2) Hypothesis Testing for Population Mean: Population Variance Unknown a) An engineer hypothesizes that the mean hardness of a certain metallic compound is greater than 170. He obtains 25 samples of the material, finding the sample mean to be 175 and the sample standard deviation to be 10. Does his sample seem to indicate that the true mean hardness of this compound is greater than 170? Use a 0.05 level of significance. Circle the correct null and alternative hypotheses. i) Ho : μ = 170 H₁ μ< 170 ii) What is a? Hoμ H₁: μ = 170 Η : μ = 170 170 H₁ μ> 170 iii) Which test statistic will you use? Circle your answer. Ꮓ T x2 iv) Calculate the value of the test statistic for the engineer's sample. v) Determine the critical value of the test statistic. Do not round or truncate. vi) Determine the P-value. vii) What is the conclusion? Accept Ho Reject Ho Fail to reject Ho Circle your response. viii) Does his sample seem to indicate that the true mean hardness of this compound is greater than 170? Circle your response. YES NO