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QUESTION 10 Suppose that you are testing a hypothesis on the mean of a normal distribution...
. Suppose a random sample of 25 is taken from a population that follows a normal distribution wit...
. Suppose a random sample of 25 is taken from a population that follows a normal distribution with unknown mean and a known variance of 144. Provide the null and alternative hypotheses necessary to determine if there is evidence that the mean of the population is greater than 100. Using the sample mean, Y, as the test statistic and a rejection region > k}, find the value of k so that α = 0.15. of the form - Using the...
QUESTION 4 a) What is meant by critical region and significance level in hypothesis testing? (2...
QUESTION 4 a) What is meant by critical region and significance level in hypothesis testing? (2 marks) b) A random sample X1, X2...., X, of size n is obtained from a normal distribution with mean, u and variance, 81. We are interested to test Ho : 4 = 100 against H, : x = 104. 1) Show that a best critical region according to Neyman-Pearson lemma is 82c. (8 marks) ii) Find the sample size, n given that the significance...
3. Testing a population mean The test statistic (Chapter 11) Aa Aa You conduct a hypothesis...
3. Testing a population mean The test statistic (Chapter 11) Aa Aa You conduct a hypothesis test about a population mean u with the following null and alternative hypotheses: Ho: u-25.8 H1: <25.8 Suppose that the population standard deviation has a known value of a observations, which provides a sample mean of % 30.7. 17.8. You obtain a sample of n =62 Since the sample size large enough, you assume that the sample mean X follows a normal distribution. Let...
Suppose that you are testing the following hypotheses: Ho: = 10 and 11: > 10. If...
Suppose that you are testing the following hypotheses: Ho: = 10 and 11: > 10. If the null hypothesis is rejected at the 1% level of significance, what statement can you make about the confidence interval on the mean? a) The lower bound of a 95% one-sided confidence interval on the mean exceeds 10. b) 9 sus 13 c) No statement can be made. d) The lower bound of a 95% one-sided confidence interval on the mean exceeds zero. If...
Choose the incorrect explanation on the following hypothesis testing: H0 x> 1.8 Ha x = 1.8...
Choose the incorrect explanation on the following hypothesis testing: H0 x> 1.8 Ha x = 1.8 Either the hypothesis should be about the population mean, not the sample OR There is no error A study with 21 transplants for 21 children was reported where ultrasounds were taken at the time of liver transplant and again 10 years later to determine the diastolic blood pressure (DBP) of the hepatic artery. It is interested if liver transplant changes the mean DBP 10...
Bonus (5 points) Suppose that you are testing the following hypotheses: Ho: 4 = 10 and...
Bonus (5 points) Suppose that you are testing the following hypotheses: Ho: 4 = 10 and H :> 10. If the null hypothesis is rejected at the 1% level of significance, what statement can you make about the confidence interval on the mean? a) The lower bound of a 95% one-sided confidence interval on the mean exceeds 10. b) 9 <u< 13 c) No statement can be made. d) The lower bound of a 95% one-sided confidence interval on the...
1. True or False? In hypothesis testing analysis, a type II error occurs if the null...
1. True or False? In hypothesis testing analysis, a type II error occurs if the null hypothesis H0 is accepted when it is true. 2. True or False? When population is not normal, sampling distribution of ¯x , for a large sample size is normally distributed, irrespective of the shape of the population.
RStudio / null & alternate hypothesis testing - Question - The population mean µ of the...
RStudio / null & alternate hypothesis testing - Question - The population mean µ of the full-body lengths (cm) is taken of an undisclosed species today (2020). Jack decides to compare this undisclosed species full-body lengths mean from 2020 with the mean from a decade ago. The mean full-body lengths from a decade ago is 50 cm. --- (Other information): Sample size = 38. Standard deviation = 4.5 Full-body lengths mean = 43.34cm --- (a) Hypothesis test, has the mean...
1) You conduct a hypothesis test on an experimental drug K-2090 and you observe a test...
1) You conduct a hypothesis test on an experimental drug K-2090 and you observe a test statistic (mean blood pressure difference) value of 0.9 calculated from a sample with size n = 100. This test statistic had a corresponding p-value of 0.064 which was greater than the significance level, and therefore failed to reject the null hypothesis. What will happen to the p-value if you observe the same test statistic for a sample of n = 10,000? a May either...
A sample from a Normal distribution with an unknown mean u and known variance o =...
A sample from a Normal distribution with an unknown mean u and known variance o = 45 was taken with n=9 samples giving sample mean of y = 3.6. (a) Construct a Hypothesis test with significance level a = 0.05 to test whether the mean is equal to 0 or it is greater than 0. What can you conclude based on the outcome of the sample? (b) Calculate the power of this test if the true value of the mean...
. Suppose a random sample of 25 is taken from a population that follows a normal distribution with unknown mean and a known variance of 144. Provide the null and alternative hypotheses necessary to determine if there is evidence that the mean of the population is greater than 100. Using the sample mean, Y, as the test statistic and a rejection region > k}, find the value of k so that α = 0.15. of the form - Using the...
QUESTION 4 a) What is meant by critical region and significance level in hypothesis testing? (2 marks) b) A random sample X1, X2...., X, of size n is obtained from a normal distribution with mean, u and variance, 81. We are interested to test Ho : 4 = 100 against H, : x = 104. 1) Show that a best critical region according to Neyman-Pearson lemma is 82c. (8 marks) ii) Find the sample size, n given that the significance...
3. Testing a population mean The test statistic (Chapter 11) Aa Aa You conduct a hypothesis test about a population mean u with the following null and alternative hypotheses: Ho: u-25.8 H1: <25.8 Suppose that the population standard deviation has a known value of a observations, which provides a sample mean of % 30.7. 17.8. You obtain a sample of n =62 Since the sample size large enough, you assume that the sample mean X follows a normal distribution. Let...
Suppose that you are testing the following hypotheses: Ho: = 10 and 11: > 10. If the null hypothesis is rejected at the 1% level of significance, what statement can you make about the confidence interval on the mean? a) The lower bound of a 95% one-sided confidence interval on the mean exceeds 10. b) 9 sus 13 c) No statement can be made. d) The lower bound of a 95% one-sided confidence interval on the mean exceeds zero. If...
Bonus (5 points) Suppose that you are testing the following hypotheses: Ho: 4 = 10 and H :> 10. If the null hypothesis is rejected at the 1% level of significance, what statement can you make about the confidence interval on the mean? a) The lower bound of a 95% one-sided confidence interval on the mean exceeds 10. b) 9 <u< 13 c) No statement can be made. d) The lower bound of a 95% one-sided confidence interval on the...
A sample from a Normal distribution with an unknown mean u and known variance o = 45 was taken with n=9 samples giving sample mean of y = 3.6. (a) Construct a Hypothesis test with significance level a = 0.05 to test whether the mean is equal to 0 or it is greater than 0. What can you conclude based on the outcome of the sample? (b) Calculate the power of this test if the true value of the mean...
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