Mathematics - Probability and Statistics - Advanced - Hypothesis testing - Conduct Hypothesis Tests

8 problems: (1) State H₀ and H₁: 'A company claims batteries last 500 hours. You suspect they last less.' (2) 'Sample of 40 batteries: mean=490, s=30. Test at α=0.05.' Calculate t-statistic and decide. (3) 'p-value is 0.03. α=0.01. Decision?' (Fail to reject). (4) 'In 200 coin flips, got 115 heads.