Which of these is NOT a correct null hypothesis? H0: p1-u2 = 0 HO: p1<µ2 O HO:p1=u 2
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- Consider the following two formulations of the bivariate PRF, where ui and εi are both mean-0 stochastic disturbances (i.e random errors): yi = β0 + β1xi + u yi = α0 + α1(xi − x¯) + ϵ a) Write the OLS estimators of β1 and α1. Are the two estimators the same? b) What is the advantage, if any, of the second model over the first?The article in the ASCE Journal of Energy Engineering (1999, Vol. 125, pp.59-75) describes a study of the thermal inertia properties of autoclaved aerated concrete used as a building material. Five samples of the material were tested in a structure, and the average interior temperatures (°C) reported were as follows: 23.01, 22.22, 22.04, 22.62, and 22.59. Test that the average interior temperature is equal to 22.5°C using alpha (a) = 0.05. This problem is a test on what population parameter? What is the null and alternative hypothesis? What are the Significance level and type of test? What standardized test statistic will be used? What is the standard test statistic? What is the Statistical Decision? What is the statistical decision in the statement form?If the value of Cronbach’s alpha is 0.07, it means ___________; a. Research instrument is not reliable b. Research instrument is internally consistent c. Data is reliable d. Data is internally consistent
- Suppose a linear model y=β0+β1xy=β0+β1x is fit to a sample data set, and a test of the null hypothesis H0:β1=0H0:β1=0 against an alternative hypothesis HA:β1≠0HA:β1≠0 is performed; a PP-value of 0.4203 is obtained. Which of the following scatter plots depicts the data set on which this model was fit and the hypothesis test was performed?If 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 parameterIf the t values in the table for a t-test are ± 2.15 at alpha level 0.05, which of following computed t value is needed in order to reject the null hypothesis? Group of answer choices – 2.35 – 1.35 1.35 2.1
- You conduct a hypothesis test and find that your data are statistically significant at alpha = 0.03. What may you conclude? A. The data would also be significant at alpha = 0.02. B. The data would also be significant at alpha = 0.05. C. Both A and B are true. D. Neither A nor B is true.Which of the following is the correct null hypothesis for a dependent samples t test? a. MD = 0 c. µ1 = µ2 b. µD = 0 d. M1 = M2If the results of the test with the following hypotheses are statistically significant, we have found evidence that: Hypotheses: h0: u1 = u2 ha: u1>u2 A: X<x2 B: x1 is not equal to x2 c: u1>u2 D: u1=u2 E: x1>x2 F: u1<u2
- Consider a real random variable X with zero mean and variance σ2X . Suppose that wecannot directly observe X, but instead we can observe Yt := X + Wt, t ∈ [0, T ], where T > 0 and{Wt : t ∈ R} is a WSS process with zero mean and correlation function RW , uncorrelated with X.Further suppose that we use the following linear estimator to estimate X based on {Yt : t ∈ [0, T ]}:ˆXT =Z T0h(T − θ)Yθ dθ,i.e., we pass the process {Yt} through a causal LTI filter with impulse response h and sample theoutput at time T . We wish to design h to minimize the mean-squared error of the estimate.a. Use the orthogonality principle to write down a necessary and sufficient condition for theoptimal h. (The condition involves h, T , X, {Yt : t ∈ [0, T ]}, ˆXT , etc.)b. Use part a to derive a condition involving the optimal h that has the following form: for allτ ∈ [0, T ],a =Z T0h(θ)(b + c(τ − θ)) dθ,where a and b are constants and c is some function. (You must find a, b, and c in terms ofthe information…When testing: H0: (alpha)1^2=(alpha)2^2. HA: (alpha)1^2>(alpha)2^2. At (alpha)=0.01, n1=5, n2=6. s1^2=15750 and s2^2=10920, what critical value do we use?An experiment was performed with three treatments (A, B, and C). Which of the following is a correct model with a categorical explanatory variable with three categories? yˆ = a +bx where x = 0 if in treatment A, x = 1 if in treatment B, and x= 2 if in treatment C yˆ = a +bxA + cxB + dxC where xA = 1 if in treatment A, and = 0 if not in treatment A xB = 1 if in treatment B, and = 0 if not in treatment B xC = 1 if in treatment C, and = 0 if not in treatment C yˆ = a + bxA + cxB where xA = 1 if in treatment A, and = 0 if not in treatment A xB = 1 if in treatment B, and = 0 if not in treatment B