Assume a 2X2 toble, Summarizing resnlts for tuo indepen dent ye, binomial variates y, and with n, Ond n trials. Remember that independence is equivalent to the homogeneity condhton, 7,=72. Then prove that the Sore test-fr H.: 7,= 72 produces th
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- A research center claims that 30% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1200 adults in that country, 33% say that they would travel into space on a commercial flight if they could afford it. At α=0.05, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. Identify the P-value?According to the American Pet Products Manufacturers Association, cat owners spend an average of $179 annually in routine veterinary visits. A random sample of local cat owners revealed that ten randomly selected owners spent an average of $205 with s = $26. Is there a significant statistical difference at α = 0.01?The test statics isAssume the pressure capacity of foundation is normal variate, Rf ~N(60, 20) psf. The peak wind pressure Pw on the building during a wind storm is given by Pw = 1.165×10-3 CV2 , in psf where C is the drag coefficient ~N(1.8, 0.5) and V is the maximum wind speed, a Type I extreme variate with a modal speed of 100, and COV of 30%; the equivalent extremal parameters are α=0.037 and u=100. Suppose the probability of failure of the given engineering system due to inherent variability is Pf=P(Rf - Pw ≤ 0). Obtain the Pf using Monte Carlo Simulation (MCS) with the sample size of n=100, 1000, 10000, and 100000. Show the estimated COVs for each simulation.
- The sample mean and standard deviation from a random sample of 30 observations from a normal population were computed as x¯=31x¯=31 and s = 9. Calculate the t statistic of the test required to determine whether there is enough evidence to infer at the 3% significance level that the population mean is greater than 28. Test Statistic =A quality control officer compares the average lifetime of four different brandsof hand phones. For each of the brand, 5 hand phone was used to calculate theaverage lifetime in minutes. The results are given as follow V =756.55 W=3 X=16 Y=5.4 Z= 46.7006 i)Assuming the populations are normally distributed, determine whichaverage lifetime of the hand phones is significantly different at ? =0.05?A z-score of –1.6 has a corresponding Stanine score of:
- Suppose X1, . . . , Xn be a random sample from the Beta(θ, 1) distribution. Find the P-value for the LRT test of the hypotheses H0 : θ ≥ 1 vs H1 : θ < 1Suppose X1, ..., Xn have been randomly sampled from a normal distribution with mean 0 and unknown variance sigma^2, and let U = c * i=1 -> n summation (X_ i)^2 , where c is a constant. Find the value of c that minimises the Mean Squared Error (MSE)Assuming that the data are normally distributed, a. Determine the z-score such that the area to its right is 18%. z= b. Determine the z-score such that the area to its left is 91%. z=
- A researcher estimates that the average height of the buildings of 30 or more stories in a large city is at most 700 feet. A random sample of 10 buildings is selected, and the heights in feet are shown. At α = 0.025, is there enough evidence to reject the claim? 485 511 841 725 615 520 535 635 616 582 What is the critical value of the t?The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−34. Calculate Var(X+Y) with a full explanationThe average number of pounds of sliced ham ordered per customer at the deli where Dennis used to work was 1.4, but at his new job, the average of the 32 people who have ordered ham so far is 1.5 pounds, with a standard deviation of 0.3 pounds. a) Write the null and alternative hypotheses to test if the average amount of ham bought is higher at the new store. H0:μ= H1:μ> b) For α=0.025, find the rejection region in terms of z. [Write your answer with 2 decimal places.] R:z≥ c) What test statistic corresponds to an x¯ of 1.5 pounds? [Round your answer to 2 decimal places.] z= d) Should you reject the null hypothesis?