Consider the following hypothesis test. Ho: μ ≤ 25 H₂:μ > 25 A sample of 40 provided a sample mean of 26.1. The population standard deviation is 6. (a) Find the value of the test statistic. (Round your answer to two decimal places.) 1.16 (b) Find the p-value. (Round your answer to four decimal places.) p-value = 0.1230 (c) At a = 0.01, state your conclusion. O Reject Ho. There is sufficient evidence to conclude that μ > 25. O Reject Ho. There is insufficient evidence to conclude that μ > 25. O Do not reject Hō. There is sufficient evidence to conclude that μ > 25. • Do not reject Ho. There is insufficient evidence to conclude that μ > 25. (d) State the critical values for the rejection rule. (Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.) test statistic ≤ 26.1 X test statistic ≥ 2.33 State your conclusion. O Reject Ho. There is sufficient evidence to conclude that μ > 25. O Reject H₂. There is insufficient evidence to conclude that μ > 25. O Do not reject Ho. There is sufficient evidence to conclude that μ > 25. Ⓒ Do not reject Ho. There is insufficient evidence to conclude that μ > 25.

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PLEase answer the question 3-8 please, show all of your work, thank you.

Eye Color Based on a study by Dr. R Sorita at Indiana University, assume that 12% of us have green eyes. In a study of 650 people, it is found that 86 of them have green eyes. a. Find the probability of at least 86 people with green eyes among 650 randomly selected people. b. Is 86 people with green eyes significantly high?