If X is a random variable for which E (X) 10 and Var (X) = 25, for what positive value of 'a' and b' does Y= a X-b have expectation 0 and variance 1. %3D
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- The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 29 adolescent girls who are developmentally delayed, and who have an average age at which they reached their adult height of 17.8 years and a sample variance of 77.4 years. You want to test the hypothesis that adolescent girls who are developmentally delayed have a different age at which they reached their adult height than all adolescent girls. In order to calculate the t statistic, you first need to calculate the estimated standard error. The estimated standard error SM = (round to four decimals)Stock Y has a beta of 1.2 and an expected return of 11.4%. Stock Z has a beta of 0.80 and an expected return of 8.06%. If the risk-free |%, respectively. (Do not round intermediate rate is 2.5% and the market risk premium is 7.2%, the reward-to-risk ratios for stocks Y and Z are and Stock Z is overvalued |and Since the SML reward-to-risk is calculations. Round the final answers to 2 decimal places.) 1%, Stock Y is undervaluedSuppose we have two SRSS from two distinct populations and the samples are independent. We measure the same variable for both samples. Suppose both populations of the values of these variables are normally distributed but the means and standard deviations are unknown. For purposes of comparing the two means, we use (a) Two-sample t procedures (b) Matched pairs t procedures (c) z procedures (d) The least-squares regression line (e) None of the above. The answer is
- 17) Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 41 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.9, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 10000. From this information, what is the number of degrees of freedom for the t-distribution used to compute critical values for hypothesis tests and confidence intervals for the individual…Imagine a family member looks over your shoulder as you look at the variance equation Σki=1(xi − μ)2P(X = xi) and asks why the P(X = xi) term is there. What would you say?The average age at which adolescent girls reach their adult height is 16 years. Suppose you have a sample of 29 adolescent girls who are developmentally delayed, and who have an average age at which they reached their adult height of 17.8 years and a sample variance of 77.4 years. You want to test the hypothesis that adolescent girls who are developmentally delayed have a different age at which they reached their adult height than all adolescent girls. In order to calculate the t statistic, you first need to calculate the estimated standard error. The estimated standard error SM= (round to four decimals)
- We are planning an experiment comparing three fertilizers. We will have six experimental units per fertilizer and will do our test at the 5% level. One of the fertilizers is the standard and the other two are new; the standard fer- tilizer has an average yield of 10, and we would like to be able to detect the situation when the new fertilizers have average yield 11 each. We expect the error variance to be about 4. What sample size would we need if we want power .9?For theoretically modelling the economic development of national economy scenarios the following 2 models for GDP increment are analysed: a. Yt = Yt-1 + at b. Yt = 1.097 Yt-1 - 0,97 Yt-2 + at, where Y - GDP increment a - White noise with zero mean and constant variance o2 =100 t- Time (quarters starting with Q1, 1993) Check by an algebraic criterion which one is stationary.11. In this same article on sleep duration and start time, researchers also considered whether school start time was related to obtaining an adequate amount of sleep. An adequate amountbof sleep was considered at least 8.5 hours of sleep, as recommended by the National Sleep Foundation. The authors used logistic regression models to associate the probability of adequate sleep to school start time. Here are some adapted logistic regression results from this study: In(odds of adequate sleep) = 6, + B,, where x1 = school start time, measured as the number of minutes after 7 AM that the school starts. For this model, B,-0.014, SE(B,)-0.005. - What Is the estimated odds ratlo of adequate sleep, and 95% CI, for students who start at 8:30 AM compared to those who start at 7:30 AM? a. 1.01 (1.00, 1.02) b. 1.52 (1.13, 2.05) C. 2.32 (1.27, 4.22) d. 4.05 (1.49, 11.02)
- Consider the following population model for household consumption: cons = a + b1 * inc+ b2 * educ+ b3 * hhsize + u where cons is consumption, inc is income, educ is the education level of household head, hhsize is the size of a household. Suppose a researcher estimates the model and gets the predicted value, cons_hat, and then runs a regression of cons_hat on educ, inc, and hhsize. Which of the following choice is correct and please explain why. A) be certain that R^2 = 1 B) be certain that R^2 = 0 C) be certain that R^2 is less than 1 but greater than 0. D) not be certainHeteroskedasticity arises because of non-constant variance of the error terms. We said proportional heteroskedasticity exists when the error variance takes the following structure: Var(et)=σt^2=σ^2 xt. But as we know, that is only one of many forms of heteroskedasticity. To get rid of that specific form of heteroskedasticity using Generalized Least Squares, we employed a specific correction – we divided by the square root of our independent variable x. And the reason why that specific correction worked, and yielded a variance of our GLS estimates that was sigma-squared, was because of the following math: (Picture 1) Where var(et)=σ^2 according to our LS assumptions. In other words, dividing everything by the square root of x made this correction work to give us sigma squared at the end of the expression. But if we have a different form of heteroskedasticity (i.e. a difference variance structure), we have to do a different correction to get rid of it. (a) what correction would you use…Diabetes Physicians recommend that children with type-I (insulin dependent) diabetes keep up with their insulin shots to minimize the chance of long-term complications. In addition, some diabetes researchers have observed that growth rate of weight during adolescence among diabetic patients is affected by level of compliance with insulin therapy. Suppose 12-year-old type-I diabetic boys who comply with their insulin shots have a weight gain over 1 year that is normally distributed, with mean = 13 lbs and variance = 13 lbs. (Assume for parts (a) and (b) that weight can be measured exactly and no continuity correction is necessary. Round your answers to four decimal places.) USE SALT (a) What is the probability that compliant type-I diabetic 12 year-old boys will gain at least 17 lbs over 1 year? X (b) Conversely, 12-year-old type-I diabetic boys who do not take their insulin shots have a weight gain over 1 year that normally distributed with mean = 7 lbs and variance = 13 lbs. Answer…