ob. 1 (2 points). Let x(t), y(t) = C¹ (R, R) satisfy: x' = sin x, and y' = sin y and they satisfy the initial condition: = x(0) = xo, y(0) = yo. Prove that for all tЄ R: |x(t) − y(t)| ≤ |xo — Yo|et| . - - - 1 1 1

This problem demonstrates a possible (though rare) situation that can occur with group comparisons. The groups are sections and the numerical variable being compared is an exam score. Section 1 Section 2 Section 3 72.9 56.6 62.1 56.6 72.1 52.1 58.6 53.8 67 63.5 46.5 62.9 50.5 29.8 60.3 67.2 68.5 63.5 69.2 32.4 59 55.5 51.4 69.5 64.4 45.6 53.8 Click Download CSV to download csv file of data or copy/paste the data into Excel. After downloading the file, you may want to save it as an Excel Workbook. a. Perform a one-way ANOVA with a = = 0.05. Report the F test statistic rounded to 3 decimal places and the P-value rounded to 4 decimal places. F= p = b. What is the conclusion from the ANOVA? O reject the null hypothesis: at least one of the group means is different O fail to reject the null hypothesis: not enough evidence to suggest the group means are different c. Calculate the group means for each section (Rounded to 2 decimal places): Section 1: 1 = Section 2:2= Section 3: 3= d. Conduct…

In a batch of 2000 bulbs, 5% are defective. If 10 bulbs are selected at random, what is the probability that at least 1 is defective?