N= 150 observations were collected on a time series that was identified as a AR(2) time series. The following statistics were computed from the data. Mean - 45.0 Variance 15.6 Autocorrelation function (up to lag 5) r1 = 0.80, r2 = .50, rз = .26, r4 = -.10, rs = 0.08: == Estimate the parameters of the model using the method of moments.
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- Stock y has a beta of 1.2 and an expected return of 11.5. Stock z has a beta of .80 and an expected return of 8.5 percentConsider the CAPM. The risk-free rate is 6% and the expected return on the market is 18%. What is the expected return on a stock with a beta of 1.3 when market is efficient?The research question is whether attractiveness affects the behavior of infants lookingat photographs of women’s faces. The researcher is expecting the infants to prefer themore attractive face. Therefore, the researcher predicts that the infants will spendmore than half of the 20-second period looking at the attractive face. Specifically, the researcher tested a sample of n = 9 infants and obtained a mean of M = 13 seconds looking at the attractive face with SS = 72. Report the critical t-value for the alpha level at 0.01.
- A sample of 20 observations is taken from the normal distribution where the sample mean is 3. The normal distribution has a mean of 0 and a variance of e^beta. a)Find the estimator for the method of moments for beta and the numerical value of it?If the df value for a two tailed test with alpha =0.05 were to increase from df=5 to df=22,what would happen to the critical values for t?Suppose that the general fertility rate, g f rt , is following an AR(1) process shown in the image below A) if y1<1, what is the expression for the mean and variance of g f t rt showing any assumptions that were made . b) suppose that Var (€|gfrt-1)= as shown in the image below. explain why you may not obtain a best linear unbiased estimator of y0 and y1 by estimating (3) using OLS.
- The following data consists of the times to relapse and the times to death following relapse of 10 bone marrow transplant patients. In the sample patients 4 and 6 were alive in relapse at the end of the study and patients 7–10 were alive, free of relapse at the end of the study. Suppose the time to relapse had an exponential distribution with hazard rate lambda and the time to death in relapse had a Weibull distribution with parameters theta and alpha (a) Construct the likelihood for the relapse rate lambda. (c) Suppose we were only allowed to observe a patients death time if the patient relapsed. Construct the likelihood for theta and alpha based on this truncated sampleIf X1 and X2 constitute a random sample of size n = 2from an exponential population, find the efficiency of 2Y1relative to X, where Y1 is the first order statistic and 2Y1and X are both unbiased estimators of the parameterThe desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with ? = 0.32 and that x = 5.21. (Use ? = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5?State the appropriate null and alternative hypotheses. H0: ? = 5.5Ha: ? ≠ 5.5H0: ? = 5.5Ha: ? ≥ 5.5 H0: ? = 5.5Ha: ? < 5.5H0: ? = 5.5Ha: ? > 5.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.Reject the null hypothesis. There is sufficient evidence…
- Department secretary has found the average number of complaints per week over the past few years is 1.4. However after a change in major requirements, the complaints over last 8 weeks averaged M = 3.0, with SS = 16. Has there been a significant increase in the number of student complaints over the past 8 weeks? What kind of t-test?______________ Test using alpha = .05 and write an APA style conclusion. 1) H0: H1: 2) Critical value: one or two-tailed? df= __ alpha = .05 __________ 3) Calculations: SS given so start w/ variance s2 SM t = M –µ SM 4) Is there a difference? Reject the Null? Write a sentence with APA stats.The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 1000 cfs (cubic feet per second). a)Of the three randomly selected afternoons, what is the probability that on at least two afternoons the demand will exceed 700 cfs?In Table 11.2 the estimated coefficient on black is 0.084 in column (1),0.688 in column (2), and 0.389 in column (3). In spite of these large differences, all three models yield similar estimates of the marginal effect of race on the probability of mortgage denial. How can this be?