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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Q: Suppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of…
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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…
- Q.8). In a regression calculation, a researcher finds that the explanatory variable x has mean 100 and SD 10, and the response variable y has mean 250 and SD 40. The regression equation is found to be y^ = 450 and y? 2x. What is the correlation between x (a) cannot tell from the information available (b) -0.8 (c) -0.5 (d) 0.4 (e) 0.1 Q.10) a) What are the differences between the data and information? b) Explain the differences between the types of Statistics2. (20) Are Men and Women Equal Talkers? A headline in USA Today proclaimed that “Men, women are equal talker.” The headline referred to a study of the numbers of words that samples of men and women spoke in a day. Data given below are the results from the study. Assume that thedata are from two independent normal populations. Number of Words Spoken in a DayMen Womenn1 = 121 n2 = 101x1 = 18000 x2 = 17000s1 = 2000 s2 = 2500 Use a 10% level of significance, do a hypothesis test to determine whether or not the population variances are the same. (Hint: This is a two detailed F test. You need the conclusion here to make a choice between a pooled or a non-pooled t test for part (b).) (10) Based on your conclusion in part (a), use a 1% level of significance to test the claim that men and women speak the same mean number of words in a day by using critical value approach, which means you need to do a two detailed t test to test whether or not men and women…3
- a. Show that the regression R2 in the regression of Y on X is the squaredvalue of the sample correlation between X and Y. That is, show thatR2 = r2XY.b. Show that the R2 from the regression of Y on X is the same as the R2from the regression of X on Y. c. Show that ^β1 = rXY (sY/sX), where rXY is the sample correlationbetween X and Y, and sX and sY are the sample standard deviationsof X and Y.5.) (10 pts) The following graphs show survival in the U.S. from 1900 (left-most curve) to 2020 (right-most curve) in 10-year intervals. Estimate the median lifespan in (a) 1900 (b) 1940, and (c) 2020. 100 90 Percent Surviving 70 60 50 40 30 10 882882820° 2020 1900 0 228288 28 28 2 2 Age5.1 Suppose X ~ N(14, 10). What is the z-score of x = 14?
- A professor gives a test worth 150 points and the resulting scores from herclass were found to be normally distributed with a mean of 97 and a standarddeviation of 20. She decides to apply a curve to the exam scores such that anA is +2σ or better, a B is between the +1σ and +2σ, a C is between the meanand +1σ, a D is between -1σ and the mean, and any score less than -1σ getsan F. What score would be needed to get an A? If there were 70 students inher class, by this curved distribution, how many student would she expect tohave an A? (Round to the nearest integer.)Suppose IQ scores were obtained for 20 randomly seleceted sets of twins. The 20 pairs of measurements yeild x=101.75, y=102.3, r= 0.909, p value= 0.000, and Y (with the ^ above it) = 18.79 + 1.19x, where x represents the IQ score of the twin born first. Find the best predicted value of Y(^) given that the twin born first has and IQ of 95? use a significance level of 0.05.The best predicted value of Y(^) is ... ?As per image An experiment analyzes imperfection rates for two processes used to fabricate silicon wafers for computer chips......