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.)
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?
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).
#1 part A.) To test H0: μ=100 versus H1: μ≠100, a random sample of size n=20 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below. (aa.) If x̅=104.4 and s=9.4, compute the test statistic. t0 = __________ (bb.) If the researcher decides to test this hypothesis at the α=0.01 level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, in...
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?
A test of H0: μ = 50 versus H1: μ ≠ 50 is performed using a significance level of α = 0.01. The value of the test statistic is z = 1.23. a. Is H0 rejected? b. If the true value of μ is 50, is the result a Type I error, a Type II error, or a correct decision? A test of H0: μ = 50 versus H1: μ ≠ 50 is performed using a significance level of α...
To test H0: mean = 80 vs. H1: mean < 80, a simple random sample of size n = 22 is obtained from a population that is known to be normally distributed. (a) If x-hat = 76.9 and s = 8.5 compute the test statistic (b) If the researcher decides to test the hypothesis at the a = 0.02 level of significance, determine the critical value. (c) Draw a t-distribution that depicts the critical region (d) Will the researcher reject...
Given the following hypothesis: H0 : μ ≤ 12 H1 : μ > 12 For a random sample of 10 observations, the sample mean was 14 and the sample standard deviation 4.80. Using the .05 significance level: (a) State the decision rule. (Round your answer to 3 decimal places.) (Click to select)Cannot rejectReject H0 if t > (b) Compute the value of the test statistic. (Round your answer to 2 decimal places.) Value of the test statistic (c)...
If we test the following: H0: μ = 17 vs. H1: μ ≠ 17 and the test statistic (tobs.) is -2.93 for n = 16, so the p-value for this test is Select one: to. .01 <value p <.02 b. .02 <value p <.05 c. .02 <value p <.01 d. 0.0034
Given the following hypotheses: H0: μ ≥ 20 H1: μ > 10 A random sample of five resulted in the following values: 18, 15, 12, 19, and 21. Assume a normal population. Using the 0.01 significance level, can we conclude the population mean is less than 20? a). Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)