Consider a test of H0 : μ = μ0 vs. H0 : μ < μ0.
Suppose this test is based on a sample of size 8, that σ2 is known, and that the underlying population is normal. If a 5% significance level is desired, what would be the rejection rule for this test?
For a test of H0 : μ = μ0 vs. H1 : μ ≠ μ0 assume that the test statistic follows a t-distribution with 18 degrees of freedom. What is the critical value of the test if a 10% significance level is desired? (Express your answer as a positive decimal rounded to three decimal places.)
A researcher is interested in testing the hypothesis H0 : μ = 8 vs H1 : μ > 8, using a sample of size 81. The population standard deviation is known to be σ = 5. The researcher decides to reject H0 if X ≥ 9. What is the significance level of this hypothesis test? Assume that the population is normal. Express your answer as a decimal (not as a percentage).
Suppose you want to test the following hypotheses: H0: p ≥ 0.4 vs. H1: p < 0.4. A random sample of 1000 observations was taken from the population. Answer the following questions and show your Excel calculation for each question clearly: (a) Let p ̂ be the sample proportion. What is the standard error of sample proportion (i.e., σ_p ̂ ) if H0 is true? (b) If the sample proportion obtained were 0.38 (i.e., p ̂=0.38), what is its p-value?...
Suppose H0: μ <= 5 and Ha : μ > 5. If σ is known, what is (are) the critical values for the hypothesis test at 0.01 significance level? Suppose H0: μ = 5 and Ha : μ ≠ 5. If σ is known, what is (are) the critical values for the hypothesis test at 0.01 significance level? Suppose H0: μ => 5 and Ha : μ < 5. If σ is known, what is (are) the critical values for...
8. Suppose that Xi,..., Xn is a sample from a normal population having unknown pa- rameters μ and σ2 a) Devise a significance level α test of the null hypothesis 0 versus the alternative hypothesis for a given positive value σ1. b) Explain how the test would be modified if the population mean μ were known in advance
8. Suppose that Xi,..., Xn is a sample from a normal population having unknown pa- rameters μ and σ2 a) Devise a...
Let X1,.....,Xn be a random sample from N(μ,σ2). If μ is unknown but σ2 is known, develop a likelihood ratio test for H0: μ >= μ0 vs. H1: μ < μ0
Consider the following hypothesis test. H0: μ ≤ 50 Ha: μ > 50 A sample of 60 is used and the population standard deviation is 8. Use the critical value approach to state your conclusion for each of the following sample results. Use α = 0.05. (Round your answers to two decimal places.) (a)x = 52.5 Find the value of the test statistic. State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the...
Consider the following hypothesis test. H0: μ ≥ 10 Ha: μ < 10 The sample size is 155 and the population standard deviation is assumed known with σ = 5. Use α = 0.05. (a) If the population mean is 9, what is the probability that the sample mean leads to the conclusion do not reject H0? (Round your answer to four decimal places.) (b) What type of error would be made if the actual population mean is 9 and...
A test of the null hypothesis H0: μ = μ0 gives test statistic z = 0.45. (Round your answers to four decimal places.) (a) What is the P-value if the alternative is Ha: μ > μ0? (b) What is the P-value if the alternative is Ha: μ < μ0? (c) What is the P-value if the alternative is Ha: μ ≠ μ0?
A test of the null hypothesis H0: μ = μ0 gives test statistic z = 0.66. (Round your answers to four decimal places.) (a) What is the P-value if the alternative is Ha: μ > μ0? (b) What is the P-value if the alternative is Ha: μ < μ0? (c) What is the P-value if the alternative is Ha: μ ≠ μ0?