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(c) Under a large sample, given a, a hypothesis test for the mean, Ho : H...
3. Determine if the following statements are true or false, OR show what they claim where...
3. Determine if the following statements are true or false, OR show what they claim where asked (one point each): T F (a) If we sample from a population coming from a normal distribution with known mean, the sampling distribution of the sample mean will be normal, regardless of the sample size. (b) For a given p-value, if p sa we fail to reject the null. (c) Under a large sample, given a, a hypothesis test for the mean, Ho...
Consider a hypothesis test (Ho: u = 10 vs H,:u > 10) on mean of a...
Consider a hypothesis test (Ho: u = 10 vs H,:u > 10) on mean of a normal population with variance known at significance level a = 0.05. Calculate P-value for each of the following test statistics and draw conclusion on whether to reject the null hypothesis. (a) zo = 2.05 (b) zo = -1.84 = 0.4 (c) zo
5. [18 points] Consider the Minitab output shown below. Test of μ = 100 vs >...
5. [18 points] Consider the Minitab output shown below. Test of μ = 100 vs > 100 The assumed standard deviation 2.4 95% Lower Bound 100.770 Mean SE Mean 101.560 3.25 25 a. Fill in the missing values in the output. Can the null hypothesis be rejected at the 0.0s level? Why? b. Is this a one-sided or a two-sided test? C. If the hypotheses had been Ho: μ = 99 versus H : μ > 99, would you reject...
Test the hypothesis at α = 0.01 Describe what type I errors are in this context....
Test the hypothesis at α = 0.01 Describe what type I errors are
in this context. Compute the p-value for this test.
A 2 sided Confidence Interval for the mean is, in analogy to the 2-sided hypothesis test, a range of values under which you would fail to reject the null hypothesis By rewriting this statement about the rejection region, under the assumption the null hypothesis is true: into a statement about the interval for μ you construct the 2-sided...
Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test, i.e., describe...
Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test, i.e., describe the values of the test statistic that would result in rejection of the null hypothesis. We wish o compare he means of two populations using paired observations. Suppose hat d: 3 12 sd 2. and n : 8 and that you wish to est e h pothesis below at he 1 % level of signiticance hat decision le ou d ou u O A....
Complete the following hypothesis test: Ho: u = 52, H: 4 < 52, a = 0.01...
Complete the following hypothesis test: Ho: u = 52, H: 4 < 52, a = 0.01 using the data below. 44 46 49 55 58 47 47 50 52 51 46 40 (a) Find t. (Round your answer to two decimal places.) (ii) Find the p-value. (Round your answer to four decimal places.) (b) State the appropriate conclusion. O Fail to reject the null hypothesis. There is significant evidence that the mean is less than 52. O Reject the null...
12. Consider a statistical inference that test the null hypothesis be Ho: c against H : esuch that c is a positive...
12. Consider a statistical inference that test the null hypothesis be Ho: c against H : esuch that c is a positive value. The test statistic associated with this mull hypothesis is given by t(b-c)/se(b) At significance level a, the test statistic is smaller than the critical value te(a/2, N - 2), that is iste(a/2, N- 2). Mark the correct alternative: (a) The test p-value increases if we increase c. (b) c does not belong to the estimated confidence interval...
Hypothesis test results: u : Mean of variable Ho: u = 2.3 Ha:u>2.3 Variable Sample Mean...
Hypothesis test results: u : Mean of variable Ho: u = 2.3 Ha:u>2.3 Variable Sample Mean Std. Err. DF Length 2.58937 0.205288 399 T-Stat 1.409581 P-value 0.0797 A data set includes data from 400 random tornadoes. The display from technology available below results from using the tornado lengths (miles) to test the claim that the mean tornado length is greater than 2.3 miles. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value, and state the...
For the following hypothesis test, where Ho S 10. vs. Hau > 10, we reject Ho...
For the following hypothesis test, where Ho S 10. vs. Hau > 10, we reject Ho at level of significance a and conclude that the true mean is greater than 10, when the true mean is really 8. Based on this information, we can state that we have O made a Type I error. O made a Type Il error. O made a correct decision increased the power of the test.
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...
3. Determine if the following statements are true or false, OR show what they claim where asked (one point each): T F (a) If we sample from a population coming from a normal distribution with known mean, the sampling distribution of the sample mean will be normal, regardless of the sample size. (b) For a given p-value, if p sa we fail to reject the null. (c) Under a large sample, given a, a hypothesis test for the mean, Ho...
Consider a hypothesis test (Ho: u = 10 vs H,:u > 10) on mean of a normal population with variance known at significance level a = 0.05. Calculate P-value for each of the following test statistics and draw conclusion on whether to reject the null hypothesis. (a) zo = 2.05 (b) zo = -1.84 = 0.4 (c) zo
5. [18 points] Consider the Minitab output shown below. Test of μ = 100 vs > 100 The assumed standard deviation 2.4 95% Lower Bound 100.770 Mean SE Mean 101.560 3.25 25 a. Fill in the missing values in the output. Can the null hypothesis be rejected at the 0.0s level? Why? b. Is this a one-sided or a two-sided test? C. If the hypotheses had been Ho: μ = 99 versus H : μ > 99, would you reject...
Test the hypothesis at α = 0.01 Describe what type I errors are
in this context. Compute the p-value for this test.
A 2 sided Confidence Interval for the mean is, in analogy to the 2-sided hypothesis test, a range of values under which you would fail to reject the null hypothesis By rewriting this statement about the rejection region, under the assumption the null hypothesis is true: into a statement about the interval for μ you construct the 2-sided...
Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test, i.e., describe the values of the test statistic that would result in rejection of the null hypothesis. We wish o compare he means of two populations using paired observations. Suppose hat d: 3 12 sd 2. and n : 8 and that you wish to est e h pothesis below at he 1 % level of signiticance hat decision le ou d ou u O A....
Complete the following hypothesis test: Ho: u = 52, H: 4 < 52, a = 0.01 using the data below. 44 46 49 55 58 47 47 50 52 51 46 40 (a) Find t. (Round your answer to two decimal places.) (ii) Find the p-value. (Round your answer to four decimal places.) (b) State the appropriate conclusion. O Fail to reject the null hypothesis. There is significant evidence that the mean is less than 52. O Reject the null...
12. Consider a statistical inference that test the null hypothesis be Ho: c against H : esuch that c is a positive value. The test statistic associated with this mull hypothesis is given by t(b-c)/se(b) At significance level a, the test statistic is smaller than the critical value te(a/2, N - 2), that is iste(a/2, N- 2). Mark the correct alternative: (a) The test p-value increases if we increase c. (b) c does not belong to the estimated confidence interval...
Hypothesis test results: u : Mean of variable Ho: u = 2.3 Ha:u>2.3 Variable Sample Mean Std. Err. DF Length 2.58937 0.205288 399 T-Stat 1.409581 P-value 0.0797 A data set includes data from 400 random tornadoes. The display from technology available below results from using the tornado lengths (miles) to test the claim that the mean tornado length is greater than 2.3 miles. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value, and state the...
For the following hypothesis test, where Ho S 10. vs. Hau > 10, we reject Ho at level of significance a and conclude that the true mean is greater than 10, when the true mean is really 8. Based on this information, we can state that we have O made a Type I error. O made a Type Il error. O made a correct decision increased the power of the test.
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...
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