(12%) Statistics (using random process): Suppose telephone calls follow a Poisson process model X(t). There are...
- (12%) Statistics (using random process): Suppose telephone calls follow a Poisson process model X(t). There are two hypotheses on the expected value: H1: E[X(t)] = l1t = 80t and H2: E[X(t)] = l2t = 85t. We will use t = 30 in this question and suppose the number of calls received is 2475.
For a value a of significance level, there are four possibilities for accepting / rejecting the hypotheses: H1 and H2 both accepted, H1 and H2 both rejected, H1 accepted and H2 rejected, H2 accepted and H1 rejected.
- Find / compute a significance level a (a = ?) that both H1 and H2 are accepted (show the calculation) or explain why such significance level does not exist.
- Find / compute a significance level a that both H1 and H2 rejected (show the calculation) or explain why such significance level does not exist.
- Find / compute a significance level a that H1 is accepted and H2 is rejected (show the calculation) or explain why such significance level does not exist.
- Find / compute a significance level a that H2 is accepted and H1 is rejected (show the calculation) or explain why such significance level does not exist.
Homework Answers
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(12%) Statistics (using random process):
Suppose telephone calls follow a Poisson process model X(t). There
are...
(16%) Statistics (using random process): Suppose telephone calls follow a Poisson process model X(t). There are...
(16%) Statistics (using random process): Suppose telephone calls follow a Poisson process model X(t). There are two hypotheses on the expected value: H1: E[X(t)] = l1t = 80t and H2: E[X(t)] = l2t = 85t. We will use t = 40 in this question and suppose the number of calls received is 3300. For a value a of significance level, there are four possibilities for accepting / rejecting the hypotheses: H1 and H2 both accepted, H1 and H2 both rejected,...
Problem 1 A Poisson process is a continuous-time discrete-valued random process, X(t), that counts the number of events...
Problem 1 A Poisson process is a continuous-time discrete-valued random process, X(t), that counts the number of events (think of incoming phone calls, customers entering a bank, car accidents, etc.) that occur up to and including time t where the occurrence times of these events satisfy the following three conditions Events only occur after time 0, i.e., X(t)0 for t0 If N (1, 2], where 0< t t2, denotes the number of events that occur in the time interval (t1,...
A random sample of 40 binomial trials resulted in 16 successes. Test the claim that the...
A random sample of 40 binomial trials resulted in 16 successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05. (a) Can a normal distribution be used for the p̂ distribution? Explain. Yes, np and nq are both less than 5.No, np is greater than 5, but nq is less than 5. No, nq is greater than 5, but np is less than 5.Yes, np and nq are both greater...
A. B. Please follow the steps of hypothesis testing, including identifying the alternative and null hypothesis,...
A.
B.
Please follow the steps of hypothesis testing, including
identifying the alternative and null hypothesis, calculating the
test statistic, finding the p-value, and making a conclusions about
the null hypothesis and a final conclusion that addresses the
original claim. Use a significance level of 0.10. Is the conclusion
affected by whether the significance level is 0.10 or 0.01?
Test Statistic=______ (Round to two decimal places)
P-Value=______ (Round to three decimal places)
Answer choices below:
a) Yes, the conclusion is...
Sample 2 11 n X Assume that both populations are normally distributed a) Test whether ,...
Sample 2 11 n X Assume that both populations are normally distributed a) Test whether , at the = 0.01 level of significance for the given sample data b) Construct a 50% confidence interval about 4-12 Sample 1 19 5078 21 11.9 Click the icon to view the Student distribution table a) Perform a hypothesis test. Determine the null and alternative hypotheses O A HOM > B. Hy: H2 OB HM, H, H2 + C Họ P = H1 H1...
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...
Given in the table are the BMI statistics for random samples of men and women. Assume...
Given in the table are the BMI statistics for random samples of men and women. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. n Male BMI Female BMI 1 12 50 50 27.5997 25 6435 8.819325 4.764227 X S a. Test the claim that males and females have...
Let x be a random variable that represents hemoglobincount (HC) in grams per 100 milliliters...
Let x be a random variable that represents hemoglobin
count (HC) in grams per 100 milliliters of whole blood. Thenx has a distribution that is approximately normal, with
population mean of about 14 for healthy adult women. Suppose that a
female patient has taken 10 laboratory blood tests during the past
year. The HC data sent to the patient's doctor are as follows.16181719141314171610(i) Use a calculator with sample mean and standard deviation
keys to find x and s. (Round your...
Suppose that you construct the following regression model to test forecast bias. Y(t) = a +...
Suppose that you construct the following regression model to test forecast bias. Y(t) = a + b*X(t-1) + error where y(t) = spot exchange rate at time t and X(t-1) = forecasted exchange rate at time t-1. Test a=0 and b=1 using 1% or 5% statistical significance level. Regression results: a b estimated coefficient 0.053 1.197 p-value 0.291 0.365 Based on the results, explain whether forecasted values are biased (overestimated or understimated) or unbiased and why. (You don't need any...
Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters...
Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows. 16 19 16 18 15 11 14 16 16 12 (i) Use a calculator with sample...
Problem 1 A Poisson process is a continuous-time discrete-valued random process, X(t), that counts the number of events (think of incoming phone calls, customers entering a bank, car accidents, etc.) that occur up to and including time t where the occurrence times of these events satisfy the following three conditions Events only occur after time 0, i.e., X(t)0 for t0 If N (1, 2], where 0< t t2, denotes the number of events that occur in the time interval (t1,...
A.
B.
Please follow the steps of hypothesis testing, including
identifying the alternative and null hypothesis, calculating the
test statistic, finding the p-value, and making a conclusions about
the null hypothesis and a final conclusion that addresses the
original claim. Use a significance level of 0.10. Is the conclusion
affected by whether the significance level is 0.10 or 0.01?
Test Statistic=______ (Round to two decimal places)
P-Value=______ (Round to three decimal places)
Answer choices below:
a) Yes, the conclusion is...
Sample 2 11 n X Assume that both populations are normally distributed a) Test whether , at the = 0.01 level of significance for the given sample data b) Construct a 50% confidence interval about 4-12 Sample 1 19 5078 21 11.9 Click the icon to view the Student distribution table a) Perform a hypothesis test. Determine the null and alternative hypotheses O A HOM > B. Hy: H2 OB HM, H, H2 + C Họ P = H1 H1...
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...
Given in the table are the BMI statistics for random samples of men and women. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. n Male BMI Female BMI 1 12 50 50 27.5997 25 6435 8.819325 4.764227 X S a. Test the claim that males and females have...
Let x be a random variable that represents hemoglobin
count (HC) in grams per 100 milliliters of whole blood. Thenx has a distribution that is approximately normal, with
population mean of about 14 for healthy adult women. Suppose that a
female patient has taken 10 laboratory blood tests during the past
year. The HC data sent to the patient's doctor are as follows.16181719141314171610(i) Use a calculator with sample mean and standard deviation
keys to find x and s. (Round your...
Suppose that you construct the following regression model to test forecast bias. Y(t) = a + b*X(t-1) + error where y(t) = spot exchange rate at time t and X(t-1) = forecasted exchange rate at time t-1. Test a=0 and b=1 using 1% or 5% statistical significance level. Regression results: a b estimated coefficient 0.053 1.197 p-value 0.291 0.365 Based on the results, explain whether forecasted values are biased (overestimated or understimated) or unbiased and why. (You don't need any...
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