Suppose that a one-sample t‑test for a population mean u is being used to test the null hypothesis H0:u=15.72 against the alternative H1:u(does not =)15.72 based on data collected from a simple random sample of size 10. The one-sample t‑statistic is calculated to be 0.881. Use this table of t‑critical values to determine the interval that captures the actual P-value of this test. Different tables have different P-values, so if you use a different table, your answers might not be marked as correct. Enter each answer as a decimal using the precision from the table. If only one limit is in the table, leave the other limit blank. P-value is greater than P-value is less than

Under what circumstances is a t statistic used instead of a z-score for a hypothesis test?     Justin wants to know whether a commonly prescribed drug does improve the attention span of students with attention deficit disorder (ADD). He knows that the mean attention span for students with ADD who are not taking the drug is 2.3 minutes long. His sample of 12 students taking the drug yielded a mean of 4.6 minutes. Justin can find no information regarding σx , so he calculated s2x =1.96. Determine the critical region using a one-tailed test with alpha = .05. Conduct the hypothesis test (Do the math and compare the t-critical and t-obtained values). State your conclusions in terms of H0 (Should you reject the H0 or fail to reject/accept the H0). Based on your analysis, is there a relationship between the drug and attention span?

A simple random sample of 80 adults is obtained, and each person’s red blood cell count is measured. The sample mean is 6.25 and a standard deviation of .65. Use a .01 significance level to test the claim that the sample is from a population with a mean less than 6.4, which is a value often used for the upper limit of the range of normal values. (For each hypothesis test state H0 and H1)

Test the claim about the population variance o² at the level of significance α. Assume the population is normally distributed. Claim: o² ≥8.5; α = 0.10 2 Sample statistics: s² = 7.78, n = 25 Write the null and alternative hypotheses. Ho: 0² ≥ 8.5 Ha: 0² < 8.5 (Type integers or decimals. Do not round.) Calculate the standardized test statistic. x² = 21.97 (Round to two decimal places as needed.) Determine the P-value. P-value = (Round to three decimal places as needed.)

8.2 Use technology to find the​ P-value for the hypothesis test described below. The claim is that for a smartphone​ carrier's data speeds at​ airports, the mean is μ=17.00 Mbps. The sample size is n=21 and the test statistic is t=−1.798

Let Y₁, Y₂, ..., Y₁ denote a random sample from a normal distribution with unknown mean and unknown variance o². For testing Ho: o² = 0 vs. Ha: o²o, show that the a-level Likelihood Ratio Test (LRT) is equivalent to the x² test

A sample of 42 observations is selected from one population with a population standard deviation of 4.5. The sample mean is 100.5. A sample of 56 observations is selected from a second population with a population standard deviation of 3.8. The sample mean is 98.5. Conduct the following test of hypothesis using the 0.10 significance level. H₂ H₁ H₂ H₁ H₁ H₂ a. Is this a one-tailed or a two-tailed test? O One-tailed test O Two-tailed test b. State the decision rule. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) The decision rule is to reject H0 if z is the interval (

Suppose that we would like to test the following hypotheses on the population correlation coefficient ρ: H0: ρ ≤ 0 and H1: ρ > 0. The sample correlation coefficient (r) for a sample with 7 observations (n = 7) on x and y is 0.35 . Then the test statistic t has a value of

Test the claim about the population variance o² at the level of significance a. Assume the population is normally distributed. Claim: o² ≤17.1; x = 0.01 Sample statistics: s² = 25.13, n = 41 Write the null and alternative hypotheses. Ho: H₂:0²