Math 329 Assignment 2 Use the following information to answer questions 1 3: The calories in a Serrano burrito are distributed normally, with mean 820 calories and a variance of 900 square calories. 1. What is the probability that you'll order a burrito that has 790 calories or less? (If your answer is 23.5% enter 23.5 as your answer, do not enter 0.235 or 23.5%) 2. Bryan works at Serrano and he is currently being monitored closely by his superiors: they're worried he's being too generous with his burritos. Suppose 100 of his burritos are randomly sampled and it is found that they contained an average of 827.5 calories with a sample standard deviation of 50 calories. What is the t-statistic associated with the test of the null-hypothesis that Bryan's burritos are average in terms of the number of calories they contain (\"average\" being 820 calories)? 3. Would you reject or fail to reject the null-hypothesis (from #2) for a critical value of em = 0.05? Use the following information to answer questions 4 12: Search engine optimizers (SEOs) are encouraged to write as many words per day for their customers as possible.' Some SEO employees work from home (H), while some work from the ofce (0). Home and ofce employees were sampled at random, and the following statistics were collected on them: Home Employees Ofce Employees Number in group sampled NNaa = 80 NNoo = 120 Mean words written on day YYHH = 8,248 words YYoo = 8,166 words sampled words written terminal on day sampled Sample standard deviation of 00mm; = 12 minutes 4. The \"higher ups\" at the SEO company are worried that employees who work from home aren't spending the required 8 hours at their work terminals (which is weird, what they should be worried abOut is the quality/quantity of work being performed, but some people just need to invent reasons to hassle employees and justify their own jobs). What is the absolute value of the t-stat for the test of the null-hypothesis that the \"Home Employees" spend an average of 8 hours (480 minutes) at their work terminals? (Enter only a positive number) 1 This is, more or less, true, which is why so many websites have crazy long \"about us" sections that seem to ramble. It's also why recipe blogs talk endlessly about the dish before getting to the recipe, though that also has to do with wanting you to scroll past ads. Either way, the intemet has some annoying tendencies, to say the least. 10. ll. 12. Would the higher-ups reject, or fail to reject, the null-hypothesis from question #4 with 99% statistical condence? What is the upper end of the 95% condence interval on the number of minutes spent at the work terminal for home employees? (Please use t = 1.96 as your 95% threshold, even though a degrees of freedom correction would suggest you use 1.990. If you have questions about this, I'm happy to answer them during ofce hours) What is the upper end of the 99% condence interval on the number of minutes spent at the work terminal for home employees? (Hint: use 2.57 rather than 1.96 in your formula) What is the lower end of the 95% condence interval on the number of words typed per day for the ofce employees? (Again, please use t = 1.96 as your 95% threshold) Monique is a Home Employee who believes that employees who work om home are more productive (in terms of words written per day) than the ofce employees. What is the absolute value of the t-statistic for the test of the null-hypothesis that the average words written by home employees is equivalent to the average words written by ofce employees? (Enter a positive number as your answer). Does the hypothesis described in question 9 correspond to a one-tailed or a two-tailed alternative hypothesis? Would y0u reject or fail to reject the null-hypothesis that home employees write the same number of words per day as ofce employees for a critical value of ac: = 0.01? (Note: I'm asking about a 1% critical value, not the typical 5% critical value). Can you use only the numbers provided in this table to perform a t-test for difference in the average number of words written per minute of time spent at one's work terminal