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gore the lecture in your streann r 10 minutes. Random variable X follows Poisson umber of...
4. An exponential random variable X has p.d.f (x,07/», x>0, c.df. F(x:0) 1-exp(-x/8) for x >...
4. An exponential random variable X has p.d.f (x,07/», x>0, c.df. F(x:0) 1-exp(-x/8) for x > 0, and mean θ. A single observation of an exponential random variable X is used to test H0 : θ-2 against H1 : θ-5. The null hypothesis is accepted if and only if the observed value of the random variable is less than 3. (a) What is the probability of committing a Type I error? (b) What is the probability of committing a Type...
Let X1, X2 ,, X8 be a random sample of size 8 from a POI(λ) distribution....
Let X1, X2 ,, X8 be a random sample of size 8 from a POI(λ) distribution. The null hypothesis that λ = 0.25 will be rejected in favor of the alternative hypothesis that λ>0.25 if ∑X ≥5. i a. Find the probability of committing a type I error. (Hint: If Xi ~ POI(λ), then ∑Xi ~ POI(nλ)). b. Find the probability of committing a type II error if λ = 0.5 . c. Find the power of the test if...
(16 points) Suppose the breaking strength of plastic bags is a Gaussian random variable Bags from company i have a mean strength of 8 kilograms and a variance of 1 kg2; Bags from company 2 have a...
(16 points) Suppose the breaking strength of plastic bags is a Gaussian random variable Bags from company i have a mean strength of 8 kilograms and a variance of 1 kg2; Bags from company 2 have a mean strength of 9 kilograms and a variance of 0.5 kg' Assume we check the sample mean X1o of the breaking strength of 10 bags, and use X1o to determine whether a batch of bags comes from company 1 (null hypothesis Ho) or...
α is the probability of a Type I error, which occurs when we accept the alternative...
α is the probability of a Type I error, which occurs when we accept the alternative H1 when the null hypothesis Ho is true. True False A Type II error occurs when when a false null hypothesis is rejected. True False If a null hypothesis is rejected at the 5% significance level but not at the 1% significance level, then the p-value of the test is less than 1%. True False The power of a test is the probability of...
In order to test whether a certain coin is fair, it is tossed ten times and the number of heads (X) is counted. Let p be the "head probability". We wish to test the null hypothesis: p = 0.5 ag...
In order to test whether a certain coin is fair, it is tossed ten times and the number of heads (X) is counted. Let p be the "head probability". We wish to test the null hypothesis: p = 0.5 against the alternative hypothesis: p > 0.5 at a significance level of 5%. (a) Suppose we will reject the null hypothesis when X is smaller than h. Find the value of h. (b) What is the probability of committing a type...
help with this hypothesis testing procedure? A manufacturing firm needs to test the null hypothesis Ho...
help with this hypothesis testing procedure?
A manufacturing firm needs to test the null hypothesis Ho that the probability p of a defective item is 0.2 or less, against the alternative hypothesis H,: p 0.2. The procedure is to select four items at random. If all four items are defective, Ho is rejected; otherwise, a fifth item is selected. If the fifth item is defective, Ho is rejected. In all other cases, Ho is accepted. What is the power of...
MA2500/18 8. Let X be a random variable and let 'f(r; θ) be its PDF where...
MA2500/18 8. Let X be a random variable and let 'f(r; θ) be its PDF where θ is an unknown scalar parameter. We wish to test the simple null hypothesis Ho: 0 against the simple alternative Hi : θ-64. (a) Define the simple likelihood ratio test (SLRT) of Ho against H (b) Show that the SLRT is a most powerful test of Ho against H. (c) Let Xi, X2.... , X be a random sample of observations from the Poisson(e)...
10 Problem 1 Let X is amount of coffeein a "100g coffeecan), EXu. With a sample...
10 Problem 1 Let X is amount of coffeein a "100g coffeecan), EXu. With a sample of size 25 you test null of coffee can"), . Let X ~N(μ, σ2) and variance is known: σ- s amount of coffee in a against μ > 100 at 5% significance level (a) Find the decision rule for that test. (b) Suppose, actually100. What will be the probability to reject null of alternative μ > 100 in that case? Plot that probability as...
In order to test whether a certain coin is fair, it is tossed ten times and...
In order to test whether a certain coin is fair, it is tossed ten times and the number of heads (X) is counted. Let p be the "head probability". We wish to test the null hypothesis: p = 0.5 against the alternative hypothesis: p > 0.5 at a significance level of 5%. (a) Suppose we will reject the null hypothesis when X is smaller than h. Find the value of h. (b) What is the probability of committing a type...
Using a random sample of 28 observations from a normally distributed population, Mike tested the null...
Using a random sample of 28 observations from a normally distributed population, Mike tested the null hypothesis of the population mean that Ho: p=30 against Hy: #30 at a significance level of 0.05 and rejected the null hypothesis. This means that: A. If the null hypothesis is really true, then the probability that Mike rejects it is 0.05. B. Mike needs a larger sample size. OC. If Mike uses another sample of 28 observations he will reject Ho again. OD....
4. An exponential random variable X has p.d.f (x,07/», x>0, c.df. F(x:0) 1-exp(-x/8) for x > 0, and mean θ. A single observation of an exponential random variable X is used to test H0 : θ-2 against H1 : θ-5. The null hypothesis is accepted if and only if the observed value of the random variable is less than 3. (a) What is the probability of committing a Type I error? (b) What is the probability of committing a Type...
(16 points) Suppose the breaking strength of plastic bags is a Gaussian random variable Bags from company i have a mean strength of 8 kilograms and a variance of 1 kg2; Bags from company 2 have a mean strength of 9 kilograms and a variance of 0.5 kg' Assume we check the sample mean X1o of the breaking strength of 10 bags, and use X1o to determine whether a batch of bags comes from company 1 (null hypothesis Ho) or...
help with this hypothesis testing procedure?
A manufacturing firm needs to test the null hypothesis Ho that the probability p of a defective item is 0.2 or less, against the alternative hypothesis H,: p 0.2. The procedure is to select four items at random. If all four items are defective, Ho is rejected; otherwise, a fifth item is selected. If the fifth item is defective, Ho is rejected. In all other cases, Ho is accepted. What is the power of...
MA2500/18 8. Let X be a random variable and let 'f(r; θ) be its PDF where θ is an unknown scalar parameter. We wish to test the simple null hypothesis Ho: 0 against the simple alternative Hi : θ-64. (a) Define the simple likelihood ratio test (SLRT) of Ho against H (b) Show that the SLRT is a most powerful test of Ho against H. (c) Let Xi, X2.... , X be a random sample of observations from the Poisson(e)...
10 Problem 1 Let X is amount of coffeein a "100g coffeecan), EXu. With a sample of size 25 you test null of coffee can"), . Let X ~N(μ, σ2) and variance is known: σ- s amount of coffee in a against μ > 100 at 5% significance level (a) Find the decision rule for that test. (b) Suppose, actually100. What will be the probability to reject null of alternative μ > 100 in that case? Plot that probability as...
Using a random sample of 28 observations from a normally distributed population, Mike tested the null hypothesis of the population mean that Ho: p=30 against Hy: #30 at a significance level of 0.05 and rejected the null hypothesis. This means that: A. If the null hypothesis is really true, then the probability that Mike rejects it is 0.05. B. Mike needs a larger sample size. OC. If Mike uses another sample of 28 observations he will reject Ho again. OD....
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