5.4.20. Given a random sample of size n from a Poisson distribution, ₁ = X₁ and ^2 = X are two unbiased esti- mators for x. Calculate the relative efficiency of ^₁ to ^^2.
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- A random sample of n, 20 winter days in Denver gave a sample mean pollution index x, = 43. Previous studles show that o,- 10. For Englewood (a suburb of Denver), a random sample of n, - 19 winter days gave a sample mean pollution Index of x, = 37. Previous studies show that g, -13. Assume the pollution Index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) what is the level of significance? State the null and alternate hypotheses. (b) what sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with known standard devtations. O The standard normal. We assume that both population…Q1. (3 points) Suppose that samples of size 36 are selected at random from a normal population with mean 78 and variance 49. What is the probability that the sample mean falls in the interval from Ax- 1.40g and ux +2.4og.Suppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of measurements yield (bar x) x=99.3, (bar y) y=99.5, r=0.943, P-value=0.000, and (^ over y) y=−5.29+1.06x, where x represents the IQ score of the younger child. Find the best-predicted value of (^ over y) y given that the younger child has an IQ of108?Use a significance level of 0.05. The critical values of the Pearson correlation coefficient r. Critical Values of the Pearson Correlation Coefficient r n α=0.05 α=0.01 NOTE: To test H0: ρ=0 against H1: ρ≠0, reject H0 if the absolute value of r is greater than the critical value in the table. 4 0.950 0.990 5 0.878 0.959 6 0.811 0.917 7 0.754 0.875 8 0.707 0.834 9 0.666 0.798 10 0.632 0.765 11 0.602 0.735 12 0.576 0.708 13 0.553 0.684 14 0.532 0.661 15 0.514 0.641 16 0.497 0.623 17 0.482 0.606 18 0.468 0.590…
- 2.2 Explain how to generate from the Beta (1, 3) distribution using the inverse- transform method.4, 12. How Call v. 13. Suppose that two raters (Rater A and Rater B) each assign pirysica attractiveness scO = not at all attractive to 10 = extremely attractive) to a set of seven facial photogranhe 21 %3D Pearson's r can be used as an index of interrater reliability or agreement on quantitative ratings. A correlation of +1 would indicate perfect rank-order agreement between rate while an r of 0 would indicate no agreement about judgments of relative attractiveness An r of .8 to .9 is considered desirable when reliability is assessed. For this example, Rater A's score is the X variable and Rater B's score is the Y variable. The ratings are as followe F follows: Photo Rater A Rater B 1 3. 5. 8. 6. 7. 8. 6. 4. 6. 10 6. 7. 5. 4. a. Compute the Pearson correlation between the Rater A and Rater B attractiveness ratings. What is the obtained r value? b. Is your obtained r statistically significant (using a =.05, two tailed)? Are the Rater A and Rater B scores "reliable"? Is there good or…tion 19.16. Random samples of 200 bolts manufactured by machine A and 100 bolts manufactured by machine B showed 19 and 5 defctive bolts respectively. Is there a significant difference between the performance of the two machines?
- 18) The populations, P, of six towns with time tt in years are given by 1 P=1900(1.195)tP=1900(1.195)^t 2 P=2800(0.8)tP=2800(0.8)^t 3 P=600(1.17)tP=600(1.17)^t 4 P=1200(1.08)tP=1200(1.08)^t 5 P=700(0.79)tP=700(0.79)^t 6 P=2300(0.96)tP=2300(0.96^)t Answer the following questions regarding the populations of the six towns above. Whenever you need to enter several towns in one answer, enter your answer as a comma separated list of numbers. For example if town 1, town 2, town 3, and town 4, are all growing you could enter 1, 2, 3, 4 ; or 2, 4, 1, 3 ; or any other order of these four numerals separated by commas. (a) Which of the towns are growing? (b) Which of the towns are shrinking? (c) Which town is growing the fastest? What is the annual percentage growth RATE of that town?( ) % (d) Which town is shrinking the fastest? What is the annual percentage decay RATE of that town?( ) % (e) Which town has the largest initial population? (f) Which town has the smallest…Show that the mean of a random sample of size n from an exponential population is a minimum variance unbiased estimator of the parameter 0.A report in LTO stated that the average age of taxis in the Philippines is 12 years. An operations manager of a large taxi company selects a sample of 40 taxis and finds the average of the taxis is 11.2 years. The o of the population is 2.3 age years. At a = of the taxis in his company is less than the national average? 0.05, can it be concluded that the average age %3D
- The authors of a paper compared two different methods for measuring body fat percentage. One method uses ultrasound, and the other method uses X-ray technology. The table gives body fat percentages for 16 athletes using each of these methods (a subset of the data given in a graph that appeared in the paper). For purposes of this exercise, you can assume that the 16 athletes who participated in this study are representative of the population of athletes. Athlete Ho: Md = 0 Ha: Ha 0 = 0 Ho: Md < 0 Ha: Md P-value = X-ray 4.75 7.00 9.25 12.00 5 17.25 6 29.50 7 5.50 8 6.00 9 8.00 10 8.50 11 9.25 12 11.00 13 12.00 14 14.00 15 17.00 16 18.00 = 0 1 2 3 4 USE SALT Ultrasound 4.75 4.00 9.00 11.75 17.00 27.75 6.50 6.75 8.75 9.75 9.50 12.00 12.25 15.75 18.00 18.50 Find the test statistic and P-value. (Use a table or SALT. Round your test statistic to one decimal place and your P-value to three decimal places.) t = 0.534 0.000 X X State the conclusion in the problem context. We fail to reiect H.…The number of clients a store has during a week is Poisson distributed with - 25. The amount of money spent by each client follows a random = el,000t+250t2. Assuming the mean A variable with moment generating function o(t) independence between the number of clients, and the amount of money spent by each client. Find the mean and variance of the amount of money received by the store every week.2.3 Explain how to generate from the Weib(a, A) distribution using the inverse- transform method.
