State the hypotheses and identily the daim with the correct hypothesis. \[ \begin{array}{l} H_{0}=\mu=8.5 \text { not daim } \quad \text { т } \\ H_{1}=\mu \geqslant 8.5 \text { daim } \quad \text {, } \end{array} \] This hypothesis test is a \( \square \) two-tailed test. Fart: \( 1 / 5 \) Part 2 of 5 Find the critical value(s). Round the answer to at least two decimal places. If there is more than one critical value, separate them with commas. Qitical value(s): \( \square \) \( \pm \square \) Skip Part Chack Save For Later 8

Below is a step‐by‐step explanation of the answer. 1. Setting Up the Hypotheses  • The null hypothesis is given as:   H₀: μ = 8.5  • The alternative hypothesis is given as:   H₁: μ ≥ 8.5  In this formulation the “claim” (sometimes called the “research claim”) is the statement made in the alternative hypothesis. That is, the claim is that the mean is at least 8.5. 2. Determining the Type of Test Because the alternative hypothesis uses “≥” (or “>”) rather than “≠”, this is a one‐tailed (specifically, right‐tailed) test. (Even though the blank in the original wording says “two‐tailed test”, the correct test, based on H₁, is one‐tailed.) 3. Finding the Critical Value(s) You are given α = 1/5, which is 0.20. For a right‐tailed test, the critical value is determined by finding the z‐score such that the area in the right tail is 0.20. Equivalently, we need the z value for which P(Z < z) = 0.80. Looking up the standard normal probability (or using a calculator), we have:   z₀.80 ≈ 0.84 Thus, the rejection region is z ≥ 0.84. In this one‐tailed test there is only one critical value. (If it were a two‐tailed test, you would have two critical values, one positive and one negative.) 4. Final Answers • Hypotheses:  H₀: μ = 8.5  H₁: μ ≥ 8.5   (The claim is that μ is at least 8.5.) • Test Type: One‐tailed (right‐tailed) test • Critical Value(s):  Critical value: 0.84 Remember that the rejection region for this test is z ≥ 0.84.