A machine is set to fill packs with a mean of 100 g; you suspect it underfills. The standard deviation is known to be 3 g. You will weigh a sample of 64 packs and test H₀: μ = 100 against H₁: μ < 100 at α = 0.01. Below which sample mean x̄c will you reject H₀?
A machine is supposed to fill bottles with 75 mL on average. The standard deviation is known to be 15 mL. A sample of 25 bottles has a mean of 80.1 mL. Find the test statistic z for H₀: μ = 75.
A sample of 64 students has a mean score of 103.6 and a sample standard deviation of 10. Find the test statistic t for H₀: μ = 100.
The mean of a population is claimed to be 500; the population standard deviation is known to be 24. A random sample of 36 observations has a mean of 508.32. Test H₀: μ = 500 against H₁: μ > 500. Find the p-value p.
A one-sided z test of H₀: μ = 500 against H₁: μ < 500 is done at α = 0.10 with a sample of 100; the standard deviation is known to be 25. In reality the mean is 495.75. Find the power 1 − β of the test in percent.
A one-sided z test of H₀: μ = 500 against H₁: μ < 500 is done at α = 0.05 with a sample of 36; the standard deviation is known to be 18. In reality the mean is 493.4. Find the power 1 − β of the test in percent.
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