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- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Business_Statistics_(OpenStax)/10%3A_Hypothesis_Testing_with_Two_Samples/10.05%3A_Two_Population_Means_with_Known_Standard_DeviationsThis page covers hypothesis testing for independent means with known population standard deviations, using examples of floor wax efficacy and U.S. senator ages. It establishes null hypotheses to compa...This page covers hypothesis testing for independent means with known population standard deviations, using examples of floor wax efficacy and U.S. senator ages. It establishes null hypotheses to compare means and finds insufficient evidence to support alternative hypotheses, concluding that wax 1 does not outperform wax 2 and that Democratic senators are not older than their Republican counterparts at a 5% significance level.
- https://stats.libretexts.org/Courses/Saint_Mary's_College_Notre_Dame/BFE_1201_Statistical_Methods_for_Finance_(Kuter)/07%3A_Hypothesis_Testing/7.11%3A_Two_Population_Means_with_Known_Standard_DeviationsEven though this situation is not likely (knowing the population standard deviations is very unlikely), the following example illustrates hypothesis testing for independent means with known population...Even though this situation is not likely (knowing the population standard deviations is very unlikely), the following example illustrates hypothesis testing for independent means with known population standard deviations. At the 5% level of significance, from the sample data, there is not sufficient evidence to conclude that the mean age of Democratic senators is greater than the mean age of the Republican senators.
- https://stats.libretexts.org/Courses/Fresno_City_College/Book%3A_Business_Statistics_Customized_(OpenStax)/10%3A_Hypothesis_Testing_with_Two_Samples/10.06%3A_Two_Population_Means_with_Known_Standard_DeviationsThe normal distribution has the following format: \[\textbf{The standard deviation is:}\nonumber\] \[\sqrt{\frac{\left(\sigma_{1}\right)^{2}}{n_{1}}+\frac{\left(\sigma_{2}\right)^{2}}{n_{2}}}\nonumber...The normal distribution has the following format: \[\textbf{The standard deviation is:}\nonumber\] \[\sqrt{\frac{\left(\sigma_{1}\right)^{2}}{n_{1}}+\frac{\left(\sigma_{2}\right)^{2}}{n_{2}}}\nonumber\] \[\textbf{The test statistic (z-score) is:}\nonumber\] \[Z_{c}=\frac{\left(\overline{x}_{1}-\overline{x}_{2}\right)-\delta_{0}}{\sqrt{\frac{\left(\sigma_{1}\right)^{2}}{n_{1}}+\frac{\left(\sigma_{2}\right)^{2}}{n_{2}}}}\nonumber\] At the 5% level of significance, from the sample data, there is n…
- https://stats.libretexts.org/Courses/Fresno_City_College/Introduction_to_Business_Statistics_-_OER_-_Spring_2023/10%3A_Hypothesis_Testing_with_Two_Samples/10.06%3A_Two_Population_Means_with_Known_Standard_DeviationsThe normal distribution has the following format: \[\textbf{The standard deviation is:}\nonumber\] \[\sqrt{\frac{\left(\sigma_{1}\right)^{2}}{n_{1}}+\frac{\left(\sigma_{2}\right)^{2}}{n_{2}}}\nonumber...The normal distribution has the following format: \[\textbf{The standard deviation is:}\nonumber\] \[\sqrt{\frac{\left(\sigma_{1}\right)^{2}}{n_{1}}+\frac{\left(\sigma_{2}\right)^{2}}{n_{2}}}\nonumber\] \[\textbf{The test statistic (z-score) is:}\nonumber\] \[Z_{c}=\frac{\left(\overline{x}_{1}-\overline{x}_{2}\right)-\delta_{0}}{\sqrt{\frac{\left(\sigma_{1}\right)^{2}}{n_{1}}+\frac{\left(\sigma_{2}\right)^{2}}{n_{2}}}}\nonumber\] At the 5% level of significance, from the sample data, there is n…
