Consider a random sample Xı, X2, ..., Xn from the pdf 1 f(x, 0) =(1+0x) -1
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Q: In a trivariate distribution: 01 = 3, 02 = 4, 03 = 5 123 = 0-4, r31 = 0-6, 13 = 0-7 %3D Determine…
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- Consider a set of data (x₁, yi), i=1,2,..0 and the Simple linear regression equation given by : 4 y₁ = B₁+ B₁²x₁ The /s Standardized random variable of given by 2= B₂₁ - B²₁₂² FSSxx find the mean and the variance of ZoNoneN= 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.
- 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.An experiment is conducted to compare the maximum load capacity in tons (the maximum weight that can be tolerated without breaking) for two alloys A and B It is Kknown that the two standard deviations in load capacity are equal at 7 tons each. The experiment is conducted on 50 specimens of each alloy (A and B) and the results are X = 75.8. X = 71.8, and X-X=4. The manufacturers of alloy A are convinced that this evidence shows conclusively that Hug and strongly supports the claim that their alloy is superior. Manufacturers of alloy 8 claim that the experiment could easily have given X-X 4 even if the two population means are equal. Complete parts (a) and (b) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Make an argument that manufacturers of alloy B are wrong. Do it by computing P(XA-XB41 PA-HB) P(XA-X > 4) - @3) For a sample of 306 students in a basic business communications course, the sample regression line y = 58.813 + 0.2875x was obtained. Here y = final student score at the end of the course x = score on a diagnostic writing skills test given at the beginning of the course The coefficient of determination was 0.1158 and the estimated standard deviation of the estimator of the slope of population regression line was 0.04566. a) Define and interpret the estimates of the regression equation. b) Interpret the coefficient of determination. c) What will happen to the final student score if his diagnostic writing test score increases by 2? d) How can you inmprove this model?
- A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.8 seconds. A random sample of 22 sedans has a mean minimum time to travel a quarter mile of 15.5 seconds and a standard deviation of 2.09 seconds. At α=0.01 is there enough evidence to support the consumer group's claim? Complete parts (a) through (d) below. Assume the population is normally distributed (a) Identify the claim and state H0 and Ha. b) THe claim is the _______ hypothesis. c) t= d) p= e) Decide whether to reject or fail to reject the null hypothesis. f) Interpret the decision in the context of the original claim.Suppose we have only ten scores representing the ages (in years) of randomly selected U.S. commercial aircraft. The average age of the ten aircraft is 14.25 years and the sample standard deviation is 9.349 years. Construct a 95% confidence interval for the mean age of all U.S. commercial aircraft. I would appreciate to see what formulas you use and the work through because I messed up.Let S1^2 be the sampling variance for a random sample of twelve values (amount of mercury in the blood) and let S2^2 be the sampling variance for a random sample of ten values (amount of lead in the blood); samples from the same population were used. The population variance for mercury measurements is assumed to be twice the corresponding population variance for lead measurements. We will further assume that S1^2 is independent of S2^2. 1. Find a number b such that P [(S1^2/S2^2)<=b]=0.95 enter such a b to three decimal places b= 2. Consider the number b calculated above, find a number a such that P[a<=(S1^2/S2^2)<=b]=0.90 enter said a to three decimal places. a=
- The table below shows the number of hours per day 11 patients suffered from headaches before and after 7 weeks of soft tissue therapy. At x = 0.01, is there enough evidence to conclude that soft tissue therapy helps to reduce the length of time patients suffer from headaches? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (f). Patient 8 9 10 11 Q 1 Daily headache hours (before) 2.3 3.4 3.3 2.6 1.8 Daily headache hours (after) 1.8 2.7 1.8 1.6 1.9 1.9 1.2 2.5 2.2 2.0 1.1 2 3 4 5 6 7 4.1 3.2 3.5 2.4 3.7 2.6 C (a) Identify the claim and state Ho and Ha The claim is "The therapy the length of time patients suffer from headaches." Let μd be the hypothesized mean of the patients' daily headache hours before therapy minus their daily headache hours after it. State Ho and H₂. Choose the correct answer below. OA. Ho: Hd=d O C. Ho: Hd ≤0 OB. Ho. Họ sở Ha: Hd >d Ha: Hdd Ha: Hd>0 OD. Ho: Hd #d Ha:Hd=d O E. Ho: Hd zd Ha: Hd 3.169…An engineer measures the peak current (in microamps) when a solution containing an amount of nickel (in parts per 10°) is added to a buffer. The experiment was repeated for eleven different values of nickel solutions. A scatterplot showing the data is given below: Peak Current in Eleven Buffers with Added Nickel Solutio 60 120 140 100 Amount of nickel (pp million) Suppose a regression line was added to the plot above. If an additional measurement had been taken with the nickel of 62 parts per 10 and a peak current of 0.38 microamps, adding this observation would: O A. increase the intercept, decrease the slope. OB. increase the intercept, increase the slope. C. decrease the intercept, increase the slope. OD. decrease the intercept, decrease the slope. E. not affect the regression line.4.5. After fitting the regression model, y= Bo + Bix1 + Brx2+ B3x3+€ on 15 cases, it is found that the mean square error s? =3 and 0.5 0.3 0.2 0.6 0.3 6.0 0.5 0.4 (X'X)-' = 0.2 0.5 0.2 0.7 0.6 0.4 0.7 3.0 Find a. The estimate of V (ß1). b. The estimate of Cov(ß¡, ß3). c. The estimate of Corr(ß1, ß3). d. The estimate of V (ß¡ – B3).