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Question 3: Two sample hypothesis testing We want to investigate the diameter of steel rods that...
We want to investigate the diameter of steel rods that are manufactured on two different sites....
We want to investigate the diameter of steel rods that are
manufactured on two different sites. We pick two different random
samples of sizes n1 = n2 = 15. The sample means are X1 = 6.2, X2 =
7.8, respectively. The sample variances are s 2 1 = 4 and s 2 2 =
6.25. Assume that both sites produce rods of diameter that is
normally distributed with the same standard deviation σ1 = σ2.
Answer the following questions.
(a)...
Hypothesis Testing_03 (two independent samples) The diameter of steel rods manufactured on two different extrusio s...
Hypothesis Testing_03 (two independent samples) The diameter of steel rods manufactured on two different extrusio steel rods manufactured on two different extrusion machines is being investigated. Two random samples of sizes , 15 and 17 are selected and the sample means and sample variances are sf = 0.35, 12 = 8.68, and s} = 0.40, respectively. e sample means and sample variances are *; -8.73 d. Write down null and alternative hypotheses to test if the machines produce rods with...
A random sample of 49 measurements from a population with population standard deviation o 3 had...
A random sample of 49 measurements from a population with population standard deviation o 3 had a sample mean of x, 9. An independeent random sample of sample mean of x, 11. Test the claim that the population means are 64 measurements from a second population with population standard deviation a2 4 had different. Use level of significance 0.01. (a) What distribution does the sample test statistic follow? Explain. The student's t. We assume that both population distributions are approximately...
z-test a sample for the null hypothesis using α = 0.05 as our threshold a) Given...
z-test a sample for the null hypothesis using α = 0.05 as our threshold a) Given a population with mean of 550 and variance of 100, what would be minimum sample mean to reject the null hypothesis if our sample size is 20? b) Given a population with mean of 550 and variance of 100, what would be maximum sample mean to reject the null hypothesis if our sample size is 20? c) Let’s assume the same population mean and...
Chapter IU! Hypothesis Testing Exercises (1): A random sample of 6 steel beams has a mean...
Chapter IU! Hypothesis Testing Exercises (1): A random sample of 6 steel beams has a mean com- pressive strength of 58,392 psi (pounds per square inch) with a standard deviation of 648 psi. Use this information and the level of significance a = 0.05 to test whether the true average compressive strength of the steel from which this sample came is 58,000 psi. Assume normality. Roelve the show verrien ifn-en 5. tereo Head Exercises (2): Studying the flow of traffic...
Problem 9-22 (modified). A quality control inspector accepts shipments of 500 precision .5" steel rods if...
Problem 9-22 (modified). A quality control inspector accepts shipments of 500 precision .5" steel rods if the mean diameter of a sample of 81 falls between .4995" and .5005". Previous evaluations have established that the standard deviation for individual rod diameters is .003". What is the probability the inspector will accept an out-of-tolerance shipment having mu=.5003? (Note: we aren't told the tolerance, but for simplicity assume that it is .0002 so that mu=.5003 is out-of-tolerance. The acceptance standard of between...
Assignment 2 Consider weights of all NBA players. Assume that we want to test the hypothesis...
Assignment 2 Consider weights of all NBA players. Assume that we want to test the hypothesis that the average weight of the population of all players is 225 lbs, against the alternative hypothesis that the average weight is less that 225 lbs. Assume also that the population standard deviation of player weights is 26 lbs. Let the probability of making a type I error (a) be 0.05. What size random sample would be necessary if we want the probability of...
A comparison is made between two bus lines to determine if arrival times of their regular...
A comparison is made between two bus lines to determine if
arrival times of their regular buses from Denver to Durango are off
schedule by the same amount of time. For 51 randomly selected runs,
bus line A was observed to be off schedule an average time of 53
minutes, with standard deviation 19minutes. For 61 randomly
selected runs, bus line B was observed to be off schedule an
average of 62 minutes, with standard deviation 15 minutes. Do the...
Question 1: Consider two discrete probability distributions with the same sample space and the same expected...
Question 1: Consider two discrete probability distributions with the same sample space and the same expected value. Are the standard deviations of the two distributions necessarily equal? Explain. (Which of the below is correct) A) Yes, because both distributions have the same sample space, they will have the same standard deviation as well. B) Yes, because both distributions have the same expected value, they will have the same standard deviation as well. C) No, the standard deviations of two different...
5. Let X ~ N( ,o2) and assume ơ--3. We are to test the null hypothesis Ho: 10 against e) Let a -0...
5. Let X ~ N( ,o2) and assume ơ--3. We are to test the null hypothesis Ho: 10 against e) Let a -0.05. Design a test to accept or reject He (b) Determine and the power of your test. (c) Plot the probability density functions under the two hypotheses in the same coordinate systern and locate the critical value, acceptance and critical regions, and designate the quantities α and β graphically. revised hypothesis we have β 0.05. Then do (c)...
We want to investigate the diameter of steel rods that are
manufactured on two different sites. We pick two different random
samples of sizes n1 = n2 = 15. The sample means are X1 = 6.2, X2 =
7.8, respectively. The sample variances are s 2 1 = 4 and s 2 2 =
6.25. Assume that both sites produce rods of diameter that is
normally distributed with the same standard deviation σ1 = σ2.
Answer the following questions.
(a)...
Hypothesis Testing_03 (two independent samples) The diameter of steel rods manufactured on two different extrusio steel rods manufactured on two different extrusion machines is being investigated. Two random samples of sizes , 15 and 17 are selected and the sample means and sample variances are sf = 0.35, 12 = 8.68, and s} = 0.40, respectively. e sample means and sample variances are *; -8.73 d. Write down null and alternative hypotheses to test if the machines produce rods with...
A random sample of 49 measurements from a population with population standard deviation o 3 had a sample mean of x, 9. An independeent random sample of sample mean of x, 11. Test the claim that the population means are 64 measurements from a second population with population standard deviation a2 4 had different. Use level of significance 0.01. (a) What distribution does the sample test statistic follow? Explain. The student's t. We assume that both population distributions are approximately...
Chapter IU! Hypothesis Testing Exercises (1): A random sample of 6 steel beams has a mean com- pressive strength of 58,392 psi (pounds per square inch) with a standard deviation of 648 psi. Use this information and the level of significance a = 0.05 to test whether the true average compressive strength of the steel from which this sample came is 58,000 psi. Assume normality. Roelve the show verrien ifn-en 5. tereo Head Exercises (2): Studying the flow of traffic...
Assignment 2 Consider weights of all NBA players. Assume that we want to test the hypothesis that the average weight of the population of all players is 225 lbs, against the alternative hypothesis that the average weight is less that 225 lbs. Assume also that the population standard deviation of player weights is 26 lbs. Let the probability of making a type I error (a) be 0.05. What size random sample would be necessary if we want the probability of...
A comparison is made between two bus lines to determine if
arrival times of their regular buses from Denver to Durango are off
schedule by the same amount of time. For 51 randomly selected runs,
bus line A was observed to be off schedule an average time of 53
minutes, with standard deviation 19minutes. For 61 randomly
selected runs, bus line B was observed to be off schedule an
average of 62 minutes, with standard deviation 15 minutes. Do the...
5. Let X ~ N( ,o2) and assume ơ--3. We are to test the null hypothesis Ho: 10 against e) Let a -0.05. Design a test to accept or reject He (b) Determine and the power of your test. (c) Plot the probability density functions under the two hypotheses in the same coordinate systern and locate the critical value, acceptance and critical regions, and designate the quantities α and β graphically. revised hypothesis we have β 0.05. Then do (c)...
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