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QUESTION 13 Let X equal the number of milliliters in a bottle that has a label...
3. (4 points) Let X equal the number of pounds of butterfat produced by a Holstein cow during the 305-day milking period following the birth of a calf. Assume that the distribution of X is N(μ, σ2-14...
3. (4 points) Let X equal the number of pounds of butterfat produced by a Holstein cow during the 305-day milking period following the birth of a calf. Assume that the distribution of X is N(μ, σ2-1402). To test the null hypothesis Ho : μ-175 against the alternative hypothesis Ha : u 715, let the crtical region be defined by 668.94, where x is the sample mean of n 25 butterfat weights from 25 cows selected at random (a). What...
Question 1 Consider the simple regression model (only one covariate): y= BoB1 u Let B1 be the OLS estimator of B1. a) W...
Question 1 Consider the simple regression model (only one covariate): y= BoB1 u Let B1 be the OLS estimator of B1. a) What are the six assumptions needed for B1 to be unbiased, have a simple expression for its variance, and have normal distribution? (3 points) b) Under Assumptions 1-6, derive the distribution of B1 conditional on x\,..., xn. (3 points) In lecture we described how to test the null hypothesis B1 bo against the alternative hypothesis B1 bo, where...
Let X1,X be a random sample from an EXP(0) distribution (0 > 0) You will use the following facts for this question:...
Let X1,X be a random sample from an EXP(0) distribution (0 > 0) You will use the following facts for this question: Fact 1: If X EXP(0) then 2X/0~x(2). Fact 2: If V V, are a random sample from a x2(k) distribution then V V (nk) (a) Suppose that we wish to test Ho : 0 against H : 0 = 0, where 01 is specified and 0, > Oo. Show that the likelihood ratio statistic AE, O0,0)f(E)/ f (x;0,)...
A plan for an executive travelers' club has been developed by an airline on the premise...
A plan for an executive travelers' club has been developed by an airline on the premise that 5% of its current customers would qualify for membership. A random sample of 500 customers yielded 40 who would qualify. (a) Using this data, test at level 0.01 the null hypothesis that the company's premise is correct against the alternative that it is not correct. State the appropriate null and alternative hypotheses. Ho: P = 0.05 Ha: p = 0.05 Ho: P =...
5. (13pts) Let ui and u 2 denote true average tread lives for two competing brands...
5. (13pts) Let ui and u 2 denote true average tread lives for two competing brands of size P205/6 data: m -55, X 51,500, s1 1200 for sample of Brand A, and n 55, y 1300 for sample of Brand B. 5R15 radial tires (Brand A and B with ?, and ? 2, respectively). Using the following 48,400, and s2 a. (5pts) Compute a 95% CI for ?-? 2. b. ( 8pts) Does this data suggest that ?-A2-2500 at a...
THERE IS QUESTION AND ANSWERS FOR #36 AND #37.... I HAVE GIVEN U THE ANSWERS....I JUST...
THERE IS QUESTION AND ANSWERS FOR #36 AND #37.... I
HAVE GIVEN U THE ANSWERS....I JUST NEED THE STEP BY STEP
SOLUTION.
Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. 36) A machine dispenses a liquid drug into bottles in such a way that the standard deviation of 36) the contents is 81 milliliters. A new machine is tested on a sample of 24...
A random sample of n = 10 observations from a normal population produced x = 47.8...
A random sample of n = 10 observations from a normal population produced x = 47.8 and s2 = 4.3. Test the hypothesis H0: μ = 48 against Ha: μ ≠ 48 at the 5% level of significance. State the test statistic. (Round your answer to three decimal places.) t = State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.) t > t <
Suppose a random sample of 100 observations from a binomial population gives a value of p...
Suppose a random sample of 100 observations from a binomial population gives a value of p = 0.45 and you wish to test the null hypothesis that the population parameter p is equal to 0.40 against the alternative hypothesis that p is greater than 0.40. Complete parts a through c. a. Noting that p = 0.45, what does your intuition tell you? Does the value of p appear to contradict the null hypothesis? O A. Yes, because p satisfies Hg:p>0.40...
Suppose that X ~ POI(μ), where μ > 0. You will need to use the following fact: when μ is not too close to 0, VR ape x N(VF,1/4). (a) Suppose that we wish to test Ho : μ-710 against Ha : μ μί a...
Suppose that X ~ POI(μ), where μ > 0. You will need to use the following fact: when μ is not too close to 0, VR ape x N(VF,1/4). (a) Suppose that we wish to test Ho : μ-710 against Ha : μ μί are given and 10 < μι. m, where 140 and Using 2 (Vx-VHo) as the test statistic, find a critical region (rejection region) with level approximately a (b) Now suppose that we wish to test Ho...
3. Z-test for the population mean u (o known) Hosmer Winery (on Cayuga Lake, New York)...
3. Z-test for the population mean u (o known) Hosmer Winery (on Cayuga Lake, New York) manufactures and bottles wine for sale. They have a machine that automatically fills the bottles. The amount of wine that the machine dispenses will naturally vary slightly from bottle to bottle. To determine whether the machine is working correctly, bottles are occasionally sampled and the volume of wine is measured. One particular sample of eight bottles showed the following amounts of wine (in milliliters):...
3. (4 points) Let X equal the number of pounds of butterfat produced by a Holstein cow during the 305-day milking period following the birth of a calf. Assume that the distribution of X is N(μ, σ2-1402). To test the null hypothesis Ho : μ-175 against the alternative hypothesis Ha : u 715, let the crtical region be defined by 668.94, where x is the sample mean of n 25 butterfat weights from 25 cows selected at random (a). What...
Question 1 Consider the simple regression model (only one covariate): y= BoB1 u Let B1 be the OLS estimator of B1. a) What are the six assumptions needed for B1 to be unbiased, have a simple expression for its variance, and have normal distribution? (3 points) b) Under Assumptions 1-6, derive the distribution of B1 conditional on x\,..., xn. (3 points) In lecture we described how to test the null hypothesis B1 bo against the alternative hypothesis B1 bo, where...
Let X1,X be a random sample from an EXP(0) distribution (0 > 0) You will use the following facts for this question: Fact 1: If X EXP(0) then 2X/0~x(2). Fact 2: If V V, are a random sample from a x2(k) distribution then V V (nk) (a) Suppose that we wish to test Ho : 0 against H : 0 = 0, where 01 is specified and 0, > Oo. Show that the likelihood ratio statistic AE, O0,0)f(E)/ f (x;0,)...
A plan for an executive travelers' club has been developed by an airline on the premise that 5% of its current customers would qualify for membership. A random sample of 500 customers yielded 40 who would qualify. (a) Using this data, test at level 0.01 the null hypothesis that the company's premise is correct against the alternative that it is not correct. State the appropriate null and alternative hypotheses. Ho: P = 0.05 Ha: p = 0.05 Ho: P =...
5. (13pts) Let ui and u 2 denote true average tread lives for two competing brands of size P205/6 data: m -55, X 51,500, s1 1200 for sample of Brand A, and n 55, y 1300 for sample of Brand B. 5R15 radial tires (Brand A and B with ?, and ? 2, respectively). Using the following 48,400, and s2 a. (5pts) Compute a 95% CI for ?-? 2. b. ( 8pts) Does this data suggest that ?-A2-2500 at a...
THERE IS QUESTION AND ANSWERS FOR #36 AND #37.... I
HAVE GIVEN U THE ANSWERS....I JUST NEED THE STEP BY STEP
SOLUTION.
Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. 36) A machine dispenses a liquid drug into bottles in such a way that the standard deviation of 36) the contents is 81 milliliters. A new machine is tested on a sample of 24...
Suppose a random sample of 100 observations from a binomial population gives a value of p = 0.45 and you wish to test the null hypothesis that the population parameter p is equal to 0.40 against the alternative hypothesis that p is greater than 0.40. Complete parts a through c. a. Noting that p = 0.45, what does your intuition tell you? Does the value of p appear to contradict the null hypothesis? O A. Yes, because p satisfies Hg:p>0.40...
Suppose that X ~ POI(μ), where μ > 0. You will need to use the following fact: when μ is not too close to 0, VR ape x N(VF,1/4). (a) Suppose that we wish to test Ho : μ-710 against Ha : μ μί are given and 10 < μι. m, where 140 and Using 2 (Vx-VHo) as the test statistic, find a critical region (rejection region) with level approximately a (b) Now suppose that we wish to test Ho...
3. Z-test for the population mean u (o known) Hosmer Winery (on Cayuga Lake, New York) manufactures and bottles wine for sale. They have a machine that automatically fills the bottles. The amount of wine that the machine dispenses will naturally vary slightly from bottle to bottle. To determine whether the machine is working correctly, bottles are occasionally sampled and the volume of wine is measured. One particular sample of eight bottles showed the following amounts of wine (in milliliters):...
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