3. A random variable that can be used to find a 0.954 confidence interval for u, the mean of the gamma distribution is (x-48) 5x 10~t(n − 1) 482/25 28 O True O False 4. The confidence interval of ß is given by 5x 5 x 2 (10+ta) 2 (10-ta
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- The fire department of a city wants to test the null hypothesis that σ = 10 minutes for the time it takes a fire truck to reach a fire site against the alternative hypothesis σ 6= 10 minutes. What can it conclude at the 0.05 level of significance if a random sample of size n = 30 yields s = 9.5 minutes? Assume normality.A manufacturer has developed a new fishing line, which he claims has a mean breaking strength of 15 kilograms with a standard deviation of 0.5 kilogram. To test the hypothesis that μ=15μ=15 kilograms against the alternative that p<15p<15 kilograms, a random sample of 50 lines will be tested. The critical region is defined to be x<14.9x<14.9(a) Find the probability of committing a type 1 error when H0H0 is true(b) Evaluate ββ for the alternatives p−14.8p−14.8 and μ=μ= 14.9 kilograms.The fire department of a city wants to test the null hypothesis that σ =10 minutes for the time it takes a fire truck to reach a fire site against thealternative hypothesis σ 6= 10 minutes. What can it conclude at the 0.05 levelof significance if a random sample of size n = 48 yields s = 9.5minutes?
- To test H0: σ=2.2 versus H1: σ>2.2, a random sample of size n=24 is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to be s=2.9, compute the test statistic. (b) If the researcher decides to test this hypothesis at the α=0.05 level of significance, use technology to determine the P-value. (c) Will the researcher reject the null hypothesis?To test H0: μ = 50 versus H1: μ < 50, a random sample of size n = 24 is obtained from a population that is known to be normally distributed with σ = 12a) If the sample is determined to be x = 47.1, compute the test statistic.b) If the researcher decides to test this hypothesis at α = 0.05 level of significance, determine the P-value.Suppose that three random variables X1, X2, X3 form a random sample from the uniform distribution on interval [0, 1]. Determine the value of E[(X1-2X2+X3)2]
- A doctor wants to research if there is any difference in the birth weights of a mother's first child and second child. Suppose that data were collected for a random sample of 10 mothers with 2 children, where each difference is calculated by subtracting the weight of the first child from the weight of the second child. Assume that the weights are normally distributed. The doctor uses the alternative hypothesis Ha:μd≠0. Suppose the test statistic t is calculated as −1.101, which has 9 degrees of freedom. If the p-value is greater than 0.10 and the significance level is α=0.10, what conclusion can be made about the birth weights of a mother's first 2 children? Select all that apply: Reject the null hypothesis. Fail to reject the null hypothesis. The conclusion of the hypothesis test is that there is sufficient evidence to suggest that the birth weights of a mother's first 2 children are different. The conclusion of the hypothesis test is that…A simple random sample of 100 water meters within a community is monitored to estimate the average daily water consumption per household over a specified dry spell. The sample mean and sample variance are found to be ȳ=12.5 and s2=1252. If we assume that there are N=10,000 households within the community, estimate μ, and place bound on the error of estimation.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 < 1