A machine is set to fill packs with a mean of 50 g; you suspect it underfills. The standard deviation is known to be 2 g. You will weigh a sample of 100 packs and test H₀: μ = 50 against H₁: μ < 50 at α = 0.10. Below which sample mean x̄c will you reject H₀?
A machine is supposed to fill bottles with 500 mL on average. The standard deviation is known to be 8 mL. A sample of 25 bottles has a mean of 496.5 mL. Find the test statistic z for H₀: μ = 500.
A sample of 100 students has a mean score of 199 and a sample standard deviation of 4. Find the test statistic t for H₀: μ = 200.
The mean of a population is claimed to be 120; the population standard deviation is known to be 4. A random sample of 64 observations has a mean of 119.48. Test H₀: μ = 120 against H₁: μ ≠ 120. Find the p-value p.
A one-sided z test at α = 0.05 must detect a shift of the mean of 3 units with a power of 80%. The standard deviation is 8. Find the minimum sample size n.
A one-sided z test of H₀: μ = 200 against H₁: μ > 200 is done at α = 0.01 with a sample of 36; the standard deviation is known to be 15. In reality the mean is 208.75. Find the power 1 − β of the test in percent.
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