find that the z-score corresponding to 5% of the area under the curve is equal to 1.645 (\(z\) = 1.64 corresponds to 0.0405 and \(z\) = 1.65 corresponds to 0.0495...If we go to the normal table, we will find that the z-score corresponding to 5% of the area under the curve is equal to 1.645 (\(z\) = 1.64 corresponds to 0.0405 and \(z\) = 1.65 corresponds to 0.0495, so .05 is exactly in between them) if we go to the right and -1.645 if we go to the left.
- https://stats.libretexts.org/Courses/Fort_Hays_State_University/Elements_of_Statistics/07%3A_Hypothesis_Testing/7.01%3A_Introduction_to_Hypothesis_TestingOur method of confidence intervals provides an interval estimate of the population parameter at a certain success rate called the confidence level. When we do not know much about the population, we ca...Our method of confidence intervals provides an interval estimate of the population parameter at a certain success rate called the confidence level. When we do not know much about the population, we can utilize random sampling to build confidence intervals to learn about populations from scratch. At other times, we have claims about a certain population that we hope to test. This quest falls within the realm of inferential statistics and is the subject of this chapter.
- https://stats.libretexts.org/Courses/Fresno_City_College/Introduction_to_Business_Statistics_-_OER_-_Spring_2023/09%3A_Hypothesis_Testing_with_One_Sample/9.04%3A_Distribution_Needed_for_Hypothesis_TestingThe horizontal axis of the bottom panel is labeled \(Z\) and is the standard normal distribution. \(Z_{\frac{\alpha}{2}}\) and \(-Z_{\frac{\alpha}{2}}\), called the critical values, are marked on the ...The horizontal axis of the bottom panel is labeled \(Z\) and is the standard normal distribution. \(Z_{\frac{\alpha}{2}}\) and \(-Z_{\frac{\alpha}{2}}\), called the critical values, are marked on the bottom panel as the \(Z\) values associated with the probability the analyst has set as the level of significance in the test, (\(\alpha\)).
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/OpenIntro_Statistics_(Diez_et_al)./06%3A_Inference_for_Categorical_Data/6.03%3A_Testing_for_Goodness_of_Fit_using_Chi-Square_(Special_Topic)The chi-square distribution is sometimes used to characterize data sets and statistics that are always positive and typically right skewed. Recall the normal distribution had two parameters - mean and...The chi-square distribution is sometimes used to characterize data sets and statistics that are always positive and typically right skewed. Recall the normal distribution had two parameters - mean and standard deviation - that could be used to describe its exact characteristics. The chi-square distribution has just one parameter called degrees of freedom (df), which inuences the shape, center, and spread of the distribution.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/OpenIntro_Statistics_(Diez_et_al)./04%3A_Foundations_for_Inference/4.04%3A_Hypothesis_TestingHypothesis testing involves the formulate two hypothesis to test against the measured data: (1) The null hypothesis often represents either a skeptical perspective or a claim to be tested and (2) The ...Hypothesis testing involves the formulate two hypothesis to test against the measured data: (1) The null hypothesis often represents either a skeptical perspective or a claim to be tested and (2) The alternative hypothesis represents an alternative claim under consideration and is often represented by a range of possible parameter values. The skeptic will not reject the null hypothesis, unless the evidence in favor of the alternative hypothesis is so strong to rejects the null hypothesis.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Statistics_Through_an_Equity_Lens_(Anthony)/01%3A_Chapters/1.05%3A_Significance_of_Statistical_Inference_MethodsThis chapter explores inferential statistics, focusing on concepts such as confidence intervals, hypothesis testing, and errors in statistical inference. It emphasizes the importance of understanding ...This chapter explores inferential statistics, focusing on concepts such as confidence intervals, hypothesis testing, and errors in statistical inference. It emphasizes the importance of understanding sampling variations and discusses tests like t-tests and chi-square tests. It also touches on the misuse of statistics in scientific racism, emphasizing the need for socially just statistical methods. The chapter links statistical inference to broader societal issues.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Visual_Statistics_Use_R_(Shipunov)/04%3A_One-Dimensional_Data/4.03%3A_Confidence_intervalsThe test statistic is a single measure of some attribute of a sample; it reduces all the data to one value and with a help of standard distribution, allows to re-create the “virtual population”. There...The test statistic is a single measure of some attribute of a sample; it reduces all the data to one value and with a help of standard distribution, allows to re-create the “virtual population”. Therefore, we reject the null hypothesis, or our initial assumption that mean tree height equals to 0 and consequently, go with the alternative hypothesis which is a logical opposite of our initial assumption (i.e., “height is not equal to 0”):
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/08%3A_Testing_Hypotheses/8.05%3A_Large_Sample_Tests_for_a_Population_ProportionBoth the critical value approach and the p-value approach can be applied to test hypotheses about a population proportion.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Mostly_Harmless_Statistics_(Webb)/08%3A_Hypothesis_Tests_for_One_Population/8.03%3A_Hypothesis_Test_for_One_MeanThere are three methods used to test hypotheses: (1) The Traditional Method (Critical Value Method), (2) the P-value Method, and (3) the Confidence Interval Method.
