answer:/imagine prompt: humanoid robot, sleek metallic body, glowing LED lights, intricate circuitry patterns, standing in a futuristic cityscape, towering skyscrapers and flying vehicles, reflecting on its polished surface, captured with a Sony A7R III camera, 35mm lens, wide-angle view to emphasize the robot's presence, composition focused on the robot's face and hands, creating a sense of awe and wonder, in a style reminiscent of Blade Runner's cyberpunk aesthetic. --ar 16:9 --v 5.2 /imagine prompt: humanoid robot, organic and biomimetic design, soft and flexible synthetic skin, realistic facial expressions, walking in a lush green forest, sunlight filtering through the trees, birds chirping in the background, captured with a Canon EOS R5 camera, 85mm lens, shallow depth of field to isolate the robot from the surroundings, composition focused on the robot's body language and environment interaction, evoking a sense of harmony between nature and technology, in a style inspired by classical paintings of idyllic landscapes. --ar 16:9 --v 5.2 /imagine prompt: humanoid robot, worn-out and weathered appearance, rusty metal plating, exposed wires and gears, exploring an abandoned industrial factory, dimly lit by flickering neon lights, machinery remnants scattered around, captured with a Panasonic Lumix GH5 camera, 24mm lens, wide-angle view to capture the vastness and emptiness of the factory, composition focused on the robot's worn-out features and the eerie ambiance of the environment, creating a sense of desolation and mystery, in a style reminiscent of gritty documentary photography. --ar 16:9 --v 5.2 /imagine prompt: humanoid robot, elegant and graceful movements, flowing lines and curves, dancing on a stage surrounded by vibrant colors and patterns, in a futuristic ballet performance, captured with a Fujifilm X-T4 camera, 50mm lens, medium shot to capture the robot's fluidity and expressiveness, composition focused on the robot's dance poses and the dynamic interaction with light and colors, evoking a sense of beauty and artistic expression, in a style inspired by abstract paintings and modern dance photography. --ar 4:3 --v 5.2

answer:To investigate if there is a difference in population mean salaries between the two institutions, we can use a two-sample t-test. The null hypothesis (H0) would be that there is no difference in population mean salaries between the two institutions. The alternative hypothesis (Ha) would be that there is a difference in population mean salaries between the two institutions. We will calculate the sample means, sample standard deviations, and sample sizes for each institution. Let's assume the sample means for the first institution are X_1 and the sample mean for the second institution is X_2. The sample standard deviations for the first and second institutions are denoted as S_1 and S_2, respectively, and the sample sizes are denoted as n_1 and n_2. We can then calculate the test statistic, t, using the following formula: t = (X1 - X2) / sqrt((S1^2 / n1) + (S2^2 / n2)) The degrees of freedom for the t-distribution is calculated using the following formula: df = (((S1^2/n1) + (S2^2/n2))^2) / (((S1^2/n1)^2 / (n1-1)) + ((S2^2/n2)^2 / (n2-1))) We can then compare the calculated t-value with the critical t-value at a desired significance level (alpha) to determine if we reject or fail to reject the null hypothesis. If the calculated t-value is greater than the critical t-value, we reject the null hypothesis and conclude that there is a significant difference in population mean salaries between the two institutions. If the calculated t-value is less than the critical t-value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference in population mean salaries.

answer:To investigate if there was a population median change in weight after the diet, we can use the Wilcoxon signed-rank test. The null hypothesis (H0) would be that there was no population median change in weight after the diet. The alternative hypothesis (Ha) would be that there was a population median change in weight after the diet. We will calculate the differences in weight before and after the diet for each individual. Let's denote the differences as D. We then rank the absolute values of the differences, ignoring the sign. In case of ties, assign each tied observation the average of their ranks. Next, we calculate the sum of the ranks for the positive differences (SP) and the sum of the ranks for the negative differences (SN). The test statistic, W, is given by the smaller of SP and SN. Finally, we compare the calculated test statistic with the critical value of the Wilcoxon signed-rank test at a desired significance level (alpha) to determine if we reject or fail to reject the null hypothesis. If the calculated test statistic is less than the critical value, we reject the null hypothesis and conclude that there was a significant population median change in weight after the diet. If the calculated test statistic is greater than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant population median change in weight.

answer:Wilcoxon signed-rank test是一种非参数统计检验方法，它没有假设数据来自特定的概率分布。因此，Wilcoxon signed-rank test不依赖于数据的分布，可以用于检验两个相关样本之间的差异。 Wilcoxon signed-rank test的原理基于秩次比较。它首先将每个样本的观测值之间的差异按照绝对值进行排序，然后对每个差异的秩次进行计算。之后，将正差异和负差异的秩次之和进行比较，得到一个称为测试统计量的值。 在执行Wilcoxon signed-rank test时，测试统计量的分布可以查表或使用计算机软件来确定临界值。这些临界值帮助决定在给定显著性水平下，是否拒绝原假设。 综上所述，Wilcoxon signed-rank test不依赖于特定的概率分布，因此它没有特定的分布。