. Urn A contains 50% black balls 50 % white balls. Urn B contains 45 %

black balls 55 % white balls. You get a sample of n randomly selected balls.

All balls in the sample belong to the same urn but you do not know which

one. Your task is to decide which urn the sample belongs to. Let the null

hypothesis be the idea that the sample comes from Urn A.

(a) Suppose there are 10 balls in the sample (i.e., n = 10).

i. What would the critical value be for a Type I error specification

of 1/20 ?

ii. What would the power specification be? NOTE: in this case we

can calculate the power because it is possible to find the distribution of the mean assuming the alternative hypothesis is true. In

general this may not be possible.

The probability of catching Lyme disease after on day of hiking in the Cuyamaca mountains are estimated at less than 1 in 10000. You feel bad after a

day of hike in the Cuyamacas and decide to take a Lyme disease test. The

test is positive. The test specifications say that in an experiment with 1000

patients with Lyme disease, 990 tested positive. Moreover. When the same

test was performed with 1000 patients without Lyme disease, 200 tested

positive. What are the chances that you got Lyme disease.

7. This problem uses Bayes' theorem to combine probabilities as subjective

beliefs with probabilities as relative frequencies. A friend of yours believes

she has a 50% chance of being pregnant. She decides to take a pregnancy

test and the test is positive. You read in the test instructions that out of

100 non-pregnant women, 20% give false positives. Moreover, out of 100

pregnant women 10% give false negatives. Help your friend upgrade her

beliefs

In a test of the hypothesis Ho: p = 42 versus Ha: p> 42, a sample of n = 100 observations possessed mean x = 41.4 and standard deviation s = 4.1. Find and interpret the p-value for this test. B The p-value for this test is . (Round to three decimal places as needed.) Interpret the result. Select the correct choice below and fill in the answer box to complete your choice. (Round to three decimal places as needed.) O A. The probability (assuming that Ho is true) of observing a value of the test statistic that is equal to the null hypothesis is O B. The probability (assuming that He is true) of observing a value of the test statistic that is at most as contradictory to the null hypothesis is O C. The probability (assuming that He is true) of observing a value of the test statistic that is at least as contradictory to the null hypothesis is Click to select your answerto) ?Using the results obtained for a study on website development below, how would we interpret the results of this hypothesis test? . The claim is the percent of customers who abandon a web page due to long load times is greater than 30%. . The significance level is 0.01. . The test statistic is 2.12. Use the curve below to show your answer. . Select the appropriate test by dragging the blue point to a right-, left- or two-tailed diagram. . Then, set the critical value(s) using the purple slider on the right. . Set the test statistic by dragging the point on the x-axis.19. Which theorem would you use to prove that the set 5=[0,1] is compact? a. Bolzano-Weierstrass Theorem. b. Extreme Value theorem C. Mean Value Theorem d. Fundamental Theorem of Calculus e. Heine Borel Theorem. f. None 20. Which theorem would you use to prove that lim sin(n) -=0. a. Extreme Value theorem b. Mean Value Theorem C. Fundamental Theorem of Calculus d. Intermediate Value Theorem. e. Sandwich/Squeeze Theorem. f. None 21. Find the infimum and supremum of the set: S = (-1)" +1-1:meN) . a) Inf=1, sup=2 b) Inf= 0, sup=1 c) Inf=0, sup= 2 d) Inf=-1, sup=2 e) No inf, no sup. f) None of these.Problem 1 Evaluate the integral using the Fundamental Theorem of Calculus: (x2 + 5x - 3) dx Problem 2 + Evaluate the integral using the Fundamental Theorem of Calculus: 2+ Problem 3 Evaluate the integral using the Fundamental Theorem of Calculus: $7 /4 sec* x da Problem 4 Use the Fundamental Theorem of Calculus to find the derivative of the function: g(z) = 1 (1 + +2) 4 -dt